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Big Ideas Math Book 5th Grade Answer Key Chapter 11 Convert and Display Units of Measure
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Lesson: 1 Length in Metric Units
Lesson: 2 Mass and Capacity in Metric Units
- Lesson 11.2 Mass and Capacity in Metric Units
- Mass and Capacity in Metric Units Homework & Practice 11.2
Lesson: 3 Length in Customary Units
Lesson: 4 Weight in Customary Units
Lesson: 5 Capacity in Customary Units
Lesson: 6 Make and Interpret Line Plots
Lesson: 7 Problem Solving: Measurement
Chapter – 11: Convert and Display Units of Measure
- Convert and Display Units of Measure Performance Task 11
- Convert and Display Units of Measure Activity
- Convert and Display Units of Measure Chapter Practice
- Convert and Display Units of Measure Practice 1-11
- Convert and Display Units of Measure STEAM Performance Task
Lesson 11.1 Length in Metric Units
Explore and Grow
Work with a partner. Find 3 objects in your classroom and use a meter stick to measure them. Record your measurements in the table.
Answer:
1 centimeter is 0.1 times as long as 1 millimeter.
1 meter is 0.01 times as long as 1 centimeter.
1 meter is 0.001 times as long as 1 millimeter.
Structure
How can you convert a metric length from a larger unit to a smaller unit? How can you convert a metric length from a smaller unit to a larger unit?
Answer:
We can convert a metric length from a larger unit to a smaller unit by Multiplying.
Example: There are 1000 meters in one kilometer. Then the answer is 5km = 5000 meters. (5 × 1000)
We can convert a metric length from a smaller unit to a larger unit by Dividing.
Example: one meter is equal to 0.001 km. 1 meter = 0.001 km ( 1m/1000=0.001km)
Think and Grow: Convert Metric Lengths
You can use powers of 10 to find equivalent measures in the metric system.
Key Idea
When finding equivalent metric lengths, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Example
Convert 6 centimeters to millimeters.
Answer:
There are 10 millimeters in 1 centimeter.
Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
6 × 10 = 60
So, 6 centimeters is 60 millimeters.
Example
Convert 14,000 meters to kilometers.
Answer: There are 1,000 meters in 1 kilometer.
Explanation:
Because you are converting from a smaller unit to a larger unit, divide.
14,000 ÷ 1000 = 14.
So, 14,000 meters is 14 kilometers.
Show and Grow
Convert the length.
Question 1.
8.5 km = 8500 m.
Answer:
8.5 × 1000 = 8500.
Explanation:
Convert from kilometers to meters.
We know that,
1 km= 1000m
8.5 km = 8.5 × 1000 = 8500 m
Question 2.
180 cm = 1.8 m
Answer: 180/100 = 1.8 m
Explanation:
Convert from centimeters to meters.
1 m = 100 cm
1 cm = 1/100 m
180 cm = 180/100 = 1.8 m
Apply and Grow: Practice
Convert the length.
Question 3.
150 m = 0.15 km
Answer:
150 m = 0.15 km
Explanation:
Convert from meters to kilometers.
(Divide the meter value by 1000)
150m/1000 = 0.15 km
Question 4.
90 cm = 900 mm
Answer: 90 cm = 900 mm
Explanation:
Convert from centimeters to millimeters.
multiply the length value (i.e., cm value) by 10
90cm × 10 = 900 mm
Question 5.
0.03 m = 3 cm.
Answer: 0.03 m = 3 cm
Explanation:
Convert from meter to centimeter
Multiply the length value by (i.e., m value ) by 100
0.03 m × 100 = 3cm
Question 6.
0.6 km = 60,000 cm
Answer: 0.6 km = 60,000 cm
Explanation:
Convert from kilometers to centimeters
multiply the length value (i.e., km value by 100000)
0.6km × 100000 = 60,000 cm
Question 7.
800 mm = 0.8 m
Answer: 800 mm = 0.8 m
Explanation:
Convert from millimeters to meters
Divide the length value(i.e., mm value by 1000)
800/1000 = 0.8 m
Question 8.
700 cm = 0.007 km
Answer: 700 cm = 0.007 km
Explanation:
Convert from centimeters to meters
Divide the length value (i.e., cm value by 100000)
700/100000 = 0.007 km
Compare.
Question 9.
Answer:
0.02 m = 20 mm
multiply the length value (i.e., m value by 1000)
0.02 × 1000 = 20mm
3mm = 0.003 m
divide the length value(i.e., mm value by 1000)
3/1000 = 0.003 m
0.02 m < 3 mm
Question 10.
Answer:
0.025 km = 25000 mm
multiply the km value by 1e+6
3,500 mm = 0.0035 km
divide the length mm value by 1e+6
Question 12.
The giant anteater has the longest tongue in relation to its body size of any mammal. Its tongue is about 0.6 meter long. How many centimeters long is its tongue?
Answer:
The giant anteater has the longest tongue in relation to its body size of any mammal. Its tongue is about 0.6 meter long. Its tongue is about 60 centimeters long.
Explanation:
(0.6 meter = 60 centimeters) multiply the length value with 100. i.e., (0.6 × 100 = 60)
Question 13.
Number Sense
The length of an object can be written as b millimeters or c kilometers. Compare the values of b and c. Explain your reasoning.
Answer:
The length of an object can be written as b millimeters or c kilometers
Let us assume that b = 2mm, c = 2km
By comparing the b and c values
c value is greater than b
kilometers is greater than millimeters ( 1km = 1000000 mm , 1mm = 1 × 10 ^ -6 km).
Question 14.
Writing
Why does the decimal point move to the left when converting from a smaller measure to a larger measure?
Answer:
As we move from a smaller unit to a larger unit, the number of larger units required will be less. Therefore the decimal point will always move to the left when you want to make a number smaller. Therefore the decimal point will always move to the right when you want to make the number Bigger.
Think and Grow: Modeling Real Life
Example
The base of Mauna Kea extends about 5.76 kilometers below sea level. What is the total height of the volcano in meters?
Convert the distance below sea level to meters.
Answer: There are 1000 meters in 1 kilometer.
Explanation:
Given,
The base of Mauna Kea extends about 5.76 kilometers below sea level.
5.76 × 1000 = 5,760
So, the volcano extends 5,760 meters below sea level.
Adding below sea level and above sea level
Given in question distance of above sea level = 4,200
The distance of below sea level = 5,760
Adding both values 4,200 + 5,760 = 9,960
So, the total height of the volcano is about 9,960 meters.
Show and Grow
Question 15.
A pool is 3.65 meters deep. A diving board is 100 centimeters above the surface of the water. What is the distance from the diving board to the bottom of the pool in centimeters?
Answer: Given pool depth = 3.65 meters
Explanation: The diving board is above the surface of water = 100 centimeters
Converting 3.65 meters into centimeters ( Since, 1m = 100 cm )
3.65 meters = 365 centimeters ( Multiply the meters value by 100 )
3.65 × 100 = 365 cm
The distance from the diving board to the bottom of the pool = 365 + 100 = 465 cm
Question 16.
You hike 1.6 kilometers from a cabin to a lookout. You plan to hike the same way back. On your way back, you stop after 1,050 meters to look at a map. How many meters have you hiked so far? How many kilometers are you from the cabin?
Answer: Given, that hike from a cabin toa lookout = 1.6 km
Explanation:
on the way you stopped after = 1,050 meters
so, 1.6 km = 1600 meters
1600 m + 1,050 m = 2,650 meters
Therefore, 2,650 meters have you hiked so far
Therefore , 550 meters from the cabin ( 1600m – 1050m = 550m )
Converting 550 meters to kilometers = 0.55 km ( divide the meter value by 1000).
Therefore,0.55 km from the cabin.
Question 17.
DIG DEEPER!
You can take one of two routes to school. Which route is longer? How much longer? Write your answer two different ways.
Answer: Here, we are taking one route to school i.e., (Route A)
Explanation: From Route A and Route B the longer route is “Route A”.
So, we are taking “Route A” values.
Here 1.3km = 1300 meters (1.3km × 1000 = 1300 meters)
[Since we know that 1kilometer(km) = 1000metres] 0.6 km = 600 meters (0.6km × 1000 = 600 meters)
So, we are adding1.3km + 0.6km
= 1300m + 600m
= 1900 meters
(OR)
Method (2): Here, we are having two routes:- Route A and Route B.
From the question, We observed that
We have to find out the longer route from Route A and Route B.
The value of Route A is 1.3km and 0.6km
The value of Route B is 625m and 800m
Now add both the routes A and B
We are converting the Route A value from “Kilometers to Meters”
Here (1.3km = 1300metres and 0.6km = 600metres)
By Adding we get 1300m+600m = 1900m
Now take Route B = 800m + 625m = 1425m
By comparing both Route A and Route B, “Route A is longer than Route B”.
Length in Metric Units Homework & Practice 11.1
Convert the length
Question 1.
0.8 cm = __ mm
Answer: 0.8 cm = 8 millimeters (mm)
Explanation:
We have to convert from centimeters to millimeters
1 mm = 0.1 cm
Multiply the 0.8 with 10 (0.8 × 10 =8)
Question 2.
7 m = _ km
Answer: 7 m = 0.007 km
Explanation:
Convert from meters to kilometers
1 km = 1000 m
Divide the length value by 1000 ( 7/1000 = 0.007)
Question 3.
6.4 km = ___ m
Answer: 6.4 km = 6400 m
Explanation:
Convert from kilometers to meters
1 km = 1000 m
Multiply the length value by 1000 (6.4 × 1000 = 6400)
Question 4.
1,300 mm = __ cm
Answer: 1,300 mm = 130 cm
Explanation:
Convert from millimeters to centimeters.
1 mm = 0.1 cm
Divide the length value by 10 ( 1300/10 = 130)
Question 5.
91,000 cm = ___ km
Answer: 91,000 cm = 0.91 km
Explanation:
Convert from centimeters to kilometers.
1 cm = 1e – 5
Divide the length value by 100000 ( 91000/100000 = 0.91)
Question 6.
20,000 mm = ___ km
Answer: 20,000 mm = 0.02 km
Explanation:
Convert from millimeters to kilometers
Multiply the value in mm by the conversion factor 1.0E-6.
So, 20000 mm times 1.0E-6 is equal to 0.02 km.
Compare
Question 7.
Answer: 1.6 m is greater than 16 cm
Explanation:
16cm = 0.16 m
16cm/100 = 0.16m
1.6 m = 1.6m × 100 = 160 cm
Question 8.
Answer:
300 mm = 0.3 m
1mm = 0.001 m ( divide the 300mm by 1000 )
0.3 m = 300 mm
1m = 1000mm ( multiply the 0.3m by 1000 )
Question 9.
Answer: 0.045 km = 45,000 mm
Explanation:
Convert from kiometers to millimeters
1km = 1000000 mm
45 mm = 4.5 × 10 ^ -5 km ( it is spelled as 10 to the power of -5) (or) 4.5 e^-5
Question 10.
Dolphins can hear sounds underwater that are 24 kilometers away. How many meters away can dolphins hear sounds underwater?
Answer:
Given,
Dolphins can hear sounds underwater that are 24 kilometers away.
24000 meters away dolphins can hear sounds underwater.
Question 11.
Reasoning
How can you convert 7.8 meters to kilometers by moving the decimal point? Explain your reasoning.
Answer:
Converting 7.8 meters to kilometers
7.8 meters = 0.0078 kilometers.
Explanation:
7.8 m / 1000 = 0.0078 km ( Divide the meter value by 1000 ) ( 1km = 1000 m )
To convert from meters to kilometers, divide the meter value by 1000
since , 1km = 1000m
divide the whole meter value by 1000, put a decimal point at the end of the number and then move it three places to the left.
(But in question we have the decimal number that is 7.8 so, that is why we have moved the decimal point to the fourth number from left).
Question 12.
