We included **H****MH Into Math Grade 6 Answer Key**** PDF** **Module 6 Lesson 3 Use Rate Reasoning to Convert Between Measurement Systems** to make students experts in learning maths.

## HMH Into Math Grade 6 Module 6 Lesson 3 Answer Key Use Rate Reasoning to Convert Between Measurement Systems

I Can write and use equivalent rates or conversion factors to convert units between measurement systems.

**Spark Your Learning**

At Winnie’s restaurant, one serving of chicken soup is 1\(\frac{1}{2}\) cups. The chef makes 48 cups of soup each night. How many servings of chicken soup are in 48 cups? Explain how you know.

Answer:

Explanation:

Given at Winnie’s restaurant, one serving of chicken soup is

1\(\frac{1}{2}\) cups. The chef makes 48 cups of

soup each night. Number of servings of chicken soup are in 48 cups are

\(\frac{1 X 2 + 1}{2}\) X 48 =

\(\frac{3}{2}\) X 48 = 72 servings.

**Turn and Talk** How is dividing fractions related to multiplying fractions?

Answer:

Dividing two fractions is the same as multiplying the

first fraction by the reciprocal of the second fraction.

Explanation:

Dividing two fractions is the same as multiplying the

first fraction by the reciprocal of the second fraction.

The first step to dividing fractions is to find the reciprocal

(reverse the numerator and denominator) of the second fraction.

Next, multiply the two numerators or When dividing the fraction,

the operation will be change into multiplication after

reciprocating the second term.

**Build Understanding**

Many countries use only the metric system of measurement. In the United States, however, we use measurements in both metric units and customary units. Sometimes we need to convert between the two systems.

The table below shows equivalences between customary and metric systems. You can use these equivalences to convert a measurement in one system to a measurement in the other system.

The systems are not related so the conversions are approximate, as indicated by the symbol ≈.

1. Daniel is 6 feet tall. He wants to know how tall he is in meters.

A. One way to solve this problem is to use a bar diagram. Each part represents 1 foot.

1 foot ≈ ______

Answer:

1 foot ≈ 0.305 m,

Explanation:

Given Daniel is 6 feet tall. He wants to know how tall he is in meters.

A. One way to solve this problem is to using a bar diagram.

Each part represents 1 foot 1 foot ≈ 0.305 m

B. How does the diagram help you solve the problem?

____________________

____________________

Answer:

The diagram shows easy representation,

Explanation:

The diagram help us to solve the Daniel given height in feet to meters.

C. You could also use a unit rate as the conversion factor.

Answer:

Explanation:

Given to use rate as the conversion factor as

\(\frac{0.305 m}{1 ft}\) X 6 ft = 1.83 m.

D. There is about meter in 1 foot. There are about meters in 6 feet.

Answer:

0.305 meter, 1.83 meters,

Explanation:

There is about 0.305 meter in 1 foot,

There are about 1.83 meters in 6 feet.

**Turn and Talk** How would the steps to solve the problem be different if you converted a metric height to feet? Explain.

Answer:

There are 3.28084 feet in 1 meter.

Explanation:

To convert meters to feet, multiply your meters figure by 3.28.

feet = meters × 3.28084,

As an example, let’s say you have 5m of wrapping paper on a roll.

If we want to know how many feet it measures,

My calculation will be: 5 × 3.28084 = 16.404 ft.

**Step It Out**

2. In the metric system, 1 gram is the mass of 1 milliliter of water. So, a 2-liter bottle of water has a mass of 2 kilograms. A gallon of water weighs about 8 pounds. What is the mass of a gallon of water to the nearest tenth of a kilogram?

Method 1: Solve using equivalent rates.

A. The first rate is the conversion factor, which is found in the table.

Answer:

\(\frac{1 lb}{0.454 kg}\),

Explanation:

The first rate is the conversion factor is

\(\frac{1 lb}{0.454 kg}\).

