All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 12 Lesson 6 Solve Measurement Problems will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 12 Lesson 6 Solve Measurement Problems
Math in My World
Example 1
Lauren lives 0.2 kilometers from Alex. Alex lives three times as far from Cohn’s house as Lauren’s house. How far away does Alex live from Colin?
Find 3 × 0.2.
You can use a number line to solve the problem.
Start at zero. Count by 0.2 three times.
3 × 0.2 = 0.6
So, Alex lives _______________ kilometer from Colin.
Check
Convert 0.2 to a fraction. Then multiply the fraction by 3.
Answer: So, Alex lives 0.6 kilometers from colin.
Explanation: Given that,
Lauren lives 0.2 kilometers from Alex.
Alex lives three times as far from Cohn’s house as Lauren’s house.
Now, we will find out how far away does Alex live from Colin.
So, the value is 0.2 x 3 = 0.6
Therefore, Alex lives 0.6 kilometers from colin.
Example 2
Javier poured 500 milliliters of lemon juice and 2 liters of water into a pitcher to make lemonade. How many milliliters of lemon juice and water did he pour into the pitcher in all?
1. Convert.
Convert 2 liters to milliliters.
Since 1 liter = 1,000 milliliters, multiply the number of liters by 1,000.
2 × 1,000 = 2,000
So, 2 liters = 2,000 milliliters.
2. Add.
2,000 milliliters + 500 milliliters = 2,500 milliliters
So, Javier poured ______________ milliliter of lemon juice and water into the pitcher.
Answer: So, Javier poured 2500 milliliters of lemon juice and water into the pitcher.
Explanation: Given that,
Javier poured 500 milliliters of lemon juice and 2 liters of water into a pitcher to make lemonade.
Now, we will find out how many milliliters of lemon juice and water did he pour into the pitcher in all.
So, the values are 2liters and 500 milliliters.
Convert the given liters value into milliliters value.
We know that 1 liter = 1000 millimeters.
Then 2 liters = 2 x 1000 millimeters = 2000 milliliters.
Now, add water and lemon juice then
2000 milliliters + 500 milliliters = 2500 milliliters.
Therefore, Javier poured 2500 milliliters of lemon juice and water into the pitcher.
Talk Math
Explain how you can check your answer for Exercise 1.
Answer: Using multiplication we can check the answer for Exercise 1.
Guided Practice
Question 1.
Evelyn is in a relay race with three other runners. Each runner runs 0.1 kilometers. What is the total distance run by all four runners? Use the number line.
Answer: The total distance run by all four runners is 0.4 kilometers.
Explanation: Given that,
Evelyn is in a relay race with three other runners.
Each runner runs 0.1 kilometers.
Now, find the total distance run by all four runners using the number line.
So, the value is 0.1 and 4
Either we can add or multiply we get the value.
Using a number line, we can add 0.1, 4 times we get
0.1 + 0.1 + 0.1 + 0.1 = 0.4
(or)
Multiply 0.1 x 4 = 0.4
Therefore, the total distance run by all runners is 0.4 kilometers.
Question 2.
A bag of potatoes has a mass of 4 kilograms. Some potatoes are taken out. The mass is now 2,305 grams. What is the mass of the potatoes in grams that were taken out of the bag?
Answer: So, the mass of the potatoes in grams that were taken out of the bag is 1695 grams.
Explanation: Given that, the data is
A bag of potatoes has a mass of 4 kilograms.
Some potatoes are taken out then the mass is now 2,305 grams.
Now, we need to find the mass of the potatoes in grams that were taken out of the bag.
First, convert the value of the given kilogram into grams.
We know that 1 kilogram = 1000 grams.
So, 4 kilograms = 4 x 1000 grams = 4000 grams.
Next, After some potatoes are taken out then the mass is 2305 grams.
Now, subtract 4000 – 2305 = 1695.
Hence, the taken-out potatoes’ mass is 1695 grams.
Independent Practice
Question 3.
A ribbon is 1 meter long. Keira cut a piece of the ribbon. The piece she cut is 0.4 meters long. How long is the other piece? Use the number line.
Answer: 0.6 meters long is the other piece.
Explanation: As given in the question,
A ribbon is 1 meter long. Keira cut a piece of the ribbon.
The piece she cut is 0.4 meters long.
Now, we will find the length of the other piece using the number line.
So, the given values are 1 meter and 0.4 meters.
We can remove 0.4 meters from 1 meter.
Then it is 1 meter – 0.4 meter = 0.6 meters.
Hence, the length of the other piece is 0.6 meters.
Question 4.
There are two books. Each has a mass of 0.4 kilograms. What is the total mass of the two books? Use the number line.
The total mass is ________________.
Answer: The total mass of the two books is 0.8 kilograms.
Explanation: Given that,
There are two books. Each has a mass of 0.4 kilograms.
Now, we will find the total mass of the two books using the number line.
So, the mass of one book is 0.4 kilograms.
The mass of 2 books is 0.4 kg + 0.4 kg = 0.8 kilograms.