YOU BE THE TEACHER
Your friend divides by 100 to convert a length from meters to centimeters. Is your friend correct? Explain.
Answer:
No, it is not correct.
Explanation:
Converting a length from meters to centimeters, We have to multiply the length value by 100.
Question 13.
Which One Doesn’t Belong? Which measurement does not belong with the other three?
Answer:
5,000 cm measurement does not belong with the other three.
Explanation:
500,000 mm = 500 m
500 m = 0.5km
But, 5000 cm = 50m (Here the value 50 m is didn’t belong with given values in question)
Question 14.
Modeling Real Life
A small chunk of ice called a growler breaks away from an ice burg. The growler sticks out of the water 840 millimeters and is 3.5 meters deep in the water. What is the total height of the growler in meters?
Answer:
Converting 840 millimeters into meters
Explanation:
840 mm = 0.84 meter
( Divide the length value by 1000)
840/1000 = 0.84 meter
Total Height of the growler = 0.84 m × 3.5 m (Multiply 0.84m and 3.5m)
= 2.94 meters.
Question 15.
DIG DEEPER!
A spaceship’s route from Earth to the moon is 384,400 kilometers long. The spaceship travels 500,000 meters. How many kilometers does it have left to travel?
Answer:
The Spaceship has left to travel from Earth to the Moon = 500 kilometers.
Explanation:
According, to the question
We are converting 500,000 meters to Kilometers ( 500,000 meters = 500 kilometers)
So, the spaceship has left to travel is 500 kilometers.
Review & Refresh
Write the fraction in the simplest form.
Question 16.
\(\frac{2}{8}\)
Answer: \(\frac{2}{8}\) = \(\frac{1}{4}\)
Question 17.
\(\frac{10}{100}\)
Answer: \(\frac{10}{100}\) = \(\frac{1}{10}\)
Question 18.
\(\frac{24}{16}\)
Answer: \(\frac{24}{16}\) = \(\frac{3}{2}\)
Lesson 11.2 Mass and Capacity in Metric Units
Explore and Grow
Use a balance and weights to help you complete the statement.
Answer: 1 kilogram is 0.001 times as much as 1 gram.
Structure
How can you convert kilograms to grams? How can you convert grams to kilograms?
Use a 1-liter beaker to help you complete the statement.
Answer: 1 liter is 0.001 times as much as 1 milliliter.
Structure
How can you convert liters to milliliters? How can you convert milliliters to liters?
Answer: Converting liters to milliliters ( 1 liter = 1000 milliliters )
Explanation:
multiply the volume (i.e., liter value by 1000 )
For example :- 0.01 liter = 10 ml
0.1 liter = 100 ml
1 liter = 1000 ml
Converting milliliters to liters ( 1 milliliters = 0.001 liters)
Divide the volume value ( i.e., liter value by 1000)
1/1000 = 0.001 liter .
Think and Grow: Convert Metric Measures
Key Idea
When finding equivalent metric masses or capacities, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Example
Convert 12.4 grams to milligrams.
Answer: There are 1000 milligrams in 1 gram.
Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
12.4 × 1000 = 12400
So, 12.4 grams is 12400 milligrams.
Example
Convert 18,000 milliliters to liters.
Answer:
There are 1000 milliliters in 1 liter.
Because you are converting from a smaller unit to a larger unit, divide.
18,000 ÷ 1000 = 18 liters .
So, 18,000 milliliters is 18 liters.
Show and Grow
Convert the mass.
Question 1.
8 kg = ___ g
Answer: 8 kg = 8000 g (8 × 1000 = 8000g)
Explanation:
Convert from kilograms to grams
1 kg = 1000 g
8 kg = 8 × 1000 g = 8000 g
Question 2.
3,800 mg = __ g
Answer: 3,800 mg = 3.8 g
Explanation:
Convert from milligrams to grams
Divide the mass value ( mg value) by 1000
( 3800/1000 = 3.8 g )
Convert the capacity.
Question 3.
22,000 mL = __ L
Answer: 22,000 mL = 22 L
Explanation:
Convert from milliliters to liters.
Divide the volume value ( mL value) by 1000
( 22000/1000 = 22 L )
Question 4.
4.6 L = __ mL
Answer: 4.6 L = 4600 mL
Explanation:
Convert from liters to milliliters
Multiply the volume value ( L value) by 1000
4.6 × 1000 = 4600 mL
Apply and Grow: Practice
Convert the mass.
Question 5.
5,000 g = ___ kg
Answer: 5,000 g = 5 kg
Explanation:
Convert from grams to kgs
Divide the mass value ( g value) by 1000
1000 grams = 1 kg
5000/1000 = 5kg
Question 6.
67 g = ___ mg
Answer: 67 g = 67000 mg
Explanation:
Convert from grams to milligrams
1 g = 1000 mg
Multiply the mass value ( g value ) by 1000
67 × 1000 = 67000 mg
Question 7.
0.2 kg = __ mg
Answer: 0.2 kg = 200000 mg
Explanation:
Multiply the mass value ( kg value) by 1e+6
Question 8.
30,000 mg = __ kg
Answer: 30,000 mg = 0.03 kg
Explanation:
Divide the mass value ( mg value ) by 1e+6
Convert the capacity.
Question 9.
8 L = ___ mL
Answer: 8 L = 8000 mL ( 8 × 1000 = 8000 mL )
Explanation:
Convert from liters to milliliters
1L = 1000 mL
( Multiply the volume ( L ) value by 1000)
8 liters = 8 × 1000 ml = 8000 ml
Question 10.
70 mL = ___ L
Answer: 70 mL = 0.07 L
Explanation:
Convert from milliliters to liters
Divide the volume ( mL ) value by 1000
70/1000 = 0.07 L
Question 11.
1.200 mL = __ L
Answer: 1.200 mL = 0.0012 L
Explanation:
Convert from milliliters to liters
Divide the volume ( mL ) value by 1000
1.200/1000 = 0.0012 L
Question 12.
0.4 L = ___ mL
Answer: 0.4 L = 400 mL
Explanation:
Convert from milliliters to liters
Multiply the volume ( L ) value by 1000
( 0.4 × 1000 = 400 mL )
Question 13.
What is the mass of the pumpkin in kilograms?
Answer:
Given, the mass of the pumpkin = 6,000 grams
According to the question, we have to find out the mass of pumpkin in kilograms.
Converting the 6,000 grams into kilograms = 6 kilograms
Explanation:
Divide the mass ( grams ) value by 1000
[1 kilogram = 1000 grams] , [ 6 kilogram = 6,000 grams ]
(6000/1000 = 6 kilograms )
So, the mass of pumpkin in kilograms is 6 kilograms.
Question 14.
Which One Doesn’t Belong? Which one does not have the same capacity as the other three?
Answer:
Here , 2000 ml = 2L
2L = 2000 ml
2 × 10³ ml =2000 ml
But 2 ml = 0.002 L
Explanation:
So, the 2ml does not have the same capacity as the other three
Question 15.
DIG DEEPER!
Order the masses from least to greatest. Explain how you converted the masses.
Answer: Order the masses from least to greatest is
14000 mg , 0.039 kg , 56 g , 0.14 kg
Explanation:
0.039 kg = 39 grams
0.14 kg = 140 grams
56 g = 0.056 kg
14,000 mg = 14 grams.
Think and Grow: Modeling Real Life
Example
You have a 5-kilogram bag of dog food. You give your dog 50 grams of food each day. How many days does the bag of food last?
Answer: Convert the mass of the bag to grams.
Explanation:
There are 1000 grams in 1 kilogram.
5 × 1000 = 5000
So, the bag contains 5000 grams of dog food.
Divide the amount of dog food in the bag by the amount you give your dog each day.
5000 ÷ 50 =100
So, the bag lasts for 100 days.
Show and Grow
Question 16.
You have 6 liters of juice to make frozen treats. You pour 30 milliliters of juice into each treat mold. How many treats can you make?
Answer: We can make 200 treats.
Explanation:
We have 6 Liters of juice
6 Liters = 6000 milliliters
From the formula ( 1 liter = 1000 milliliter )
30 milliliters of juice is poured into each treat mold
so , 6000 / 30 = 200
so, we can make 200 treats.
Question 17.
Your goal is to eat no more than 2.3 grams of sodium each day. You record the amounts of sodium you eat. How many more milligrams of sodium can you eat and not exceed your limit?
Answer: Given 2.3 grams of sodium you have to eat each day
Explanation:
convert 2.3 grams into milligrams
2.3 grams = 2300 milligrams ( multiply the value of the gram by 1000 )
subtract the sodium you eat values
2300 – 210 – 250 – 690 = 1150
so, you can take 1150 more milligrams of sodium.
Question 18.
Which contains more juice, 3 of the bottles, or 32 of the juice boxes? How much more? Write your answer in milliliters.
Answer: 1 bottle of juice contains = 2 L
1 juice box contains = 200 mL
Explanation:
from the question, we have to find 3 juice bottles quantity and 32 juice boxes quantity in milliliters.
1 L = 1000 mL ( from formula )
2L = 2000 mL
for 3 juice bottles = 3 × 2000 = 6000 ml
for 32 juice boxes = 32 × 200 = 6400 ml
so, 6400 – 6000 = 400 ml
400 mL is more
Therefore, 32 juice boxes contain more juice than 3 juice bottles.
Mass and Capacity in Metric Units Homework & Practice 11.2
Convert the mass
Question 1.
9 g = 9000 mg
Answer: 9 g = 9000 mg
Explanation:
Convert from grams to milligrams
1 g = 1000 mg
9 g = 9000 mg ( multiply the g value by 1000 )
Question 2.
78 g = 0.078 kg
Answer: 78 g = 0.078 kg
Explanation:
Convert from grams to kilograms.
1 g = 0.001 kg
78 g = 0.078 kg ( divide the g value by 1000 )
Question 3.
260,000 mg = _0.26_ kg
Answer: 260,000 mg = 0.26 kg
Explanation:
Convert from milligrams to kilograms.
1 mg = 1e + 6
260,000 mg = 0.26 kg
Question 4.
0.148 kg = 148000 mg
Answer: 0.148 kg = 148000 mg
Explanation:
Convert from kilograms to milligrams
1kg = 1000000 mg
0.148 kg = 148000 mg
Convert the capacity
Question 5.
600 mL = 0.6 L
Answer: 600 mL = 0.6 L
Explanation:
Convert from milliliters to liters.
1mL = 0.001 L
600 mL = 0.6 L
divide the mL by 1000
Question 6.
3 L = 3000 mL
Answer: 3 L = 3000 mL
Explanation:
Convert from liters to milliliters.
1 L = 1000 mL
3 L = 3000 mL ( multiply the L value by 1000 )
Question 7.
0.21L = 210 mL
Answer: 0.21 L = 210 mL
Explanation:
Convert from liters to milliliters.
1 L = 1000 mL
0.21 L = 210 mL ( multiply the L value by 1000 )
Question 8.
35 mL = 0.035 L
Answer: 35 mL = 0.035 L
Explanation:
Convert from milliliters to liters.
1 mL = 0.001 L
35 mL = 0.035 L
divide the mL value by 1000
Question 9.
There are 3.2 liters of iced tea in a pitcher. How many milliliters of iced tea are in the pitcher?
Answer: Given that iced tea in a pitcher = 3.2 Liters
we have to find out iced tea in the pitcher in milliliters
Explanation:
Convert from liters to milliliters.
3.2 Liters = 3200 milliliters
1 Liter = 1000 milliliter
3.2 Liters = 3200 milliliters ( multiply the Liters value by 1000 )
so, therefore 3200 milliliters of iced tea are in the pitcher.
Question 10.
YOU BE THE TEACHER
Your friend says that 0.04 kilogram is less than 4 × 105 milligrams. Is your friend correct? Explain.