B. The second rate relates the known amount to the unknown converted amount.

Answer:

\(\frac{8 lb}{x kg}\),

Explanation:

The second rate relates the known amount to the unknown

converted amount is \(\frac{8 lb}{x kg}\).

C. Set the rates equal to one another.

Answer:

\(\frac{1 lb}{0.454 kg}\) = \(\frac{8 lb}{x kg}\),

Explanation:

The rates equal to one another is

\(\frac{1 lb}{0.454 kg}\) = \(\frac{8 lb}{x kg}\).

D. Multiply both parts of the left rate by a number that will make the number of pounds in the two rates the same.

Answer:

Explanation:

Multiplied both parts of the left rate by a number that

will make the number of pounds in the two rates the same.

Method 2: Solve using the conversion factor.

A. Write the conversion factor as a rate.

Answer:

\(\frac{0.454 kg}{1 lb}\),

Explanation:

The conversion factor is \(\frac{0.454 kg}{1 lb}\).

B. Multiply 8 pounds by the conversion factor. Round the result.

Answer:

,

Explanation:

Multiplied 8 pounds by the conversion factor,

rounded the result as 3.632 kg.

C. Notice _____ the units cancel, resulting in an answer given in ___.

Answer:

Pounds, Kg,

Explanation:

Notices pounds lb the units cancel,

resulting in an answer given in kg.

D. When you choose a conversion factor, the unit you are converting to is the (first / second) quantity in the rate.

Answer:

First,

Explanation:

When I choose conversion factor, the unit

I am converting to is the first quantity in the rate.

**Turn and Talk** Which method is easier to use, equivalent rates method or the conversion method? Explain.

Answer:

Equivalent rates,

Explanation:

When a conversion is necessary, the appropriate conversion

factor to an equal value must be used. For example,

to convert inches to feet, the appropriate conversion

value is 12 inches equal 1 foot. To convert minutes to hours,

the appropriate conversion value is 60 minutes equal 1 hour.

3. Many water bottles contain 16 fluid ounces, or 1 pint, of water. Drink labels often show the number of fluid ounces and the number of milliliters in a container. How many milliliters are in a 16-fluid-ounce drink?

Solve using equivalent rates.

A. One rate is the conversion factor.

Answer:

\(\frac{29.6 ml}{1 fl oz}\),

Explanation:

As 1 fl oz is 29.6 ml so it is

\(\frac{29.6 ml}{1 fl oz}\).

B. The other rate relates the known amount to the unknown converted amount.

Answer:

\(\frac{x ml}{16 fl oz}\),

Explanation:

The other rate relates the known amount to the

unknown converted amount is \(\frac{x ml}{16 fl oz}\).

C. Set the rates equal to one another.

Explanation:

\(\frac{29.6 ml}{1 fl oz}\) = \(\frac{x ml}{16 fl oz}\),

Explanation:

Setted the rates equal to one another as

\(\frac{29.6 ml}{1 fl oz}\) = \(\frac{x ml}{16 fl oz}\).

D. Multiply both parts of the left rate by a number that will make the number of fluid ounces in the two rates the same.

There are about milliliters in 16 fluid ounces.

Answer:

There are about 473.6 milliliters in 16 fluid ounces,

Explanation:

Multiplying both parts of the left rate by a number

that will make the number of fluid ounces in the

two rates the same we get about 473.6 milliliters in 16 fluid ounces.

**Turn and Talk** When converting units using equivalent rates, does it matter which unit is in the numerator? Explain.

Answer:

Yes,

Explanation:

The centimeters in the numerator of the conversion factor

become the units of the final answer. Because the numerator and

denominator of a conversion factor are equal,

multiplying any quantity by a conversion factor is

equivalent to multiplying by the number 1 and

so does not change the intrinsic value of the quantity.

**Check Understanding**

Question 1.

Robert enters a race. The race is 10 kilometers long, but he is more familiar with miles than kilometers. How many miles are in 10 kilometers to the nearest tenth of a mile?

