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Conversion of Customary Units by Dividing

Convert from smaller units to larger units of measurement by dividing.

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Conversion of Customary Units by Dividing

License: CC BY-NC 3.0

Ned is an amateur bee keeper. This season, he was able to harvest 40 cups of honey from his hive. He wants to store the honey in quart jars. How many jars will Ned need?

In this concept, you will convert customary units of measure using division. 

Converting Customary Units by Dividing

When converting from a larger unit to a smaller unit, you multiplied by the unit equivalence. To convert from a smaller unit to a larger unit, divide by the unit equivalence.

Let’s consider pennies.

5,000 pennies = ____ dollars

The penny is a smaller unit than the dollar. You need more of a smaller unit to equal a larger unit. Divide the number of pennies by the unit equivalence. You know that there are 100 pennies in one dollar.

100 pennies = 1 dollar

Divide 5,000 by 100 to get the equivalent value in dollars.

5000 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} 50

Therefore, 5,000 pennies is equivalent to 50 dollars.

Apply this to your work with converting measurements. Remember to think about the equivalent units of length, capacity and weight when dividing.

Here are some equivalence tables.

Customary Units of Length

inch (in.) foot (ft) yard (yd) mile (mi)
12 1
3 1
1,760 1

Customary Units of Weight

ounces (oz) pounds (lb) tons (T)
16 1
2,000 1

Customary Units of Capacity

fluid ounces (fl oz) cups (c) pints (pt) quarts (qt) gallon (gal)
8 1
16 2 1
32 4 2 1
128 16 8 4

1

Let's look at a conversion problem.

5,500 pounds = ____ tons

A pound is smaller than a ton. To solve this problem, divide the number of pounds by the unit equivalence. 

2,000 pounds = 1 ton 

5,500 \begin{align*}\div\end{align*} 2,000 = 2.75 or \begin{align*}2\frac{3}{4}\end{align*} tons

Notice that you can write the answer in fraction or decimal form. Therefore, 5,500 pounds is equivalent to 2.75 or \begin{align*}2 \frac{3}{4}\end{align*} tons.

Examples

Example 1

Earlier, you were given a problem about Ned and his honey.

Ned has 40 cups of honey that he wants to store in quart jars. Convert the 40 cups to quarts to find out how many jars Ned will need.

40 cups = _____ quarts

First, check if he will multiply or divide. A cup is smaller than a quart. Divide when converting a smaller unit to a larger unit.

Then, find the unit equivalence.

4 cups = 1 quart

Next, divide the number of cups by the unit equivalence.

40 ÷ 4 = 10

40 cups = 10 quarts

Ned will need 10 jars to store the honey.

Example 2

Convert the following unit of measure: 1,250 inches = _____ feet.

To solve this problem, convert inches to feet. Divide the number of inches by the unit equivalence.

12 inches = 1 foot

1,250 ÷ 12 = 104.16

The answer is 1,250 inches is equivalent to 104.16 feet.

Example 3

Convert the following unit of measure: 84 inches = ____ feet.

Divide the number of inches by the unit equivalence.

12 inches = 1 foot

84 ÷ 12 = 7

The answer is 84 inches is equivalent to 7 feet.

Example 4

Convert the following unit of measure: 40 cups = ____ pints.

Divide the number of cups by the unit equivalence.

2 cups = 1 pint

40 ÷ 2 = 20

The answer is 40 cups is equivalent to 20 pints.

Example 5

Convert the following unit of measure: 800 pounds = ____ tons.

Divide the number of pounds by the unit equivalence.

2,000 pounds = 1 ton

800 ÷ 2,000 = 0.4 

The answer is 800 pounds is equivalent to 0.4 tons.

Review

Convert the following units of measure.

  1. 6 quarts = ____ gallons
  2. 24 inches = ____ feet
  3. 18 inches = ____ feet
  4. 4 quarts = ____ gallons
  5. 12 pints = ____ quarts
  6. 25 pints = ____ quarts
  7. 1 quart = ____ gallons
  8. 9 quarts = ____ gallons
  9. 15 quarts = ____ gallons
  10. 99 inches = ____ feet
  11. 98 pints = ____ gallons
  12. 12,000 pounds = ____ tons
  13. 22,000 pounds = ____ tons
  14. 5,000 pounds = ____ tons
  15. 20,000 pounds = ____ tons

Review (Answers)

To see the Review answers, open this PDF file and look for section 7.17. 

Resources

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Vocabulary

Capacity

The volume of liquid an object or item can hold. Customary units of capacity include fluid ounces, cups, pints, quarts and gallons.

Equivalent

Equivalent means equal in value or meaning.

Length

Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.

Weight

Weight is a measurement of the heaviness or mass of someone or something. The customary units of weight included ounces, pounds, and tons.

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