Answer: 0.04 kilogram = 40,000 mg
4 × 105 mg = 0.4 kg
Explanation:
yes, your friend is correct
0.04 kg is less than 4 × 105 mg
Question 11.
Number Sense
How does the meaning of each prefix relate to the metric units of mass and capacity?
Answer: The metric system is the system of measurement primarily used in science and in countries outside of the united states.
Explanation:
The metric system includes units of length ( meters ), mass ( grams ), and capacity (liters).
from the given question we have to relate each prefix to the metric units of mass and capacity is:-
metric units of mass of prefix kilo are:- kilo is the prefix of the kilogram(kg), kilogram (kg)=1000 grams
Milli is the prefix of milligram(mg) , milligram(mg) = 0.001 gram
metric units of the capacity of prefix kilo is:- kilo is the prefix of Kiloliter(KL), Kiloliter (KL) = 1000 liters
Milli is the prefix of Milliliter(mL), Milliliter (mL) = 0.001 liters
Question 12.
Modeling Real Life
You have 9 kilograms of corn kernels. You put 450 grams of corn kernels in each bag. How many bags can you make?
Answer: we can make 20 bags.
Explanation:
Given that you have 9 kilograms of corn kernels
convert 9 kilograms to grams = 9 kilograms = 9000grams
you put 450 grams of corn kernels in each bag.
we have to find out the how many bags we can make
so, divide the 9000 grams by 450 grams = 9000/450 = 20
so, we can make 20 bags.
Question 13.
DIG DEEPER!
Your teacher has one of each of the beakers shown. You need to measure exactly 2 liters of liquid for an experiment. What are three different ways you can do this?
Answer: We have 3 beakers as shown in figure with 400ml , 600ml , 1L
Explanation:
We have to measure exactly 2 Liters of liquid for each beaker ( 2L = 2000 ml )
The three different ways we can do this is :-
for first beaker = 400ml × 5 = 2000ml
for second beaker = 600ml × 2 + 400ml × 2
= 1200ml + 800ml = 2000ml
for third beaker = 1 L + 1 L = 2 L
Review & Refresh
Question 14.
Newton rides to the store in a taxi. He owes the driver $12. He calculates the driver’s tip by multiplying $12 by 0.15. How much money does he pay the driver, including the tip?
Answer:
Given that newton rides to the store in a taxi.
He owes the driver $12.
so, he multiplies the drivers tip by $12 by 0.15
$12 × 0.15 + $12 = 13.8
so, newton paid the driver including a tip is 13.8
Lesson 11.3 Length in Customary Units
Explore and Grow
Work with a partner. Use a yardstick to draw 3 lines on a whiteboard that are 1 yard, 2 yards, and 3 yards in length. Then measure the lengths of the lines in feet and in inches. Record your measurements in the table:-
Table values are:-
1 Length(yards) = 3 (feet) , 36(inches)
2 Length(yards) = 6 (feet) , 72(inches)
3 Length(yards) = 9 (feet) , 108(inches)
Answer:
1 foot is 12 times as long as 1 inch.
1 yard is 3 times as long as 1 foot.
1 yard is 3 × 12 times as long as 1 inch.
Structure
How can you convert a customary length from a larger unit to a smaller unit? How can you convert a customary length from a smaller unit to a larger unit?
Answer:
When converting customary units of measure from a larger unit to a smaller unit, multiply the larger unit by its smaller equivalent unit.
when converting customary units of measure from a smaller unit to a larger unit, divide the smaller unit by its larger equivalent unit.
Think and Grow: Convert Customary Lengths
Key Idea
When finding equivalent customary lengths, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Example
Convert 3 miles to yards.
Answer: There are 1760 yards in 1 mile.
Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
3 × 1760 = 5280
So, 3 miles is 5280 yards.
Example
Convert 42 inches to feet and inches.
Answer: There are 12 inches in 1 foot.
Because you are converting from a smaller unit to a larger unit, divide.
Answer:
There are 12 inches in 1 foot
so, 42 inches is 3 feet 6 inches ( 42 / 12 = 3.5 )
Show and Grow
Convert the length.
Question 1.
Answer:
6 1/2 ft = 78 inches
Explanation:
Convert from feet to inches
1 foot = 12 inches
6 feet = 6 × 12 = 72 inches
1/2 ft = 6 inches
72 + 6 = 78 inches
multiply the ft value by 12
6 1/2 ft = 78 inches
Question 2.
94 in. = ft in.
Answer: 94 in = 7 ft 10 in
Explanation: divide the inch value by 12
Apply and Grow: Practice
Convert the length.
Question 3.
Answer: 3 × 3/4 ft = 45 in.
Explanation: multiply the ft value by 12
Question 4.
60 in. = _5_ ft
Answer:- 60 in = 5 f
Explanation:
divide the in value by 12
Question 5.
375 ft = __ yd
Answer: 375 ft = 125 yd
Explanation: divide the ft value by 3
Question 6.
Answer: 12 × 2/3 yd = 38 feet
Explanation:
Convert from yards to feet.
1 yard = 3 feet
multiply the yd value by 3
Question 7.
51 in. = __ ft___in.
Answer: 51 in = 4 feet 3 inches
Explanation:
Convert from inches to feet.
divide the 51-inch value by 12
Question 8.
5 yd = __ in.
Answer: 5 yd = 180 inches
Explanation:
Convert from yards to inches.
1 yard = 36 inches
multiply the yd value by 36
5 yards = 5 × 36 = 180 inches
Compare.
Question 9.
Answer: 7 × 1/3 yd = 22 ft
Explanation:
Convert from yards to feet.
multiply the yd value by 3
22 ft = 7.333 yd
divide the ft value by 3
Question 10.
Answer: 54 in = 4 feet 6 inches
Explanation:
Convert from inches to feet.
divide the inch value by 12
4 ft 8 in = 56 inches
multiply the length value by 12
Question 11.
Answer: 216 in = 6 yards
Explanation:
Convert from inches to yards.
divide the in value by 36
6 yd = 216 inches
multiply the yd value by 36
Question 12.
A dugong is 8\(\frac{1}{3}\) feet long. How many inches long is the dugong?
Answer: A dugong is 8 × 1/3 feet long
8 × \(\frac{1}{3}\) feet = 32 inches
Explanation:
Therefore 32 inches long is the dugong.
Question 13.
DIG DEEPER!
Order the lengths from shortest to longest. Explain how you converted the lengths.
Answer:
1) 5 × \(\frac{1}{2}\) =\(\frac{5}{2}\) feet
5/2 feet = 30 inches
multiply the feet value by 12
2) 5 feet 3 inches = 63 inches
multiply the 5 feet 3 inches value by 12
3) 5 × \(\frac{2}{3}\) feet = 40 inches
multiply the feet value by 12
4) 5 × \(\frac{3}{4}\) feet = 45 inches
multiply the feet value by 12
So, order from shortest to longest = 5 × 1/2 , 5 × 2/3 , 5 × 3/4 , 5 feet 3 inches .
Think and Grow: Modeling Real Life
Example
A golfer uses a device to determine that his golf ball is 265 feet from a hole. After his next shot, his ball is 15 feet short of the hole. How many yards did the golfer hit his ball?
Because the golfer’s ball is 15 feet short of the hole after his next shot, subtract 265 from 15 to find how many feet the golfer hit his ball.
265 – 15 = _250_ feet
Answer: 265 – 15 = 250 feet
Explanation:
There are 3 feet in 1 yard.
250/3 = 83.33 yards
= 83 × \(\frac{1}{3}\) yards.
Show and Grow
Question 14.
A tree is 27 feet tall. After the tree is struck by lightning, it is 96 inches shorter. How many feet tall is the tree after it is struck by lightning?
Answer:
Given a tree is 27 feet tall. After the tree is struck by lightning, it is 96 inches shorter
we have to find the feet of the tree after it is struck by lightning.
27 feet = 324 inches
Subtract 324 – 96 = 228 inches
converting 228 inches to feet ( i.e., 228 inches = 19 feet )
So, therefore after the tree is struck by lightning its feet tall = 19 feet
Question 15.
DIG DEEPER!
The rope ladder is 2\(\frac{1}{2}\) yards tall. Each knot is made using 16 inches of rope. How many feet of rope are used to make the ladder? Explain.
Answer: 22 feet of rope are used to make the ladder.
Explanation:
2 yards = 6 feet
1 knot is 16 inches
Total 12 knots
12 × 16 = 16 feet , 16 + 16 = 22 feet.
Question 16.
DIG DEEPER!
The Chesapeake Bay Bridge is 4\(\frac{3}{10}\) miles long. Road work begins 1,200 yards from one end of the bridge and ends 2 miles from the other end of the bridge. How many yards long is the road work?
Answer: 11760 yards
Explanation:
Given,
The Chesapeake Bay Bridge is 4\(\frac{3}{10}\) miles long.
Road work begins 1,200 yards from one end of the bridge and ends 2 miles from the other end of the bridge.
1760 × 4 = 7,040
1760 × 2 = 3,520
given 1200 yards
so, 7040 + 3520 + 1200 = 11760 yards ( since 1 mile = 1760 yards )
Length in Customary Units Homework & Practice 11.3
Convert the length.
Question 1.
2\(\frac{1}{3}\) yd = __ in.
Answer:- 2 × \(\frac{1}{3}\) yd = 84 in
Explanation:-
Convert from yards to inches
1 yard = 36 inches
Multiply the yd value by 36
Question 2.
5 mi = __ yd.
Answer: 5 mi = 8800 yards
Explanation:
Convert from miles to yards
1 mile = 1760 yards
multiply the mi value by 1760
5 miles = 5 × 1760 yards
5 mi = 8800 yards
Question 3.
3\(\frac{1}{3}\) yd = __ ft
Answer:
Convert from yards to feet.
multiply the yd value by 3
3 × 1/3 yd = 1 yd
1 yd = 3 feet
Question 4.
27 in. = __ ft __ in.
Answer: 27 in = 2 feet 3 inches
Explanation:
Convert from inches to feet.
divide the 27 inches value by 12
Question 5.
108 in. = __ yd
Answer: 108 in = 3 yards
Explanation:
Convert from inches to yards
1 yard = 36 inches
divide the in value by 36
Question 6.
34 in. = __ ft
Answer: 34 in = 2 feet 10 inches
Explanation:
Convert from inches to feet
1 foot = 12 inches
Divide the in value by 12
Compare.
Question 7.
Answer:
5 × 3/4 ft = 45 inches
65 in = 5 feet 5 inches ( divide the in value by 12 )
Question 8.
Answer:
19 in = 1 feet 7 inches
1 ft 5 in = 17 inches
Question 9.
Answer:
2 mi = 10560 feet
10,650 ft = 2.017 miles
Question 10.
A football player runs 93 yards. How many feet does he run?
Answer:
Given a football player runs 93 yards
we have to find how many feet does he run
convert 93 yards to feet
93 yards = 279 feet
So, therefore a football player runs 279 feet
Question 11.
Precision
Write whether you would use multiplication or division for each conversion.
Answer:
yards to feet:- 1 yard = 3 feet ( multiply the yard value by 3 )
miles to inches:- 1 mile = 63360 inches ( multiply the mile value by 63360 )
feet to miles:- 1 feet = 0.000189 mile ( divide the feet value by 5280 )
inches to feet :- 1 inch = 0.0833 feet ( divide the inch value by 12 )
miles to yards:- 1 mile = 1760 yards ( multiply the mile value by 1760 ).
Question 12.
Reasoning
Match each measurement with the best customary unit of measure.
Answer:
the height of jump = feet
length of a crayon = inches
length of river = miles
length of football field = yards.
Question 13.
Modeling Real Life
How long is the velociraptor in yards?
Answer: we have to find the value of velociraptor in yards
Explanation:
Given velociraptor in ft = 28 ft
Converting 28 ft into yards = 28 ft = 9.333 yards
Divide the ft value by 3.
Question 14.
DIG DEEPER!