Thus, the mass of the two books is 0.8 kilograms.
Convert to solve each problem. Draw a number line if needed.
Question 5.
One insect is 47 millimeters long. Another insect is 3 centimeters long. What is the total length in millimeters of the insects?
Answer: The total length in millimeters of the insects is 77 millimeters.
Explanation: Given that, the data is
One insect is 47 millimeters long.
Another insect is 3 centimeters long.
Now, we will find the total length in millimeters of the insects.
First, convert the value of the given centimeters into millimeters.
We know that 1 centimeter = 10 millimeters.
So, 3 centimeters = 3 x 10 millimeters = 30 millimeters.
Now, Add the two insects’ lengths
i.e., 47 millimeters + 30 millimeters = 77 mm.
Therefore, the total length of insects in millimeters is 77 millimeters.
Question 6.
A table has a mass of 7 kilograms. A chair has a mass of 4,048 grams, What is the total mass in grams of the table and the chair?
Answer: The total mass in grams of the table and the chair is 11048 grams.
Explanation: Given that, the data is
A table has a mass of 7 kilograms.
A chair has a mass of 4,048 grams.
Now, we need to find the total mass in grams of the table and the chair.
First, convert the value of the given kilograms into grams
We know that 1 kilogram = 1000 grams.
So, 7 kilograms = 7 x 1000 grams = 7000 grams.
Now, Add the mass of the table and chair.
i.e., 7000 g + 4048 g = 11048 grams.
Therefore, the total mass of the chair and table in grams is 11048 grams.
Problem Solving
Question 7.
Cole has a plastic cup that has 125 milliliters of water in it. He drinks 37 milliliters of water. How much water is left in the cup?
Answer: 88 milliliters of water are left in the cup.
Explanation: Given that,
Cole has a plastic cup that has 125 milliliters of water in it.
He drinks 37 milliliters of water.
Now, we will find the left of the water in the cup.
So, the values are 125 milliliters and 37 milliliters.
Remove the drinking water from the cup of water.
i.e., 125 ml – 37 ml = 88ml.
Therefore, the water left in the cup is 88 ml.
Question 8.
Mathematical PRACTICE Justify Conclusions Sam had 0.3 of a dollar. Then he found four nickels and a penny. Does he have enough money to buy something that costs 50¢? Explain.
Answer: yes, sam has enough by 1 penny.
Explanation: As given in the question,
Sam had 0.3 of a dollar.
Then he found four nickels and a penny.
Now, we will find out his money is enough or not to buy something that costs 50¢.
So, the money is $0.3, 4 nickels, one penny.
i.e., 0.3 + 0.20 + 0.01 = 0.51 (or) 51 cents.
Hence, yes sam has enough by 1 penny.
Question 9.
Each sports bag can hold 6 kilograms of equipment. The golf balls have a total mass of 3,402 grams. The hockey pucks have a total mass of 2,932 grams. How many sports bags will be needed to hold the equipment? Explain.
Answer: 2 sports bags will be needed to hold the Equipment. Because 334 grams will be extra grams.
Explanation: Given that,
Each sports bag can hold 6 kilograms of equipment.
The golf balls have a total mass of 3,402 grams.
The hockey pucks have a total mass of 2,932 grams.
Now, we will find out how many sports bags will be needed to hold the equipment.
The total weight of golf balls and hockey pucks is,
3402 grams + 2932 grams = 6334.
Therefore, 334 grams is extra we need two bags.
HOT Problems
Question 10.
Mathematical PRACTICE Use Symbols Compare. Write <, >, or =.
3 L + 2,492 mL 
2 L + 1,301 mL + 2,191 mL
Answer: The symbol = (Equal to) is used in between the given values.
Explanation: Given the values are,
3L + 2492 mL and 2L+1301 mL +2191 mL.
Now, we can add the values. Before that convert the liters into milliliters.
We know that 1 liter = 1000 milliliters.
So, the value is 3L = 3 x 1000 = 3000 mL and 2L = 2 x 1000 = 2000 mL.
i.e., 3000 + 2492 =5492 mL.
Next, the value is 2000 + 1301 + 2191 = 5492 mL
Therefore, both values are equal. So, we can use the Equal symbol.
Question 11.
Building on the Essential Question How do I know when it is necessary to convert units before solving a problem?
Answer: It is necessary to convert units before solving a problem when
1. Incompatible systems are involved, such as English versus metric units
2. Units are given which will not produce the desired result (such as the amount of water needed to cover one acre of land)
3. When the problem statement requires certain units.
McGraw Hill My Math Grade 4 Chapter 12 Lesson 6 My Homework Answer Key
Practice
Question 1.
Chloe buys 3 jars of peanut butter for the food drive. Each jar has a mass of 0.2 kilograms. What is the mass of all 3 jars of peanut butter? Use the number line.
Answer: Using a number line, the mass of all 3 jars of peanut butter is 0.6 kilograms.
Explanation: Given that,
Chloe buys 3 jars of peanut butter for the food drive.
Each jar has a mass of 0.2 kilograms.