____________________

Answer:

6.2 miles,

Explanation:

Given Robert enters a race. The race is 10 kilometers long,

but he is more familiar with miles than kilometers.

Number of miles are in 10 kilometers to the nearest tenth of a mile are

as 1 kilometer is 0.62 mile so 10 kilometers is equal to

10 X 0.62 miles = 6.2 miles.

Question 2.

Scott is 72 inches tall and Chris is 185 centimeters tall. Who is taller? Show your work.

____________________

Answer:

Chris is taller,

Explanation:

Given Scott is 72 inches tall and Chris is 185 centimeters tall.

The taller among them are as 1 inch is equal to 2.54 cms

so Scott is 72 X 2.54 = 182.88 centimeters now comapring

Scott and Chris as 182.88 is smaller than 185 cms, So

Chris is taller.

**On Your Own**

Question 3.

**Reason** Kathy is following a recipe for punch that calls for 3 liters of juice. She has 3 quarts of juice. Without using an equation, does Kathy have enough juice for the punch? Explain.

____________________

Answer:

No, Kathy have not enough juice for the punch,

Explanation:

Given Kathy is following a recipe for punch that

calls for 3 liters of juice. She has 3 quarts of juice.

Without using an equation, No, Kathy have not

enough juice for the punch as 3 quarts of juice is equal to

2.83 lts which is less than 3 liters.

Question 4.

Simon measures the length of an insect that is 2.5 inches long for a science project. He needs to record his data in centimeters. How long is the insect in centimeters?

____________________

Answer:

6.35 centimeters,

Explanation:

Given Simon measures the length of an insect that is 2.5 inches

long for a science project. He needs to record his data in centimeters.

So long is the insect in centimeters is as 1 inch = 2.54 centimeters,

theerfore it is 2.5 X 2.54 centimeters = 6.35 centimeters.

Question 5.

An Olympic-size swimming pool is 50 meters long. How many yards long is the pool, to the nearest tenth of a yard?

____________________

Answer:

54.65 or 55 yards long,

Explanation:

Given an Olympic-size swimming pool is 50 meters long.

Number of many yards long is the pool

to the nearest tenth of a yard is as 1 meter = 1.09361 yards,

So 50 meters = 50 X 1.093 yards = 54.65 yards approximately

equal to 55 yards long.

Question 6.

How many kilograms are in 1 ton, or 2,000 pounds?

____________________

Answer:

1,000 kilograms,

Explanation:

Number of kilograms are in 1 ton or 2,000 pounds is

1 ton = 1,000 kilograms.

Question 7.

Many newborn babies have a mass between 2,500 grams and 4,000 grams. How many pounds does a 2,500-gram baby weigh, to the nearest tenth of a pound?

[16 ounces = 1 pound] Show your work.

Answer:

5.5 pounds,

Explanation:

Given many newborn babies have a mass between 2,500 grams and

4,000 grams. How many pounds does a 2,500-gram baby weigh,

to the nearest tenth of a pound as 1 gram = 0.0022 pounds,

So 2,500 X 0.0022 pounds = 5.5 pounds.

Question 8.

Shane is following an English recipe for scones. The recipe calls for 1.2 kilograms of flour. How many pounds of flour, to the nearest tenth of a pound, does he need?

Answer:

2.6448 pounds of flour,

Explanation:

Given Shane is following an English recipe for scones.

The recipe calls for 1.2 kilograms of flour. Number of

pounds of flour, to the nearest tenth of a pound, does he need is

as 1 kilogram = 2.204 pound So 1.2 kilogram = 1.2 X 2.204 pounds =

2.6448 pounds of flour.

**For Problems 9-14, convert the units to the nearest tenth.**

Question 9.

10 feet ≈ ___ meters

Answer:

3 meters,

Explanation:

As 1 feet = 0.3048 meter, so given to find 10 feet =

10 X 0.3048 meters = 3.048 meters ≈ 3 meters.

Question 10.

____ yards ≈ 25 meters

Answer:

27 meters,

Explanation:

As 1 meter = 1.09361 yard, so given to find 25 meters =

25 X 1.09361 = 27.34025 ≈ 27 meters.

Question 11.