You wrap a cube-shaped box with ribbon as shown. The ribbon is wrapped around all of the faces of the cube. You use 9 inches of ribbon for the bow. How many inches of ribbon do you use altogether? Explain.
Answer: Cube sides = 6
Explanation:
one side height = 1 feet 9 inches
so, 12 + 9 = 21 inches
6 × 21 inches = 126 inches
9 inches for the bow
so, 126 + 9 = 135 inches
Therefore 135 inches of ribbon is used altogether.
Review & Refresh
Find the quotient.
Question 15.
3,200 ÷ 40 = 80
Answer: 3,200 ÷ 40 = 80
Question 16.
5,400 ÷ 9 = _600__
Answer: 5,400 ÷ 9 = 600
Question 17.
600 ÷ 20 = _30_
Answer: 600 ÷ 20 = 30
Lesson 11.4 Weight in Customary Units
Explore and Grow
Work with a partner. Use the number line to help you complete each statement.
The vehicle weighs _2000_ pounds.
Answer: 2000 pounds
Explanation:
1 US ton = 2000 pounds
The whale shark weighs _15 US_ tons.
Answer: 15 US tons
Explanation: divide the 30,000 by 2000
Structure
How can you convert tons to pounds? How can you convert pounds to tons?
Answer:
we can convert tons to pounds by multiply the ton value by 2000 (i.e., 1 US ton = 2000)
we can convert pounds to tons by dividing the pound value by 2000 (i.e., 1 pound = 0.0005 us ton)
Think and Grow: Convert Customary Weights
Key Idea
When finding equivalent customary weights, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
A
Answer: 4 × 1/4 tons = 2000 pounds
Explanation:
There are 2000 pounds in 1 ton.
so, 4 × 1/4 tons = 2000 pounds.
A
Answer: 40 ounces = 2.5 pounds
Explanation:
Convert from ounces to pounds
divide the ounces value by 16
40 / 16 = 2.5
so, 40 ounces is 2.5 pounds.
Show and Grow
Convert the weight.
Question 1.
9 T = __ lb
Answer: 9 T = 19841.604 lb
Explanation:
Convert from tonns to pounds.
multiply the T value by 2205.
Question 2.
6\(\frac{1}{2}\) lb = __ oz
Answer: 6 × \(\frac{1}{2}\) lb = \(\frac{6}{2}\) = 3
Explanation:
Convert from pounds to ounces
3 lb = 48 oz
multiply the lb value by 16
Question 3.
6,000 lb = __ T
Answer: 6,000 lb = 3 US tons
Explanation:
Convert from pounds to tonn
divide the lb value by 2000
Question 4.
80 oz = __ lb
Answer: 80 oz = 5 lb
Explanation:
Convert from ounces to pounds.
divide the oz value by 16
Apply and Grow: Practice
Convert the weight.
Question 5.
10,000 lb = __ T
Answer: 10,000 lb = 4.536 T
Explanation:
divide the lb value by 2205.
Question 6.
8 lb = __ oz
Answer: 8 lb = 128 oz
Explanation:
Convert from pounds to ounces.
multiply the lb value by 16
Question 7.
240 oz = __ lb
Answer: 240 oz = 15 lb
Explanation:
Convert from ounces to pounds
divide the oz value by 16
Question 8.
7\(\frac{1}{4}\) T = ___ lb
Answer: 7 × \(\frac{1}{4}\) = 1.75
1.75 T = 3858.09 lb
Explanation:
Convert from tonnes to pounds
multiply the T value by 2205.
Question 9.
150 oz = ___ lb __ oz
Answer: 150 oz = 9.375 lb 150 oz
Explanation:
Convert from pounds to ounces
divide the oz value by 16
Question 10.
32,000 oz = __ T
Answer: 32,000 oz = 1 US ton
Explanation:
Convert from pounds to tonn
divide the oz value by 32000
Compare.
Question 11.
Answer: 30 T = 60000 lb
Explanation:
multiply the T value by 2000
6,000 lb = 3 US tons
divide the lb value by 2000
Question 12.
Answer: 53 oz = 3.312 lb
Explanation:
divide the oz value by 16
3 × 1/2 lb = 1.5 lb
1.5 lb = 0.00068 t
divide the lb value by 2205
Question 13.
Answer:
8 T = 256000 oz
Explanation:
multiply the oz value by 32000
224,000 oz = 7 US tons
divide the oz value by 32000
Question 14.
What is the weight of the hippopotamus in tons?
Answer:
Given the weight of hippopotamus = 4000 pounds
convert 4000 pounds to tons
4000 pounds = 2 US tons
divide the pound’s value by 2000
so, the weight of hippopotamus in tons = 2 US tons
Question 15.
Reasoning
Compare 10 pounds and 165 ounces using mental math. Explain.
Answer:
0 pounds = 160 ounces
multiply the value of the pound by 16
165 ounces = 10.3125 pounds
divide the value of the ounce by 16
By comparing both the values 165 ounces is greater than 10 pounds.
Question 16.
Number Sense
Which measurements are equivalent to 60 ounces?
Answer:
3 × 3/4 lb = 36 oz
3 × 1/2 lb = 56 oz
3 lb 12 oz = 60 oz
3 lb 4 oz = 52 oz
Explanation:
3 lb 12 oz measurement is equivalent to 60 ounces (oz)
Think and Grow: Modeling Real Life
Example
A newborn baby boy weighs 122 ounces. A newborn baby girl weighs 6 pounds 4 ounces. Which baby weighs more? How much more?
Convert the weight of the boy to pounds and ounces.
Answer: There are 16 ounces in 1 pound.
Explanation:
Given boy weighs = 122 ounces
122 / 16 = 7.625
= 2 – 6 × 16 + 4 = 100 ounces
so, 122 >100
Boy weigh is more than girl weigh = 22 ounces more
Show and Grow
Question 17.
Which box of cereal weighs more? How much more?
Answer:
1/2 pounds = 8 ounces
17 ounces = 1.062 pounds
Explanation:
17 ounces box of cereal weighs more
0.562 much more
Question 18.
A male rhinoceros weighs 2\(\frac{1}{4}\) tons. Which rhinoceros weighs more? How much more? Write your answer as a fraction in simplest form.
Answer: male rhinoceros = 2 × 1/4 = 2/4 = 1/2 tons
Explanation:
1/2 tons = 1000 pounds ( converting tons to pounds)
Given in figure female rhinoceros = 3,500 lb
3,500 lb = 1.75 US tons ( converting pounds to tons )
Female rhinoceros weigh more than male rhinoceros
1.75 tons – 1/2 tons => 1.75 – 0.5 = 1.25 tons
1.25 tons weigh is more
we can write 1.25 in simplest form as, we have 2 digits after the decimal point so multiply both numerator and denominator by 100, so that there is no decimal point in the numerator.
1.25 × 1001 × 100 = 125100
125 / 25100 / 25 = 54
simplest form of 1.25 = 5/4
Question 19.
DIG DEEPER!
Can all of the passengers listed in the table ride the boat at once? Explain.
Answer: Yes, all passengers who are listed on the table can ride the boat at once.
Explanation:
Add all the passenger weights 91+184+150+248+170+215+132+145+265+126+259+175 = 2260 pounds
we have to convert 2260 pounds to tons
2260 pounds = 1.13 US tons ( divide the pounds value by 2000 ).
Weight in Customary Units Homework & Practice 11.4
Convert the weight.
Question 1.
10 T = __ lb
Answer: 10 T = 20000 lb
Explanation:
Convert from tonn to pounds
1 tonn = 2000 pounds
multiply the T value by 2000
Question 2.
32 oz = ___ lb
Answer: 32 oz = 2 pounds
Explanation:
Convert from ounces to pounds
divide the oz value by 16
Question 3.
48,000 lb = __ T
Answer: 48,000 lb = 24 US tons
Explanation:
Convert from pounds to tons
divide the lb value by 2000
Question 4.
50 lb = __ oz
Answer: 50 lb = 800 oz
Explanation:
Convert from pounds to ounces.
multiply the mass value by 16
Question 5.
5\(\frac{3}{4}\)T = __ lb
Answer: 5 × \(\frac{3}{4}\) = 15/4 =3.75 T
3.75 t = 8267.1957671958 lb
Question 6.
8\(\frac{1}{2}\) lb = __ oz
Answer: 8 × \(\frac{1}{2}\) = 8/2 = 4 lb
4 lb = 64 ounces
Explanation:
Convert from pounds to ounces.
multiply the lb value by 16
Question 7.
168 oz = __ lb __ oz
Answer: 168 oz = 10.5 lb 168 oz
Explanation:
Convert from ounces to pounds.
divide the oz value by 16
Question 8.
96,000 oz = __ T
Answer: 96,000 0z = 2.7216 T
Explanation:
Convert from ounces to the ton.
96,000 0z = 2.7216 T
Compare
Question 9.
Answer: 16 lb = 0.01 T
32,000 T = 64000000 lb
Question 10.
Answer: 128 oz = 8 lb
Explanation:
divide the oz value by 16
8 × 1/4 lb = 8/4 = 2 lb
2 lb = 32 oz
multiply the lb value by 16
Question 11.
Answer:
11 T = 388013.581 oz
multiply the T value by 35274
384,000 oz = 10.886 T
divide the oz value by 35274
Question 12.
A newborn puppy weighs 3 pounds 5 ounces. What is the weight of the puppy in ounces?
Answer:
Given a new born puppy weighs 3 pounds 5 ounces
we have to find the weight of the puppy in ounces
3 pounds 5 ounces = 1500 grams
convert 1500 grams to ounces
1500 grams = 52.911 ounces
divide the value of the gram by 28.35
The weight of puppy in ounces = 28.35
Question 13.
Number Sense
How many tons are equal to 500 pounds? Write your answer as a fraction in simplest form.
Answer: 500 pounds = 0.25 US tons
Explanation:
divide the value of the pound by 2000
when 0.25 reduced to the simplest form is (25/25)(100/25) = 14
Open-Ended
Complete the statement.
Question 14.
__ pounds > 72 ounces
Answer: 4.6 pounds > 72 ounces
Explanation:
4.6 pounds = 73.6 ounces
multiply the pound’s value by 16
Question 15.
13 tons < __ pounds
Answer: 13 tons < 27000 pounds
Explanation:
Convert from tons to pounds
1 ton = 2000 pounds
divide the value of the pound by 2000.
Question 16.
Modeling Real Life
An employee at a juice cafe uses 10 ounces of kale and \(\frac{3}{4}\) pound of apples to make a drink. Does the employee use more kale or apples? How much more?
Answer: Given that an employee at a juice cafe uses of kale = 10 ounces
and he uses pound of apples to make a drink = 3/4 pounds
Explanation:
converting 10 ounces to pounds = 0.625 pound
divide the value of the ounce by 16
converting 3/4 pounds to ounces = 12 ounces
12 ounces is greater than 0.625 pounds
The employee uses more apples than kale
0.125 is more.
Question 17.
Modeling Real Life
You have a 3-pound bag of clay. You use 8 ounces of clay to make an ornament. How many ornaments can you make using all of the clay?
Answer:
Given that you have a 3 pound bag of clay
you use 8 ounces of clay to make an ornament.
we have to find out the how many ornaments you can make using all of the clay
Converting 3 pounds to ounces is
3 pounds = 48 ounces ( multiply the pounds value by 16 )
you have used the 8 ounces of clay to make an ornament
so, divide the 48 / 8 = 6
Therefore, we can make 6 ornaments by using all of the clay.
Review & Refresh
Find the product. Check whether your answer is reasonable.
Question 18.
Answer: Multiply the value 145 × 12 = 1740
Question 19.
Answer: multiply the value 561 × 87 = 48,807
Question 20.
Answer: multiply the value 823 × 65 = 53,495
Lesson 11.5 Capacity in Customary Units
Explore and Grow
Describe the relationship between cups and fluid ounces (fl oz). Then complete the table.
