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# 7.7: Converting Customary Units

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## Introduction

The Amazon

Jacob is in Julie’s class and he loves to play jokes. When he finds out that Julie is working on a rainforest project, he decides to play a joke on her. Since the Amazon River is a key part of the rainforest, Jacob focuses on this feature.

“Hey Julie, did you know that the Amazon River is twenty-one million, one hundred and twenty thousand feet long?” Jacob asks, leaning on Julie’s desk as she works.

“It is not,” Julie says smiling. “It is 4000 miles long.”

“Those measurements are one and the same,” Jacob says. “Also, the Amazon is thirty-one thousand six hundred and eighty feet wide.”

“That is not accurate,” Julie says. “It is 6 miles wide.”

“Again, those are the same,” Jacob says.

Who is correct? Convert each measurement having to do with the Amazon and figure out whether Jacob or Julie is correct.

What You Will Learn

By the end of this lesson, you will be able to complete the following:

• Convert customary units of measure using multiplication.
• Convert customary units of measure using division.
• Add and subtract customary units of measure.
• Solve real-world problems involving customary units of measure.

Teaching Time

I. Convert Customary Units of Measure Using Multiplication

In our last lesson, we began looking at equivalent units of measure. We did some conversions of customary units of measure involving weight and capacity. In this lesson, we are going to expand on what we just learned. Let’s look at converting units of measure using multiplication.

Why do we multiply when converting customary units of measure?

When converting customary units of measure from a large unit to a smaller unit, we multiply. You may already be wondering why we need to multiply as opposed to some other operation. The key is that a large unit is going to be a smaller number than a smaller unit. Let’s think about money to demonstrate this.

Example

100 pennies = 1 dollar

There are 100 pennies in one dollar. The penny is a smaller unit, so we need more of them to equal one of a large unit, the dollar. The same is true when working with length, weight and capacity. We need more of a smaller unit to equal a larger unit.

When we multiply, we are working with groups. To convert from a larger unit to a smaller unit, we multiply to change the larger unit to its smaller equivalent unit. To work on this lesson, you will need to think back to all of the units of length, weight and capacity that we have previously learned about.

Example

John has a rope that is 10 feet long. How long is his rope in inches?

Notice, we are going from feet to inches. A foot is larger than an inch. In fact a foot is equal to 12 inches. To solve this problem, we take the equivalent of one foot in inches and multiply it by the length of the rope in feet. This will give us the measurement in inches.

10 $\times$ 12 $=$ 120 inches

Example

Jason’s baby brother drank 3 cups of milk. How many fluid ounces did he drink?

Once again, we are going from a larger to a smaller unit. A cup is larger than a fluid ounce. There are 8 fluid ounces in one cup. If we multiply the number of cups times the number of fluid ounces in one cup, we will successfully convert to fluid ounces.

3 $\times$ 8 $=$ 24

Our answer is 24 fluid ounces.

Try a few of these conversions on your own.

1. 4 tons = ____ pounds
2. 5 feet = ____ inches
3. 3.5 pints = ____ cups

Take a minute to check your work with a partner. Did you remember your conversion equivalents?

II. Convert Customary Units of Measure Using Division

When converting from a larger unit to a smaller unit, we multiplied. When converting from a smaller unit to a larger unit, we divide by an equivalent unit. Let’s look at the pennies again.

Example

5000 pennies = ____ dollars

We know that there are 100 pennies in one dollar. This is the equivalent unit. If we divide 5000 by 100, we will have the number of dollars.

5000 $\div$ 100 $=$ 50 dollars

Let’s apply this to our work with measurement. Remember to think about the equivalent units of length, capacity and weight when dividing.

Example

5500 pounds = ____ tons

A pound is smaller than a ton so we divide. There are 2000 pounds in 1 ton, that is our equivalent unit. We divide 5500 by 2000.

5500 $\div$ 2000 = 2.75 or $2\frac{3}{4}$ tons

Our answer is 2.75 or $2 \frac{3}{4}$ tons.

Take this information and apply it when converting the following units of measure.

1. 84 inches = ____ feet
2. 40 cups = ____ pints
3. 800 pounds = ____ tons

Take a few minutes to check your work.

III. Add and Subtract Customary Units of Measure

We use customary units of measure every day. We can measure when cooking, we can measure when building, we can measure when carrying or moving things. Commonly, we need to add and subtract customary units of measure.

Example

Jeff’s van can hold 2000 pounds. He wants to move $\frac{1}{2}$ ton of wood. Then his friend gives him another 500 pounds of wood. Can Jeff carry all of this in his truck or will he need to make two trips?