____ kilometers ≈ 50 miles

Answer:

80.45 kilometers ≈ 80 kilometers,

Explanation:

As 1 mile = 1.609 kilometer, so given to find 50 miles =

50 X 1.609 kilometer = 80.45 kilometers ≈ 80 kilometers.

Question 12.

____ grams ≈ 10 ounces

Answer:

283.49 grams ≈ 283 grams,

Explanation:

As 1 ounce = 28.349 grams, so given to find 10 ounces =

10 X 28.349 grams = 283.49 grams ≈ 283 grams.

Question 13.

8 fluid ounces ≈ ___ milliliters

Answer:

236.56 milliliters ≈ 237 milliliters,

Explanation:

As 1 fluid ounce = 29.57 milliliters, so given to find 8 fluid ounces =

8 X 29.57 milliliters = 236.56 milliliters ≈ 237 milliliters.

Question 14.

6 inches = ___ centimeters

Answer

15.24 centimeters ≈ 15 centimeters,

Explanation:

As 1 inch = 2.54 centimeters, so given to find 6 inches =

6 X 2.54 centimeters = 15.24 centimeters ≈ 15 centimeters.

Question 15.

Which distance is longer, 500 kilometers or 250 miles? Explain.

Answer:

500 kilometers,

Explanation:

Given to find distance longer in between

500 kilometers or 250 miles as 1 mile = 1.609 kilometers,

So 250 miles = 250 X 1.609 kilometers = 402.25 kilometers,

As 500 kilometers is greater than 402.25 kilometers so

500 kilometers is greater.

Question 16.

The tank of a car holds 10 gallons of gas. How many liters does the tank hold?

____________________

Answer:

37.84 liters or approximately 38 liters of gas,

Explanation:

As 1 gallon = 3.784 liter, so given to find 10 gallons =

10 X 3.784 liters =37.84 liters ≈ 38 liters of gas.

Question 17.

Wendy drives a car 110 kilometers per hour. What is this rate, in miles per hour, to the nearest tenth?

Answer:

68.31 miles per hour or 68 miles per hour,

Explanation:

Given Wendy drives a car 110 kilometers per hour.

Miles per hour as1 kilometer = 0.621 miles,

So Wendy drives 110 X 0.621 miles per hour =

68.31 miles per hour or 68 miles per hour.

Question 18.

Jim sits on a seesaw. If Jim weighs loo pounds. what mass in kilograms does the person on the other side need to be for the seesaw to be balanced?

____________________

Answer:

The person on the other side need to be 45.3 kilograms,

Explanation:

Given Jim sits on a seesaw. If Jim weighs 100 pounds.

Mass in kilograms does the person on the other side need

to be for the seesaw to be balanced as 1 pound = 0.453 kilogram

so it is 100 X 0.453 kilogram = 45.3 kilograms.

Question 19.

Caitlyn is 160 centimeters tall. How tall is she in feet and inches, rounded to the nearest inch?

____________________

Answer:

5.12 feet or nearly 5 feet and

62.88 inches ≈ 63 inches,

Explanation:

Given Caitlyn is 160 centimeters tall.

She in feet tall is as 1 cm = 0.032 foot,

160 X 0.032 foot = 5.12 feet or nearly 5 feet and

1 cm = 0.393 inch, so 160 X 0.393 inch = 62.88 inches

approximately 63 inches.

**For Problems 20—25, compare the measurements using <, =, or>.**

Question 20.

2 meters 7 feet

Answer:

2 meters < 7 feet,

Explanation:

As 1 meter = 3.28 feet, so 2 meters = 6.56 feet,

now comparing 2 meter is less than 7 feet, so

2 meters < 7 feet.

Question 21.

50 pounds 25 kilograms

Answer:

50 pounds < 25 kilograms,

Explanation:

As 1 pound = 0.453 kilogram,

So 50 pounds = 22.65 kilograms,

now comparing as 22.65 kilograms is less than 25 kilograms,

so 50 pounds < 25 kilograms.