1 cup is _8 US_ times as much as 1 fluid ounce.
Answer:
Relationship between cups and fluid ounces is :-
A cup of water happens to equal both 8 fluid ounces ( in volume ) and 8 ounces( in weight) ,
so you might naturally assume that 1 cup equals to 8 ounces of weight universally in recipes.
Explanation:
About table values
1 capacity (cups ) = 8 US fluid ounces ( multiply the cups value by 8 )
2 capacity ( cups ) = 16 US fluid ounces
3 capacity ( cups ) = 24 US fluid ounces
4 capacity ( cups ) = 32 US fluid ounces
Structure
How can you convert cups to fluid ounces? How can you convert fluid ounces to cups?
Answer:
We can convert cups to fluid ounces by multiplying the value of the cup by 8
1 cup = 8 fluid ounces
We can convert fluid ounces to cups by dividing the value of the fluid ounce by 8
1 fluid ounce = 0.125 US cup .
Think and Grow: Convert Customary Capacities
Key Idea
When finding equivalent customary capacities, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Show and Grow
Convert the capacity
Question 1.
9 gal = __ qt
Answer: 9 gal = 36 Us liquid qt
Explanation:
Convert from gal to quart
1 gal = 4 quart
multiply the gal value by 4
Question 2.
20 pt = __ c.
Answer: 20 pt = 48.038 c
Explanation:
Convert from pints to cups
multiply the pt value by 2.402
Question 3.
42 pt = __ qt
Answer: 42 pt = 25.2199 qt
Explanation:
Convert from pints to quarts
divide the pt value by 1.665
Question 4.
68 qt = __ gal
Answer: 68 qt = 17 gal
Explanation:
Convert from quarts to gal
divide the qt value by 4
Apply and Grow: Practice
Convert the capacity.
Question 5.
7 c = fl oz
Answer: 7 c = 56 US fl oz
Explanation:
Convert from cups to fluid ounces
multiply the c value by 8
Question 6.
6 pt = __ qt
Answer: 6 pt = 3.60285 qt
Explanation:
Convert from pints to quarts
1 pint = 0.5 quart
divide the pt value by 1.665
Question 7.
16 qt = __ gal
Answer: 16 qt = 4 US liquid gal
Explanation:
Convert from quarts to gal
1 quart = 0.25 gal
divide the qt value by 4
Question 8.
15 pt = __ c
Answer: 15 pt = 36.0285 US c
Explanation:
Convert from pints to cups.
multiply the pt value by 2.402
Question 9.
Answer: 2 1/4 c = 2/4 = 1/2 c
1/2 c = 4 fl oz
Compare.
Question 11.
Answer:
14 c = 7 US liquid pt
divide the c value by 2
10 pt = 24.019 US c
multiply the pt value by 2.402
Question 12.
Answer:
38 qt = 9.5 US liquid gal
divide the qt value by 4
8 × 1/2 = 8/2 = 4
4 gal = 16 US liquid qt
Multiply the gal value by 4
Question 13.
Answer:
4 gal = 26.6456pt
multiply the gal value by 6.661
32 pt = 4.8038 US liquid gal
divide the pt value by 6.661
Question 14.
You fill your turtle’s aquarium with 40 pints of water. How many gallons of water do you use?
Answer:
Given turtles, aquarium fill with water = 40 pints
we have to find the 40 pints of water into gallons
converting 40 pints to gallons
40 pints = 5 US liquid gallons
Divide the pints value by 8
so, therefore 5 gallons of water is used.
Question 15.
Number Sense
Newton’s water cooler contains 1\(\frac{1}{2}\) gallons of water. How many times can he fill his 16-fluid ounce canteen with water from the water cooler? Explain.
Answer:- Given newton’s water cooler contains 1 × 1/2 = 1/2 = 0.5 gallons
Explanation:- converting 0.5 gallons = 64 US fluid ounces ( multiply the gallons value by 128 )
Given 16 fluid ounce
He can fill 4 times his 16 fluid ounce canteen with water from the water cooler
( i.e., 16 × 4 = 64 fluid ounce ) .
Question 16.
DIG DEEPER!
Order the capacities from least to greatest. Explain how you converted the capacities.
Answer:
i. 8 × 1/2 c => 8/2 = 4 c
4 c = 32 fl oz ( multiply the c value by 8 )
ii. 72 fl oz = 9 US c
divide the fl oz value by 8
iii. 7 × 3/4 c => 21/4 = 5.25 c
5.25 c = 42 fl oz
iv. 56 fl oz = 7 c
divide the fl oz value by 8
Order of capacities from least to greatest = 8 × 1/2 c , 7 × 3/4c , 56 fl oz , 72 fl oz .
Think and Grow: Modeling Real Life
Example
A car’s engine contains 4\(\frac{1}{2}\) quarts of oil. Can a mechanic use a 24-cup container to drain all of the oil?
First, convert the quarts of oil to pints.
There are __2pints in 1 quart.
Answer:
Given car engine contains = 4 × 1/2 quarts = 4/2 = 2 quarts
Explanation:
2 quarts = 4 pints
multiply the quarts value by 2
1 pint = 2 cups
converting 2 quarts to cups
2 quarts = 8 cups
multiply the quarts value by 4
So, a mechanic can use just 8 cups
8 cups are enough to drain engine oil.
Show and Grow
Question 17.
An adult has 192 fluid ounces of blood in his body. How many pints of blood are in his body?
Answer: Given an adult has 192 fluid ounces of blood in his body
we have to find the pints of blood in his body
Converting 192 fluid ounces to pints
192 fluid ounces = 12 US liquid pints
divide the value of the fluid ounce by 16
Therefore, 12 pints of blood are in his body.
Question 18.
DIG DEEPER!
You make 4\(\frac{1}{2}\) cups of soup. One serving is 12 fluid ounces. How many servings of soup do you make?
Answer:
Given 4 × 1/2 cups of soup
4 × 1/2 = 4/2 = 2 cups of soup
2 cups of soup converting to fluid ounces
2 US cups = 16 US fluid ounces
Given that serving = 12 fluid ounces
Subtract 16 fluid ounces – 12 fluid ounces = 4 fluid ounces
so, therefore you can make servings of soup in 4 fluid ounces.
Question 19.
DIG DEEPER!
A scientist has two beakers of a solution, one containing 5 cups and the other containing 1\(\frac{1}{2}\) pints. How many gallons of the solution does the scientist have? Write your answer as a fraction in simplest form.
Answer:
Given that scientist has two beakers of solution one contains 5 cups and other contains
1 × 1/2 pints.
we have to find gallons of solution
Converting 5 cups to gallons
5 cups = 0.312 US gallons
Converting 1 × 1/2 pints to gallons
1 × 1/2 => 1/2 = 0.5 pints
0.5 pints = 0.0625 US gallons
By adding both the solutions ( i.e., )
5 cups + 0.5 pints
0.312 gallons + 0.0625 gallons = 0.3745 gallons
So, the scientist has 0.3745 gallons of solution.
0.3745 in simplest form we can write as 749 / 2000.
Capacity in Customary Units Homework & Practice 11.5
Convert the capacity
Question 1.
9 pt = __ c
Answer: 9 pt = 18 c
Explanation: multiply the pt value by 2
Question 2.
72 fl oz = ___ c
Answer: 72 fl oz = 9 c
Explanation:
Convert from fluid ounces to cups.
1 fl oz = 0.125 c
divide the fl oz value by 8
Question 3.
6 c = __ fl oz
Answer: 6 c = 48 fl oz
Explanation:
Convert from cups to fluid ounces
1 cup = 6 fluid ounces
6 cups = 6 × 8 fluid ounces
multiply the c value by 8
Thus 6 c = 48 fl oz
Question 4.
Answer: 3 3/4 gal = 15 qt
Explanation:
Convert from gal to quart
1 gal = 4 quart
4 × 15/4 gal = 15 qt
multiply the gal value by 4
Question 5.
Answer: 5 1/2 qt = 11 pt
Explanation:
Convert from quarts to pints
1 quart = 2 pints
multiply the qt value by 2
5 1/2 = 11/2
11/2 × 2 = 11 pints
Question 6.
40 pt = __ gal
Answer: 40 pt = 5 gal
Explanation:
Convert from pints to gal
1 pint = 0.125 gal
40 pint = 40 × 0.125 = 5 gal
Thus 40 pt = 5 gal
Question 7.
64 qt = __ c
Answer: 64 qt = 256 c
Explanation:
Convert from quarts to cup
1 quart = 4 cups
multiply the qt value by 4
Question 8.
112 fl oz = __ pt
Answer: 112 fl oz = 7 US liquid pt
Explanation: divide the fl oz value by 16
Compare.
Question 9.
Answer:
48 qt = 12 gal
divide the qt value by 4
12 gal = 48 qt
multiply the gal value by 4
Therefore 48 qt = 12 gal
Question 10.
Answer: 24 fl oz = 3 c
divide the fl oz value by 8
3 × 1/4 c = 3/4 c = 6 fl oz
multiply the 3/4 c value by 8
Therefore 24 fl oz is greater than 3 × 1/4 c
Question 11.
Answer:
10 qt = 40 c
multiply the qt value by 4
24 c = 6 qt
divide the c value by 4
So, therefore 10 qt is greater than 24 c.
Question 12.
You buy 2 gallons of apple cider. How many cups of apple cider do you buy?
Answer:
Given that 2 gallons of apple cider
we have to find the cups of apple cider
Converting 2 gallons to Cups
2 gallons = 32 cups
multiply the gallons value by 16
So, you buy the 32 cups of apple cider.
Question 13.
Logic
Your friend makes a table of equivalent capacities. Write two pairs of customary units represented by the chart.
Answer:
We can relate the numbers as they are resembling quarts to cups relation and gallons to quarts relation.
Two pairs of the customary unit represented by the chart are :-
1 quart = 4 cups 1 gallon = 4 quarts
2 quart = 8 cups 2 gallon = 8 quarts
Question 14.
DIG DEEPER!
Which measurements are greater than 16 pints?
Answer:
Converting fluid ounces to pints
300 fluid ounces = 18.75 pints ( divide the value of the fluid ounce by 16 )
Converting cups to pints
28 cups = 14 pints ( divide the value of the cup by 2 )
Converting quarts to pints
10 quarts = 20 pints ( multiply the quarts value by 2 )
Converting gallon to pints
1 gallon = 8 pints ( multiply the gallon value by 8 )
Converting fluid ounces to pints
275 fluid ounces = 17.188 pints ( divide the value of the fluid ounce by 16 )
Converting cups to pints
35 cups = 17.5 pints ( divide the value of the cup by 2 )
Therefore, 300 fluid ounces, 10 quarts, 275 fluid ounces, 35 cups measurements are greater than 16 pints
Question 15.
Modeling Real Life
Your friend buys 8 quarts of frozen yogurt. How many cups of frozen yogurt does she buy?
Answer: Given that quart of frozen yogurt = 8
Explanation:
we have to find cups of frozen yogurt
converting 8 quarts to cups
8 quarts = 32 cups ( multiply the quarts value by 4 )
Therefore, she buys 32 cups of frozen yogurt
Question 16.
Modeling Real Life
A recipe calls for 2\(\frac{1}{4}\) cups of milk. You want to make 2 batches of the recipe. Should you buy a pint, quart, or half gallon of milk?
Answer: Given 2 × 1/4 => 2/4 = 1/2 cups of milk
Explanation: we want to make 2 batches of recipe (i.e., 2 × 1/2 = 1 cup )
1 pint = 2 cups
1 cup = 1/2 pint
Review & Refresh
Question 17.
0.5 × 0.7 = _0.35_
Answer:
multiply the 0.5 × 0.7 = 0.35
Question 18.
46.2 × 0.68 = _31.416_
Answer:
multiply the 46.2 × 0.68 = 31.416
Question 19.
