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7.18: Conversion of Customary Units by Multiplying

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Remember Julie and the rainforest? Take a look at this dilemma.

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.

Guidance

In our last Concept, we began looking at equivalent units of measure. We did some conversions of customary units of measure involving weight and capacity. In this Concept, 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.

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 Concept, you will need to think back to all of the units of length, weight and capacity that we have previously learned about.

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

Our answer is 120 inches.

Try a few of these conversions on your own.

Example A

4 tons = ____ pounds

Solution: 8000 pounds

Example B

5 feet = ____ inches

Solution: 60 inches

Example C

8 pints = ____ cups

Solution: 16 cups

Now back to figuring out who is correct when it comes to the Amazon.

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

Here are the vocabulary words in this Concept.

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.

Guided Practice

Here is one for you to try on your own.

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

Answer

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.

Video Review

Here are videos for review.

Khan Academy Converting Pounds to Ounces

Converting Customary Units

James Sousa Converting Customary Units

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

15. 8 miles = _____ feet

16. 3 feet = _____ inches

17. 12 miles = _____ feet

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Date Created:

Oct 29, 2012

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Oct 28, 2014
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