Question 22.

100 inches 254 centimeters

Answer:

100 inches = 254 centimeters

Explanation:

As 1 inch = 2.54 centimeters,

So 100 inches = 100 X 2.54 centimeters = 254 centimeters,

now comparing as 254 centimeters is equal to 254 centimeters,

so 100 inches = 254 centimeters.

Question 23.

10 miles 6.2 kilometers

Answer:

10 miles > 6.2 kilometers,

Explanation:

As 1 mile = 1.609 kilometers,

So 10 miles = 10 X 1.609 kilometers = 16.09 kilometers,

now comparing as 16.09 kilometers is greater than 6.2 kilometers,

so 10 miles > 6.2 kilometers.

Question 24.

6 liters 2 gallons

Answer:

6 liters < 2 gallons,

Explanation:

As 1 liters = 0.264 gallon,

So 6 liters = 6 X 0.264 gallons = 1.584 gallons,

now comparing as 1.584 gallons is less than 2 gallons,

so 6 liters < 2 gallons.

Question 25.

24 ounces 600 grams

Answer:

24 ounces < 600 grams,

Explanation:

As 1 ounces = 24.3495 grams,

So 24 ounces = 24 X 24.3495 grams = 584.388 grams,

now comparing as 584.388 grams is less than 600 grams,

so 24 ounces < 600 grams.

**I’m in a Learning Mindset!**

What types of decisions did I make when solving Problem 8? Which strategy did I use?

_______________________

_______________________

Answer:

Conversion methods,

Multiplication,

Explanation:

Divide the number of pounds by 2.2046 to use the standard equation.

Given Shane is following an English recipe for scones.

The recipe calls for 1.2 kilograms of flour. Number of

pounds of flour, to the nearest tenth of a pound, does he need is

as 1 kilogram = 2.204 pound So 1.2 kilogram = 1.2 X 2.204 pounds =

2.6448 pounds of flour.

**Lesson 6.3 More Practice/Homework**

**Use Rate Reasoning to Convert Between Measurement Systems**

Question 1.

**Reason** An elevator can hold at most 2,500 pounds. If 10 adults with an average mass of 80 kilograms each get on the elevator, can the elevator carry them? Show your work.

Answer:

Yes, the elevator can carry them.

Explanation:

Given an elevator can hold at most 2,500 pounds.

If 10 adults with an average mass of 80 kilograms

each get on the elevator, So 10 X 80 kilograms = 800 kilograms,

As 1 kg = 2.204 pounds means 800 X 2.204 pounds =

1,763.2 pounds as 1,763.2 is less than 2,500 pounds

the elevator can carry them.

Question 2.

**Math on the Spot** Find the weight, in pounds, of the dog shown. Round to the nearest tenth.

Answer:

11.88 pounds nearer to 12 pounds,

Explanation:

To find the weight in pounds of the dog,

given dog with mass 5,400 grams as 1 gram =

0.0022 pounds, So pounds of dog is 5,400 X 0.0022 pounds =

11.88 pounds nearer to 12 pounds.

Question 3.

**Critique Reasoning** Dwayne estimated his mass as 6 kilograms. Is his estimate reasonable? Explain your answer.

Answer:

Not reasonable,

Explanation:

Generally an adult body weight will be roughly

60 to 70 kilograms but it is estimated 6 kilograms,

So his estimate is not reasonable as

6 kilograms is very less than 60 to 70 kilograms.

Question 4.

In 2004, Kenenisa Bekele of Ethiopia ran 5,000 meters (5 kilometers) in 12 minutes, 37.35 seconds. What is this distance to the nearest tenth of a mile?

____________________

Answer:

3.105 miles or 3 miles,

Explanation:

Given in 2004, Kenenisa Bekele of Ethiopia ran 5,000 meters

(5 kilometers) in 12 minutes, 37.35 seconds.