1.4 × 0.3 = _0.42_
Answer:
multiply the 1.4 × 0.3 = 0.42
Lesson 11.6 Make and Interpret Line Plots
Explore and Grow
Measure and record your height to the nearest quarter of a foot. Collect the heights of all the students in your class and create a line plot of the results.
Construct Arguments
Make two conclusions from the line plot.
Think and Grow: Make Line Plots
Example
The table shows the amounts of water that 10 students use for a science experiment. Make a line plot to display the data. How many students use more than \(\frac{1}{2}\) cup?
Step 1: Write the data values as fractions with a common denominator.
The denominators of the data values are 2, 4, and 8. Because 2 and 4 are factors of 8, use a denominator of 8.
Step 2: Use a scale on a number line that shows all of the data values.
Step 3: Mark an X for each data value.
Show and Grow
Question 1.
The table shows the distance your friend swims each day for 10 days. Make a line plot to display the data.
How many days does your friend swim \(\frac{3}{4}\) mile or more?
Answer:- From the table we observed that your friend swim 3/4 miles or more than 3/4 miles in 6 days.
Apply and Grow: Practice
Question 2.
The table shows the amounts of mulch a landscaping company orders on 10 different days. Make a line plot to display the data.
What do you notice about the data?
Answer:
From the table we observed that except 1/4 and 1/2 the remaining days like 7/8 and 3/4 company use more than 1/2 ton of mulch .
Question 3.
DIG DEEPER!
Your teacher has the three packages of seeds shown. She divides the first package into bags weighing \(\frac{1}{2}\) ounce each. She divides the second package into bags weighing \(\frac{1}{4}\) ounce each. She divides the third package into bags weighing \(\frac{1}{8}\) ounce each. Find the total number of bags of seeds. Use a line plot to display the results.
Answer:
Given that we observed from figures each bag is 2 ounces
Explanation:
given 1st bag = 1/2 ounce each
2 ounces = 1/2 + 1/2 +1/2 + 1/2 = 4(1/2) = 2
4 bags
2nd bag = 1/4 ounce each
2 ounces = 1/4 + 1/4 +1/4 +1/4 + 1/4 + 1/4 + 1/4 + 1/4
= 8 (1/4) = 2
8 bags
3rd bag = 1/8 ounce each
2 ounces = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
= 16 (1/8) = 2
16 bags
Total number of bags of seeds = 4 bags + 8 bags + 16 bags = 28 bags
Think and Grow: Modeling Real Life
Example
You record the amounts of time you skateboard each day for 8 days. Your friend skateboards the same total amount of time, but for an equal number of hours each day. How long does your friend skateboard each day?
Step 1: You and your friend skateboard the same total amount of time. Use the line graph to find the number of hours you each skateboard.
Step 2: Divide the number of hours by the number of days.
Show and Grow
Question 4.
You record the amounts of trail mix you pour into 12 bags. Your friend has the same total amount of trail mix, but equally divides it among 12 bags. How much trail mix does your friend pour into each bag?
Answer:- your friend pour trail mix into each bag is equal to the amount of trail mix you pour into the bag.
Make and Interpret Line Plots Homework & Practice 11.6
Question 1.
The table shows the amounts of time that 10 students take to land three balls in a row in a game. Make a line plot to display the data. How many pygmy marmosets weigh more than \(\frac{1}{2}\) ounce?
Answer: Here 1/2 = 0.5 ounce
Except 1/2 ounce
5/8 , 7/8 , 3/4 ounces pygmy weighs more than 1/2 ounce.
Use the table.
Question 2.
The table shows the amounts of berries required to make 10 different smoothie recipes. Make a line plot to display the data.
Answer: The most common amount of berries required is 3/4
Six times as many recipes use 3/4 cup of berries as 1/4 cup of berries
from table 4 × (3/4) = 12/4 = 3
2 × (1/4) = 2/4 = 1/2
= 3/(1/2) = 6
Question 3.
DIG DEEPER!
How many total cups of berries are needed to make one of each smoothie?
Answer: Total 2 to 3 cups of berries are needed to make one of each smoothie.
Use the line plot.
Question 4.
Modeling Real Life
The line plot shows the number of miles you run each day for 10 days. Your friend runs the same total number of miles, but runs an equal number of miles each day. How far does your friend run each day?
Answer: Your friend runs 4/5 miles each day for 10 days
Explanation: 0 + 0 + 0.5 + 0.5 + 0.5 + 1 + 1 + 1 + 1.5+ 2 = 8
He runs same miles each day = 8/10 = 0.8
0.8 = 4/5
Question 5.
DIG DEEPER!
Your cousin runs a total amount that is 6 times as far as your friend runs in one day. How far does your cousin run?
Answer: Let us assume that, If the friend runs 0.8 per day
Explanation: 0.8 = 4/5
so, cousin run 6 times more than a friend
so, 6 × 0.8 = 4.8 ( cousin runs per day is 4.8 )
Review & Refresh
Question 6.
561 ÷ 7 = 80.142
Answer: divide the 561 ÷ 7 = 80.142
Question 7.
3,029 ÷ 4 = 757.25
Answer: divide the 3,029 ÷ 4 = 757.25
Question 8.
2,814 ÷ 9 = 312.6
Answer: divide the 2,814 ÷ 9 = 312.6
Lesson 11.7 Problem Solving: Measurement
Explore and Grow
Make a plan to solve the problem.
A fruit vendor sells fruit by the pound. You have a tote that can hold up to 4 pounds. A bag of oranges weighs 2\(\frac{1}{4}\) pounds. A bag of apples weighs 28 ounces. Can your tote hold both bags of fruit? Explain.
Answer: Given that vendor sells fruit by the pound.
Explanation:
The tote can hold up to 4 pounds
A bag of oranges weighs = 2 × 1/4 = 2/4 = 1/2 pounds
A bag of apples weighs = 28 ounces
we have to find that can tote to hold both bags
Convert 28 ounces to pounds
28 ounces = 1.75 pounds ( divide the value of the ounce by 16 )
Given in question that tote can hold up to 4 pounds
so, adding 1/2 pounds and 1.75 pounds
= 1/2 pounds = 0.5
0.5 pounds + 1.75 pounds = 2.25 pounds
Therefore tote holds both the bags of fruit.
Precision
Which bag of fruit is heavier? Explain.
Answer: Bag of apple is heavier ( i.e., a bag of apple weighs 28 ounces )
Explanation:
28 ounces = 1.75 pounds
bag of orange is 0.5 pounds
1.74 > 0.5 (So, apple bag weigh is heavier)
Think and Grow: Problem Solving: Measurement
Example
A recipe calls for 2\(\frac{1}{4}\) cups of milk. You have \(\frac{1}{4}\) pint of whole milk and 1\(\frac{1}{2}\) cups of skim milk. Do you have enough milk for the recipe?
Answer: Given that , a recipe calls for 2 × 1/4 cups of milk
Explanation: 2 × 1/4 => 1/2 = 0.5 cups of milk
you have 1/4 pint of milk = 0.25 pints
0.25 pints = 0.5 cups
and 1 × 1/2 cups of skim milk => 1/2 = 0.5 cups
Recipe calls for 0.5 cups of milk
Yes, we have enough milk for the recipe.
Understand the Problem
What do you know?
- The recipe calls for 2 cups of milk.
- You have \(\frac{1}{4}\) pint of whole milk and 1\(\frac{1}{2}\) cups of skim milk.
What do you need to find?
You need to find whether you have enough milk for the recipe.
Answer: Given that recipe calls for 2 cups of milk
you have 1/4 pint of whole milk => 1/4 pint = 0.25 pint
0.25 pint = 0.5 cups
and 1 × 1/2 cups of skim milk => 1/2 cups = 0.5 cups
adding cups values => 0.5 + 0.5 = 1
So, you don’t have enough milk for the recipe .
Make a Plan
How will you solve?
- Convert \(\frac{1}{4}\) pint of whole milk to cups.
- Add the amounts of whole milk and skim milk.
- Compare the amount of milk you have to the amount needed.
Solve
Step 1: Convert \(\frac{1}{4}\) pint to cups.
Step 2: Add the amounts of whole milk and skim milk.
Answer: So, you _1.5_cups have enough milk for the recipe.
2/4 cups = 1/2
1/2 = 0.5 cups
Show and Grow
Question 1.
Explain how you can check whether the answer above is reasonable.
Answer: By calculating we get whole milk = 0.5 cups
By calculating we get skim milk = 0.5 cups
By adding whole milk and skim milk => 0.5 + 0.5 = 1 cup
Apply and Grow: Practice
Understand the problem. What do you know? What do you need to find? Explain.
Question 2.
Your friend buys 1 pound of walnuts, 16 ounces of peanuts, and \(\frac{1}{2}\) pound of cashews. How many ounces do the nuts weigh in all?
Answer: Given walnuts = 1 pounds
peanuts = 16 ounces
cashews = 1/2 pounds
we have to find weight of all nuts in ounces
Explanation: walnuts = 1pounds
converting pounds to ounces
1 pounds = 16 ounces
peanuts = 16 ounces
cashews = 1/2 pounds
converting pounds to ounces
1/2 pounds = 8 ounces
Adding peanuts , cashews , walnuts weight = 16 + 8 + 16 = 40 ounces
The nuts weigh in all = 40 ounces
Question 3.
A bottle of orange juice contains 64 fluid ounces. How many cups of orange juice are in 3 bottles?
Understand the problem. Then make a plan. How will you solve? Explain.
Answer:
Given that a bottle of orange juice contains = 64 fluid ounces.
Converting 64 fluid ounces to cups
64 fluid ounces = 8 cups
8cups × 3 bottles = 8 × 3 = 24 cups
Question 4.
Your friend wants to buy curtains that hang from the top of the window to the floor. Curtain lengths are typically measured in inches. What length curtains should he buy?
Answer:
Given the length ( ft ) values in figure
we have to measure ft value in inches
5 ft = 60 inches
3 ft = 36 inches ( He should by 60 inches and 30 inches length curtains ).
Question 5.
Your friend runs a total distance of 1 kilometer at track practice by running 100-meter hurdles. How many times does he run the hurdles?
Answer: Given your friend runs a total distance = 1 km
Convert 1 km to meters
1 km = 1000 meters
your friend practice 100 meter hurdles by running
so 100 × 10 = 1000
so , 10 times he run the hurdles
Question 6.
A trailer can carry 13\(\frac{1}{2}\) tons. It has room to carry 6 cars at once. Can the trailer carry 6 cars that each weigh 3,800 pounds? Explain.
Answer: Convert tons to pounds
13 × 1/2 tons = 13000 pounds
Given total 6 cars
each car weigh 3,800 pounds
so, 6 cars × 3,800 pounds = 6 × 3,800 = 22,800 pounds
so, the trailer cannot carry 6 cars at once
Question 7.
DIG DEEPER!
You walk your dog 4 laps around the block each day. Each block is 400 meters. How many total kilometers do you walk your dog around the block after 35 weeks?
Answer: Given, you walk your dog around the block each day = 4 laps
Each block = 400 meters
Explanation: There are 7 days in a week
given 35 weeks
4 × 400 × 7 × 35 = 392000 meters
Convert 392000 meters to km
392000 meters = 392 km
Therefore, 392 km you walk your dog around the block after 35 weeks
Think and Grow: Modeling Real Life
Example
A crew member needs to put a temporary fence around the perimeter of the rectangular football field. How many feet of temporary fencing does the crew member need?
Think: What do you know? What do you need to find? How will you solve?
Step 1: Convert the length of the field to feet.
There are __ feet in 1 yard.
120 × __ = __
The length of the field is __ feet.
Step 2: Use a formula to find the perimeter of the field.
Show and Grow
Question 8.
An artist puts a wood border around the perimeter of the rectangular mural. How many feet of wood does the artist need?