This problem involves some conversions and some addition. We know that 2000 pounds is equal to one ton. Jeff is going to move $\frac{1}{2}$ of a ton first, so that is equal to 1000 pounds. Then he is given another 500 pounds.

1000 + 500 = 1500 pounds of wood

Jeff’s truck can hold 2000 pounds, so Jeff can carry all the wood in one trip.

2000 - 1500 = 500

There is also a difference of 500 pounds between the weight that the truck can hold and the weight of the wood.

This problem was simple addition and subtraction. Sometimes, we will need to convert units from smaller to larger too.

Example

Mary is making four cakes. One cake requires 2 cups of milk. How many pints of milk will Mary need for the four cakes?

First, we need to figure out how many cups she needs for four cakes. Then we can convert the cups to pints. We begin by adding.

2 + 2 + 2 + 2 = 8 cups

There are 2 cups in one pint. Mary will need 4 pints of milk because 8 divided by 2 is four. It makes more sense for Mary to use quarts because 2 quarts is equal to four pints.

When working with real life problems, we will often use adding, subtracting, multiplying and dividing to figure out measurements. Always keep the equivalent unit in mind as you work and you will figure out the accurate measurement needed.

## Real Life Example Completed

The Amazon

Now that you have learned all about conversions, it is time to figure out who is correct. Here is the problem once again. Start by underlining all of the important information.

Jacob is in Julie’s class and he loves to play jokes. When he finds out that Julie is working on a rainforest project, he decides to play a joke on her. Since the Amazon River is a key part of the rainforest, Jacob focuses on this feature.

“Hey Julie, did you know that the Amazon River is twenty-one million, one hundred and twenty thousand feet long?” Jacob asks, leaning on Julie’s desk as she works.

“It is not,” Julie says smiling. “It is 4000 miles long.”

“Those measurements are one and the same,” Jacob says. “Also, the Amazon is thirty-one thousand six hundred and eighty feet wide.”

“That is not accurate,” Julie says. “It is 6 miles wide.”

“Again, those are the same,” Jacob says.

Who is correct? Convert each measurement having to do with the Amazon and figure out whether Jacob or Julie is correct.

We need to figure out the measure of the length and width of the Amazon in feet and miles. There are 5,280 feet in one mile.

4000 miles = ____ feet

To go from a large unit to a smaller unit, we multiply, 4000 $\times$ 5,280 $=$ 21,120,000 ft.

Jacob is right on this one-the two measures are the same.

Next, let’s figure out the width.

6 miles = ____ feet

6 $\times$ 5,280 $=$ 31,680 feet

Jacob is right on this one too!!

## Vocabulary

In this lesson, you will see and use the following vocabulary words.

Equivalent
equal amount or unit
Length
measuring how long something is-customary units are inches, feet, yards and miles
Weight
measuring how heavy something is-customary units are ounces, pounds and tons.
Capacity
measuring how much liquid something can hold-customary units are fluid ounces, cups, pints, quarts and gallons.

## Resources

Here are a few websites where you can read about the Amazon River.

## Time to Practice

Directions: Convert the following larger units of measure to a smaller unit of measure.

1. 5 tons = ____ pounds

2. 6 feet = ____ inches

3. 9 tons = ____ pounds

4. 8 pounds = ____ ounces

5. 2.5 feet = ____ inches

6. 3.5 tons = ____ pounds

7. 2.25 pounds = ____ ounces

8. 9 cups = ____ fl. oz.

9. 5 pints = ____ cups

10. 7 pints = ____ cups

11. 8 quarts = ____ pints

12. 1 quart = ____ pints

13. 6 gallons = ____ quarts

14. 7.75 gallons = ____ quarts

Directions: Convert each smaller unit of measure to its larger equivalent using division.

15. 6 quarts = ____ gallons

16. 24 inches = ____ feet

17. 18 inches = ____ feet

18. 4 quarts = ____ gallons

19. 12 pints = ____ quarts

20. 25 pints = ____ quarts

21. 1 quart = ____ gallon

Directions: Add or subtract the following units and convert to a larger or smaller unit as needed.

22. 1 cup + 5 cups = ____ cups = ____ pints

23. 12 inches + 18 inches = ____ inches = ____ ft.

24. 5000 pounds - 1000 pounds = ____ pounds = ____ tons

25. 3 tons + 4 tons = ____ tons = ____ pounds

Feb 22, 2012

Oct 23, 2014