Now, we will find the mass of all 3 jars of peanut butter using the given number line.
So, the mass of one jar is 0.2kg.
The mass of 3 jars is 3 x 0.2 kg = 0.6 kg.
Therefore, the mass of all 3 jars of peanut butter is 0.6 kilograms.
Problem Solving
Question 2.
Aidan mixes 630 milliliters of blue paint with 2 liters of red paint to make purple paint. How many milliliters of purple paint does Aidan have?
Answer: Aidan has 2630 milliliters of purple paint.
Explanation: Given that,
Aidan mixes 630 milliliters of blue paint with 2 liters of red paint to make purple paint.
Now, we will find out how many milliliters of purple paint Aidan have.
So, the values are 2liters and 630 milliliters.
Convert the given liters value into milliliters value.
We know that 1 liter = 1000 milliliters.
Then 2 liters = 2 x 1000 millimeters = 2000 milliliters.
Now, add blue paint and red paint then
2000 milliliters + 630 milliliters = 2630 milliliters.
Therefore, after mixing the purple paint is 2630 milliliters.
Question 3.
Celine is knitting a scarf. The finished length will be 1.2 meters. So far she has knitted 0.8 meters. How many more meters does Celine need to knit? Draw a number line to solve.
Answer: The number line of a given problem is below,
i.e., 1.2 meters – 0.8 meters = 0.4 meters.
Celine needed to knit 0.4 meters.
Explanation: Given that,
Celine is knitting a scarf.
The finished length will be 1.2 meters. So far she has knitted 0.8 meters.
Now, we will find out how many more meters Celine needs to knit and draw a number line to solve.
So, the values are 1.2 meters and 0.8 meters.
Subtract the 0.8 meters from 1.2 meters.
i.e., 1.2 – 0.8 = 0.4 meters.
Hence, Celine needed to knit 0.4 meters.
Question 4.
Joanie’s bag of trail mix has a mass of 0.75 kilograms. She and some friends eat 0.5 kilograms of the mix. How many kilograms of trail mix are left? Draw a number line to solve.
Answer: The number line is below,
i.e., 0.75 – 0.5 = 0.25.
So, 0.25 kilograms of trail mix is left.
Explanation: Given that,
Joanie’s bag of trail mix has a mass of 0.75 kilograms.
She and some friends eat 0.5 kilograms of the mix.
Now, we will find out how many kilograms of trail mix is left and draw a number line to solve.
So, the values are 0.75 and 0.5.
Subtract 0.75 – 0.5 = 0.25.
Therefore, 0.25 kilograms of trail mix is left.
Question 5.
Mathematical PRACTICE Use Math Tools Ross found 5 ladybugs. Each is 0.8 centimeters long. If he lays the ladybugs in a row, what is the total length in millimeters?
Answer: If he lays the ladybugs in a row, the total length in millimeters is 40mm.
Explanation: Given that,
Ross found 5 ladybugs. Each is 0.8 centimeters long.
Now, we will find the total length, If he lays the ladybugs in a row.
So, the values are 5 and 0.8.
First, convert the centimeter value into millimeters.
we know that 1 cm = 10 millimeters.
i.e., 0.8 cm = 0.8 x 10mm = 8mm.
Now, the total length of the row in millimeters is,
5 x 8 mm = 40mm.
Question 6.
Lucas is riding his bike to the park which is 2 kilometers from his house. When he is one-fourth of the way to the park, it starts to rain. Lucas turns around and rides back home. How many meters did Lucas ride?
Answer: Lucas ride 1000 meters.
Explanation: Given that,
Lucas is riding his bike to the park which is 2 kilometers from his house.
When he is one-fourth of the way to the park, it starts to rain.
Lucas turns around and rides back home.
Now, we will find out how many meters Lucas rode.
First, convert the given kilometers value into meters.
We know that 1 kilometer = 1000 meters.
So, 2 kilometers = 2000 meters.
One-fourth of 2000 meters is 500 meters.
i.e., (1/4) x (2000) = 2000/4 = 500.
So, he rides 500 meters and turns to back then the distance is another 500 meters.
Therefore, Lucas ride 500 + 500 = 1000meters.
Test Practice
Question 7.
Grayson stacked 17 kilograms of firewood on Saturday and 15 kilograms of firewood on Sunday. How many more grams of firewood did he stack on Saturday?
(A) 2,000 grams
(B) 3,200 grams
(C) 20,000 grams
(D) 32,000 grams
Answer: Option A
Explanation: Given that,
Grayson stacked 17 kilograms of firewood on Saturday and 15 kilograms of firewood on Sunday.
Now, we will find out how many more grams of firewood did he stack on Saturday.
So, the values are 17 kilograms and 15 kilograms.
We want more grams of firewood, he stacks on Saturday.
Subtract Sunday firewood from Saturday firewood, we get the value.
i.e., 17 kilograms – 15 kilograms = 2 kilograms.
The value in grams is 2 kilograms = 2 x 1000 = 2000 grams.
Hence, option A is correct.