Answer: 1 yard = 3 feet
Given 10/3 yd = 3.33 yd
3.33 yd × 3 = 9.99 feet
perimeter of rectangular mural
p = ( 2 × L ) + ( 2 × W )
= 2 × 8 + 2 × 9.99
= 16 + 19.98
= 35 feet
Artist need 35 feet of wood .
Question 9.
DIG DEEPER!
The sports jug contains 5 gallons of water. The paper cup holds 8 fluid ounces of water. How many paper cups can 3 sports jugs fill? Justify your answer.
Answer: Convert 5 gallons of water to fluid ounces
Explanation:
5 gallons = 640 fluid ounces
Given paper, cup holds = 8 fluid ounces of water
1 sport jug = 5 gallons
3 sport jugs = 3 × 5 = 15 gallons
15 gallons = 1920 fluid ounces
8 × 240 = 1920
240 paper cups can fill 3 sports jug .
Problem Solving: Measurement Homework & Practice 11.7
Understand the problem. Then make a plan. How will you solve? Explain.
Question 1.
A robotic insect has a mass of 80 milligrams. The mass of a quarter is 5.67 grams. How many more grams is the mass of a quarter than the mass of the robotic insect?
Answer: Given robotic insect mass = 80 milligrams
The mass of quarter = 5.67 grams
Convert 80 milligrams to grams
80 milligrams = 0.008 grams
subtract 5.67 grams – 0.008 grams = 5.662
Therefore the mass of quarter 5.662 grams is more than the mass of robotic insect
Question 2.
Newton pours water out of a filled 2-liter beaker. Now it only has 1,025 milliliters of water in it. How many milliliters of water did Newton pour out?
Answer: Given newton pours water out of a filled beaker = 2 Liters
Explanation:
Now it has water = 1,025 milliliters
Convert 2 Liters to millimeters
2 liters = 2000 milliliters
2000 – 975 = 1,025
Newton pour out 975 millimeters of water
Question 3.
You run 5 laps around a track. Each lap is 400 meters. How many total kilometers do you run?
Answer: Given you run 5 laps around a track
Each lap = 400 meters
Explanation:
5 × 400 = 2000 meters
convert meters to kilometers
2000 meters = 2 kilometers
Therefore you run 2 kilometers
Question 4.
Two hotel workers have a total of 30 bags of luggage each weighing 50 pounds. One worker weighs 150 pounds, and the other weighs 210 pounds. Can they transfer themselves and all of the bags in the elevator at once? Explain.
Answer:
Given in figure elevator weight limits = 2.5 tons
Explanation:
Convert 2.5 tons to pounds
2.5 tons = 5000 pounds
Given works have total 30 bags
1 bag weight = 50 pounds
30 bags weight = 50 × 30 = 1500 pounds
Given one worker weight = 150 pounds
second worker weight = 210 pounds
By adding all the values 1500 + 150 + 210 = 1860 pounds
Yes, they can transfer themselves and all of the bags in the elevator once.
Question 5.
DIG DEEPER!
You have 84 feet of streamers. You cut 24 pieces that are \(\frac{1}{2}\) each yard long. How many feet of streamers do you have left?
Answer:
Given steamers = 84 feet
24 pieces are 1/2 = 0.5 each yard long
24 × 0.5 = 12 yard long
12 yards = 36 feet
84 – 36 = 48 feet of streamers you have left .
Question 6.
Writing
Write and solve a two-step word problem involving units of measure.
Question 7.
Modeling Real Life
You want to hang a wallpaper border around the perimeter of the rectangular bathroom shown. How many yards of wallpaper border do you need?
Answer:
Given length = 6 ft , width = 1 y
Explanation:
Convert 6 ft to yd
6 ft = 2 yd
perimeter of rectangle = 2 (L + W)
= 2(2 + 1 )
= 2(3) = 6 yd
6 yd of wallpaper border you need
Question 8.
DIG DEEPER!
You need 
gallon of fertilizer to cover a lawn. What is the least amount of money that you can pay and have enough fertilizer?
Answer: Given one lawn fertilizer is 128 fluid ounces
Explanation:
Take 2 gallons = $ 40 × 2 = 80
Given another lawn fertilizer 16 fluid ounces
2 gallons = $ 11 × 16 = 176
80 is the least amount of money that you can pay and have enough fertilizer
128 fluid ounces is cheap when compared to 16 fluid ounces.
Review & Refresh
Divide. Then check your answer.
Question 9.
Answer: 5,343 divide by 25
5,343 ÷ 25 = 213.72
Question 10.
Answer: 2,064 divide by 24
2,064 / 24 = 86
Convert and Display Units of Measure Performance Task 11
Passenger airliners come in many different sizes. Plane A and Plane B are two different types of wide-body jet airliners.
Question 1.
The table shows some facts about Plane A.
a. The length of Plane B is 80 yards. Which is longer, Plane A or Plane B? How much longer?
Answer:- Given, length of plane B = 80 yards
We observed from the table that the length of plane A = 250 ft 2 in
Convert 250 ft 2 into yards
250 ft 2 in = 83.389 yards
So, Length of plane A = 83.389 yards
Length of plane B = 80 yards
Plane A is longer than Plane B
3.389 is longer.
b. The wingspan of Plane B is 37\(\frac{1}{12}\) feet longer than the Wingspan of Plane A. What is the wingspan of Plane B?
Answer: The wingspan of plane B = 37 × 1/2 = 36.852 inches
Question 2.
Before an airliner can take off, the pilot has to make sure it weighs less than the maximum takeoff weight.
a. Plane A weighs 404,600 pounds and can carry at most 422,000 pounds of fuel. How many pounds can the airliner hold in passengers and cargo?
b. The maximum landing weight of Plane A is 300,000 pounds less than the maximum takeoff weight. Why does an airliner weigh less at the end of a flight than at the beginning?
c. Plane A uses 20 quarts of fuel for each mile it flies. How many gallons of fuel does the plane use during a 3,200-mile flight?
Question 3.
Plane B can hold 544 passengers. Plane A can hold \(\frac{3}{4}\) of passengers that Plane B can hold.
a. How many passengers can Plane A hold?
Answer: Plane A hold 3/4 = 0.75 passengers
b. An airline estimates that each passenger weighs about 200 pounds, including carry-on baggage. How much passenger and carry-on weight does the airline estimate for Plane B?
Answer: 408 passenger and carry on weight does the airline estimate for plane B
Convert and Display Units of Measure Activity
Directions:
- Players take turns.
- On your turn, place a counter on a yellow hexagon.
- Solve for the missing measurement and cover the answer with another counter. If you surround a monster, then put a counter on the monster. If you do not surround a monster, then your turn is over.
- Continue playing until all measurements are covered.
- The player who captures the most monsters wins!
Convert and Display Units of Measure Chapter Practice
11.1 Length in Metric Units
Convert the length.
Question 1.
4 cm = __ mm
Answer: 4 cm = 40 mm
Explanation:
Convert from centimeter to millimeter
1 cm = 10 mm
4 cm = 4 × 10 mm = 40 mm
multiply the cm value by 10
Question 2.
81 m = _8100__ cm
Answer: 81 m = 8100 cm
Explanation:
Convert from meter to centimeter.
1 m = 100 cm
multiply the m value by 100
81 m = 81 × 100 cm = 8100 cm
Question 3.
0.56 km = _56000_ cm
Answer: 0.56 km = 56000 cm
Explanation:
Convert from kilometer to centimeter.
Multiply the km value by 100000
Question 4.
9 mm = 0.009__ m
Answer: 9 mm = 0.009 m
Explanation:-
Convert millimeter to meter.
divide the mm value by 1000
Compare.
Question 5.
Answer:- 73 m = 0.073 kilometer
Explanation:- divide the m value by 1000
Answer:- 7.3 km = 7300 m
Explanation:- multiply the km value by 1000
Question 6.
Answer:
0.6 cm = 0.006 m
divide the cm value by 100
0.06 m = 6 cm
multiply the m value by 100
Question 7.
Answer:
2mm = 0.2 cm
divide the mm value by 10
0.2 cm = 2mm
multiply the cm value by 10
11.2 Mass and Capacity in Metric Units
Convert the mass.
Question 8.
3 kg = _3000__ g
Answer:
3 kg = 3000 g
Explanation:
Convert from kg to gram
1 kg = 1000 grams
multiply the kg value by 1000
3 kg = 3 × 1000 gram = 3000 gram
Question 9.
0.006g = _6__ mg
Answer: 0.006 g = 6 mg
Explanation:
Convert from grams to milligrams
multiply the g value by 1000
Question 10.
70 g = _0.07_ kg
Answer: 70 g = 0.07 kg
Explanation:
Convert from grams to kilograms
divide the g value by1000
Question 11.
29,000 mg = _0.029_ kg
Answer: 29,000 mg = 0.029 kg
Explanation:
Convert from milligrams to kilograms
divide the mg value by 1e + 6
29,000 mg = 0.029 kg
Convert the capacity.
Question 12.
400 mL = _0.4_ L
Answer: 400 mL = 0.4 L
Explanation:
Convert from milliliters to liters
divide the mL value by 1000
Question 13.
10 L = 10000 mL
Answer: 10 L = 10000 mL
Explanation:
Convert from liters to milliliters
1 L = 1000 ml
10 L = 10 × 1000 = 10000 mL
multiply the L value by 1000
Question 14.
7 mL =0.007 L
Answer: 7 mL = 0.007 L
Explanation:
Convert from milliliters to liters
divide the mL value by 1000
7 mL = 0.007 L
Question 15.
0.65 L = 650mL
Answer: 0.65 L = 650 mL
Explanation:
Convert from liters to milliliters
1 L = 1000 mL
multiply the L value by 1000
0.65 L = 0.65 × 1000 = 650 mL
So, 0.65 L = 650 mL
11.3 Length in Customary Units
Convert the length.
Question 16.
2 mi = ___ yd
Answer: 2 mi = 3520 yards
Explanation:
Convert from miles to yards
1 mi = 1760 yards
multiply the mi value by 1760
2 mi = 2 × 1760 yards = 3520 yards
Question 17.
14\(\frac{2}{3}\) yd = ___ ft
Answer: 14 × 2/3 yd = 28 ft
Question 18.
103 in. = __ ft __ in.
Answer: 103 in = 8 ft 7 in
Explanation:
Convert from inches from feet.
divide the 103 in value by 12
Question 19.
2,340 in. = yd
Answer: 2,340 in = 65 yd
Explanation:
Convert from inches to yards
divide the 2,340 in value by 36
Compare.
Question 20.
Answer: 5 × 2/3 yd = 10 ft
17 ft = 5.667 yd
Explanation:
Convert yards to feet.
divide the 17 ft value by 3
Question 21.
Answer: 67 in = 5 feet 7 inches
Explanation:
divide the in value by 12
5 ft 10 in = 70 in
multiply the 5 ft 10 in value by 12
Question 22.
Answer:
16 mi = 84480 ft
multiply the mi value by 5280
84,000 ft = 15.909 mi
divide the ft value by 5280
Weight in Customary Units
Convert the weight.
Question 23.
Answer: 4/2 T = 2 (By solving 4/2 we get 2)
so we take 4/2 as 2
1 T = 2000 lb
2 T = 4000 lb
Question 24.
100,000 lb = ___ T
Answer: 100,000 lb = 45.359237 T
Explanation:
100,000 lb × 0.00045359237 = 45.359237 T
Convert the weight.
Question 25.
217 oz = __ lb __ oz
Answer: 217 oz = 13 lb 9 oz
Question 26.
956 oz = __ lb
Answer: 956 oz = 59 lb
Compare.
Question 27.
Answer: 5×1/4 T = 2755 lb
15,000 lb = 6.696 T
Question 28.
Answer: 258 oz = 16.125 lb
divide the oz value by 16
17 lb 12 oz = 284 oz
multiply the lb oz value by 16
Question 29.