This distance to the nearest tenth of a mile is as

1 kilometer = 0.621 mile so 5 kilometers is equal to

5 X 0.621 mile = 3.105 miles or 3 miles.

Question 5.

Sprinters who run 100 yards now often run 100 meters. How many meters longer to the nearest tenth is 100 meters than 100 yards?

____________________

Answer:

8.56 meters more approximately 9 meters more is

100 meters than 100 yards,

Explanation:

Given Sprinters who run 100 yards now often run 100 meters.

Number of meters longer to the nearest tenth is

100 meters than 100 yards as 1 yard is equal to 0.9144 meter,

So 100 yards = 100 X 0.9144 meters = 91.44 meters more is

100 meters – 91.44 meters = 8.56 meters more approximately

9 meters more.

Question 6.

**Health and Fitness** The average adult has 1.2 to 1.5 gallons of blood in their body. How much blood does the average adult have in liters? Round your answer to the nearest tenth liter.

____________________

Answer:

Nearly 5 liters to 7 liters of blood,

Explanation:

As the average adult has 1.2 to 1.5 gallons of blood in their body.

The blood does the average adult have in liters are as

1 gallon = 4.546 liters, So 1.2 gallons = 1.2 X 4.546 liters =

5.4552 litersapproximately 5 liters to 1.5 gallons =

1.5 X 4.546 liters = 6.819 liters approximately 7 liters.

**For Problems 7—12. convert to the unit indicated in parentheses. Then compare the measurements using <, =, or >. (Round to nearest tenth if necessary.)**

Question 7.

100 inches 250 centimeters; (centimeters)

Answer:

100 inches < 250 centimeters

Explanation:

As 1 inch = 2.54 centimeters,

So 100 inches = 100 X 2.54 centimeters = 254 centimeters,

now comparing as 254 centimeters is less than 250 centimeters,

so 100 inches < 250 centimeters.

Question 8.

4 pounds 2 kilograms; (pounds)

Answer:

4 pounds < 2 kilograms,

Explanation:

As 1 kilogram = 2.204 pounds,

So 2 kilograms = 2 X 2.204 pounds = 4.408 pounds,

now comparing as 4 pounds is less than 4.408 pounds,

so 4 pounds < 2 kilograms.

Question 9.

3 miles 5 kilometers; (miles)

Answer:

3 miles < 5 kilometers,

Explanation:

As 1 kilometer = 0.621 miles,

So 5 kilometers = 5 X 0.621 miles = 3.105 miles,

now comparing as 3 miles < is less than 3.105 miles,

so 3 miles < 5 kilometers.

Question 10.

5 feet 2 meters; (meters)

Answer:

5 feet < 2 meters,

Explanation:

As 1 foot = 0.3048 meters, so 5 feet = 1.524 meters ,

now comparing 1.524 meters is less than 2 meters, so

5 feet < 2 meters.

Question 11.

5 liters 5 quart; (liters)

Answer:

5 liters > 5 quart,

Explanation:

As 1 quart = 0.946 liter, so 5 quart = 5 X 0.946 liter =

4.73 liters now comparing 5 liters is greater than 4.73 liters,

so 5 liters > 5 quart.

Question 12.

6 inches 15.24 centimeters; (centimeters)

Answer:

6 inches = 15.24 centimeters,

Explanation:

As 1 inch = 2.54 centimeters, so 6 inches = 6 X 2.54 centimeters =

15.24 centimeters now comparing 15.24 is equal to 15.24 centimeters,

So 6 inches = 15.24 centimeters.

**Test Prep**

Question 13.

Write the following measurements in order from least to greatest: 600 centimeters, 200 inches, 4 meters, 10 feet.