Answer: 192,000 oz = 6 T
7 T = 250,880 oz
Question 30.
Number Sense
Which measurements are equivalent to 52 ounces?
Answer: 3 lb 4 oz measurement is equivalent to 52 ounces.
11.5 Capacity in Customary Units
Convert the capacity.
Question 31.
18 qt = __ pt
Answer: 18 qt = 29.9762706 pt
Explanation:
1qt equals to 1.6653484 pt
1.6653484 × 18pt = 29.9762706 pt
Question 32.
Answer: 24 fl oz
Explanation:
4 × 3/4c , by solving this we get 12/4c=3c
from formula= 1c = 8 floz
3c = 8 fl oz × 3c = 24 floz
Question 33.
72 pt = __ gal
Answer: 72 pt = 9 gal
Explanation:
1 pt = 0.125 gal
72 pt = 0.125 × 72 = 9 gal
Question 34.
81 qt = __ gal
Answer: 81 qt = 20.25 gal
Explanation:
1 qt = 0.25 gallons
81 qt = 81 × 0.25 = 20.25 gal
Compare.
Question 35.
Answer:
5/4 gal = 5 US qt
multiply the gal value by 4
21 qt = 5.25 US gal
divide the qt value by 4
Question 36.
Answer:
Convert from pints to cups
7/2 pt = 7 c
9 c > 7 c
3 1/2 pt < 9 c
Question 37.
Answer:–
Convert from quart to cups.
1 quart = 4 cups
4 qt = 16 c
4 qt < 20 c
Question 38.
Modeling Real Life
You have 2\(\frac{1}{4}\) gallons of apple juice. How many pints of apple juice do you have?
Answer: Given 2 × 1/4 (gallons of apple juice)
By solving 2 × 1/4 we get 1/2=>0.5 gallons
so, we have 4 pints of apple juice
Explanation:
we have to find out pints of apple juice
0.5 gallons is equal to 4 pints
from the formula multiply the gallon value (i.e., 0.5 with 8 = 0.5 × 8 = 4 pints)
11.6 Make and Interpret Line Plots
Question 39.
The table shows the amounts of clay made by 10 students. Make a line plot to display the data.
How many students made more than \(\frac{3}{4}\) cup of clay?
Answer: 3/4 = 0.75
only one student ( 7/8 )made more than 3/4 cup of clay ( i.e., 7/8 = 0.875 )
What is the most common amount of clay made?
Answer: The most common amount of clay made is 3/4
11.7 Problem Solving: Measurement
Question 40.
A recipe calls for 2\(\frac{3}{4}\) cups of fava beans. You have 1\(\frac{1}{4}\)– pint can of fava beans and \(\frac{1}{2}\) cup of cooked fava beans. Do you have enough fava beans for the recipe?
Answer: Yes, you have enough fava beans for the recipe
Explanation:
Given that a recipe calls for 2 × 3/4 = 0.5 cups of fava beans
you have 1 × 1/4 pints = 0.5 cups of fava beans ( convert 1/4 pints to cups )
and 1/2 = 0.5 cups of cooked fava beans
So, the recipe calls 0.5 cups of fava beans are equal to you have 0.5 cups of fava beans.
Convert and Display Units of Measure Practice 1-11
Question 1.
Your friend estimates that a bookcase is 2\(\frac{1}{2}\) feet wide. The actual width is \(\frac{2}{3}\) foot longer. What is the width of the bookcase?
Answer: 2 × 1/2 = 1 estimation feet
2/3 = 0.667 actual width feet
1 – 0.667 = 0.34
Question 2.
What is the product of 845 and 237?
Answer: Option C
product (Multiply) the 845 and 237 = 200,265
Explanation: 845 × 237 = 200,265
Question 3.
How many milliliters are equal to 0.6 liter?
Answer:- Option D (600 mL)
Explanation: 1 liter = 1000 mL
0.6 liter = 0.6L × 1000mL
= 600mL
Question 4.
Which are equivalent to 
?
Answer: 6 × 3/10 is equivalent to 18 × 1/10
Explanation:
6 × 3/10 = multiply 6 with 3 we get 18, denominator remains same
so the answer is 18 × 1/10.
Question 5.
To find 34 + (16 + 23), your friend adds 34 and 16. Then she adds 23 to the sum. Which property did she use?
Answer:- Option B
She used the Associative property of addition.
Question 6.
An Eastern Hognose Snake is 2\(\frac{1}{2}\) feet long. It grows another foot. What is the new length of the snake in inches?
Answer: 2 × 1/2 = 1 feet
Explanation:
It grows another foot = 1
so, 1 + 1 = 2 feet
convert 2 feet to inches
2 feet = 24 inches
So, the new length of the snake is 24 inches.
Question 7.
What common factor should you divide the numerator and denominator of \(\frac{16}{24}\) by so that it is in the simplest form?
Answer: 8 is the common factor that divides the numerator and denominator of 16/24 in simplest form
Explanation:
The simplest form is nothing but if the top and bottom(i.e., numerator and denominator) have no common factors other than 1.
16/24 = solve it by 8
By solving we get 2/3.
Question 8.
A salesperson at a fabric store has 30 yards of fabric. He puts the same number of yards of fabric on each of 4 rolls for a display. How many yards of fabric does the salesperson put on each roll?
Answer:
Option B
2/15 yard
Explanation:
Given 30 yards of fabric
rolls= 4
rolls/yards = 4/30 = 2/15yard
Question 9.
Descartes estimates 96.3 × 42 by rounding each number to the nearest ten. What is Descartes’s estimate?
Answer: Option D (4,000)
Explanation: Here we have to multiply the given number 96.3 × 42
96.3 ~ 100 (96.3 is the nearest value to 100)
42~40 (42 is the nearest value to 40)
so, multiply both the values 100 × 40 = 4000
Question 10.
The fifth-grade classes are making a mural to hang in the front hallway of the school.
Part A Each class creates a square for the mural that has side lengths of \(\frac{1}{2}\) meter. What is the area of each square?
Answer: area of square =s×s
1/2 × 1/2 = 0.5 × 0.5 = 0.25 meters
Part B
There are 12 classes. What is the area of the entire mural? Explain.
12 × 0.25 = 3 meters
Question 11.
Which expressions have a quotient of 4.6?
Answer: All expressions have a quotient of 4.6 except 15.64÷34 does not have a quotient of 4.6
Explanation: we can find out the quotient value by this method
quotient = Dividend ÷ divisor (i.e., from the above question we are taking one value 124.2 ÷ 27 = 4.6)
Question 12.
What is the quotient of 5 and \(\frac{1}{8}\) ?
Answer:- The quotient of 5 and 1/8 = 40
Explanation:- Divide the 5 and 1/8
Question 13.
You need thirty 5-foot pieces of string for a project. A store sells string by the yard. How many yards of string will you need to buy?
Answer:- 11.655
Explanation: Given foot pieces = 35
1 foot = 0.333 yard
1 yard = 3 foot or 3 feet
we have to find yards of string.
foot pieces × yards = 35 × 0.333
= 11.655
Question 14.
In which equations does k = \(\frac{3}{4}\) ?
Answer: Option D
3/6 × 3/2 =k
Explanation:
we have equated k value as 3/4
so, by solving 3/6 × 3/2 we get 3/4
Question 15.
Newton brings 3 bags of popcorn that are all the same size to a club. There are 12 people at the club. Each person eats the same amount of popcorn and all of the popcorn is eaten. What fraction of a bag of popcorn does each person eat?
Answer: Bags = 3 , People = 12
so, divide 3/12 = 1/4
Option A is the answer
Question 16.
Evaluate
Answer:
Convert the decimal values to fractions
4.5 = 9/2
13.68 = 342/25
13.70 = 137/10
15.70 = 157/10
Question 17.
What is the sum of \(\frac{5}{6}\) and \(\frac{1}{4}\) ? 
Answer: Option D
5/6 + 1/4 = 13/12
Question 18.
What is 40,071 written in word form?
A. four thousand, seventy-one
B. four hundred, seventy-one
C. forty thousand, seventy-one
D. forty thousand, seven hundred ten
Answer: Option C
Forty thousand, seventy-one
Convert and Display Units of Measure STEAM Performance Task
Sound is created from vibrations in the air called sound waves. In music, when you hear different pitches, it is because the sound waves are traveling at different speeds. The frequency of a pitch measures the number of sound waves per second. Higher pitches have higher frequencies, and lower pitches have lower frequencies. Frequencies are measured in Hertz.
Question 1.
A4 is the musical note commonly used to tune instruments. The frequency of A4 is 440 Hertz, because the sound vibrates 440 times per second.
a. The frequency of A3 is \(\frac{1}{2}\) the frequency of A4. The frequency of A2 is \(\frac{1}{2}\) the frequency of A3. What is the frequency of A2?
Answer: frequency of A2 = 110
b. Is the pitch of A2 higher or lower than the pitch of A4? Explain.
c. How can you use the frequency of A4 to find the frequency of A5? Explain.
d. The frequency of B4 is 493.88 Hertz. What is the frequency of B3?
e. A computer software program can correct the frequency of a sound so it has perfect pitch. A violin plays a note that has a frequency of 255.1 Hertz. Explain how to change the frequency so it has the pitch of B3.
Question 2.
Use the Internet or some other resource to learn about how audio processors can help to correct a singer’s pitch, or to alter the way a song sounds. Write one interesting thing you learn.
Answer:
Auto-Tune is an audio processor introduced in 1997 by and registered trademark of Antares Audio Technologies, which uses a proprietary device to measure and alter pitch in vocal and instrumental music recording and performances. It was originally intended to correct off-key inaccuracies, allowing vocal tracks to be perfectly tuned despite originally being slightly off-pitch.
Pitch correction is an electronic effects unit or audio software that changes the highness and lowness in pitch of an audio signal so that all pitches will be notes from the equally tempered system(i.e., like the pitches on a piano). Pitch correction first detects the pitch of an audio signal (using a live pitch detection algorithm), then calculates the desired change and modifies the audio signal accordingly. The widest use of pitch corrector devices is in western popular music on vocal lines.
Question 3.
You borrow a guitar to learn how to play. Use the Guitar table to decide which guitar you should borrow.
a. Based on your height, you need a guitar that is close to 1 yard long. Which guitar is closer?
Answer: 1 yard = 36 inches
Guitar A is 37 inches
So, Guitar A is closer
b. You also need a guitar that is close to 8 pounds. Which guitar do you think you should borrow? Explain.
Answer: Guitar B you should borrow
176 ounces = 11 pounds which is closer to 8 pounds .
c. Guitar B is called a full-size guitar and Guitar A is called a \(\frac{7}{8}\)-size guitar. Is the length of Guitar A \(\frac{7}{8}\) the length of Guitar B? Explain
Answer: From the table Length of Guitar B = 40 inches
Given guitar A = 7/8 = 10.5 inches
No, the length of Guitar A is not equal to Guitar B
d. The scale length on a guitar affects the pitch. To find the scale length of a guitar, multiply the distance between the nut and the 12th fret by 2. On your guitar, that distance is 12\(\frac{3}{4}\) inches. What is the scale length of your guitar?
Answer: 9 × 12 × 2 = 216
The scale of the length of the guitar is 216
e. The strings on your guitar are \(\frac{3}{8}\) inch longer than the scale length to allow you to tune the strings to correct pitch. What are the string lengths on your guitar?
Answer:- The string length on your guitar = 3/8
3/8 = 4.5 inches
f. When you tune a string, you adjust it tighter to make the pitch higher, or looser to make pitch lower. You use a tuning instrument to help you string has a tune your guitar. It says that your A4 string has a frequency of 436.2 Hertz. How should you adjust the string to get the pitch in tune?
Answer:- we have to adjust the string to get the pitch in tune = 440 Hertz
its wavelength (cm) = 78.41
Conclusion:
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