____________________

Answer:

10 feet, 4 meters, 200 inches and 600 centimeters,

Explanation:

Given the measurements in order from least to greatest:

600 centimeters,

200 inches, as 1 inch = 2.54 cm, So 200 inches = 508 centimeters,

4 meters as 1 meter = 100 cm, so 4 meters = 4 X 100 = 400 centimeters,

10 feet as 1 feet = 30.48 cm, so 10 feet = 10 X 30.48 cm =

304. 8 centimeters, Now checking as

304.8 cm < 400 cm < 508 cm < 600 cm, therefore order is

10 feet, 4 meters, 200 inches and 600 centimeters.

Question 14.

About how many kilograms are in 2,000 pounds (1 ton)?

A. 90.8 kilograms

B. 440.5 kilograms

C. 908 kilograms

D. 4,405 kilograms

Answer:

C. 908 kilograms,

Explanation:

Number of kilograms are in 2,000 pounds are

as 1 pound = 0.453592 kilograms so 2,000 X 0.453592 kilograms =

907.184 kilograms nearly 908 kilograms which matches

with bit C.

Question 15.

Which rate gives the lower unit price, $4.89 per kilogram or $4.89 per pound? Justify your answer.

Answer:

The lower unit price is $4.89 per pound.

Explanation:

Given to compare rate that gives lower unit price between

$4.89 per kilogram or $4.89 per pound as

1 pound = 0.453592 kilograms so $4.89 X 0.453592 kilograms =

2.218 kilograms, therefore the lower unit price is

$4.89 per pound.

Question 16.

Match each measurement on the left with the measurement that it is closest to on the right.

Answer:

Explanation:

Matched each measurement on the left with the

measurement that it is closest to on the right as

1 inch = 2.54 cm,

So 6 in = 6 X 2.54 cm = 15.24 cm,

1 cm = 0.393701 inch,

So 10 cm = 10 X 0.393701 inch = 3.93701 inch approximately 3.94 inch,

8 cm = 8 X 0.393701 inch = 3.149608 inch approximately 3.15 inch and

2 in = 2 X 2.54 cm = 5.08 cm respectively.

**Spiral Review**

Question 17.

Write three equivalent ratios to the ratio described by the given situation. The ratio of 3 red marbles for every 2 blue marbles.

Answer:

30:20,

6:4,

9:6,

Explanation:

Asking for equivalent ratios to the ratio described by

the given situation. The ratio of 3 red marbles for

every 2 blue marbles is 3: 2 so the ratios equivalent

are 30:20, 6:4, 9:6 as we get 30 : 20 when divided by 10

we get= 3:2 , when 6: 4 is divided by 2 we get 3:2 and

when 9:6 divided by 3 we get 3:2, therefore ratio of

3 red marbles for every 2 blue marbles equivalent is 30:20, 6:4, 9:6.

Question 18.

A wall is 4\(\frac{1}{2}\) feet long and has an area of 15\(\frac{3}{4}\) square feet. What is its height in feet?

____________________

Answer:

Explanation:

Given a wall is 4\(\frac{1}{2}\) feet long and

has an area of 15\(\frac{3}{4}\) square feet.

So its height in feet is 15\(\frac{3}{4}\) square feet ÷

4\(\frac{1}{2}\) feet = \(\frac{15 X 4 + 3}{4}\) feet ÷

\(\frac{4 X 2 + 1}{2}\) feet = \(\frac{63}{4}\) X

\(\frac{2}{9}\) = \(\frac{63 X 2}{4 X 9}\) =

\(\frac{7}{2}\) as numerator is greater than denominator

we write in mixed fraction as 3\(\frac{1}{2}\).

Question 19.

Adam runs 6.75 kilometers each day for 4 days. On the fifth day, he runs 9.5 kilometers. How many kilometers has he run altogether?

____________________

Answer:

Altogether Adam has ran 36.5 kilometers,

Explanation:

Given Adam runs 6.75 kilometers each day for 4 days.

On the fifth day, he runs 9.5 kilometers.

Number of kilometers has he run altogether is

6.75 kilometers X 4 + 9.5 kilometers = 36.5 kilometers or

6.75 kilometers + 6.75 kilometers + 6.75 kilometers +

6.75 kilometers + 9.5 kilometers = 36.5 kilometers.