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3.21: Conversion of Customary Units of Measurement

Difficulty Level: At Grade Created by: CK-12
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Remember the tables that Mr. Potter suggested? Take a look at this dilemma.

Tyrone has his first measurement done when he meets Mr. Potter in the auditorium. He has written the measurement of the first table on the paper.

The first table is \begin{align*}8' \times 4'\end{align*}8×4.

When Tyrone arrives at the auditorium, Mr. Potter has another table all clean and set up for Tyrone to check out.

“I think this one is larger than the other one,” Mr. Potter says. “It measures \begin{align*}96'' \times 30''\end{align*}96′′×30′′.”

Tyrone looks at the table. He doesn’t think this one looks larger, but he can’t be sure.

On his paper he writes.

Table \begin{align*}2 = 96'' \times 30''\end{align*}2=96′′×30′′

To figure out which table is larger, Tyrone will need to convert customary units of measure. Then he will need to compare them.

This Concept will teach you all that you need to know about how to do this. When finished, you will know which table is larger and so will Tyrone.

Guidance

Imagine that you are cooking with a recipe that calls for 13 tablespoons of whipping cream. Since you are cooking for a large banquet you need to make 4 times what the recipe makes. So you are multiplying all of the ingredient quantities by 4 and combining them in a very large bowl. You realize that this requires you to use 52 tablespoons of whipping cream. To measure out 1 tablespoon 52 times will take forever!

Don’t worry, though.

You can convert tablespoons to a larger unit of measurement like cups and be able to measure out the whipping cream in larger quantities.

Look at the chart of customary units again.

Customary Units of Length

\begin{align*}& \text{inch} \ (in)\\ & \text{foot} \ (ft) && 12 \ in.\\ & \text{yard} \ (yd) && 3 \ ft.\\ & \text{Mile} \ (mi) && 5,280 \ ft.\end{align*}inch (in)foot (ft)yard (yd)Mile (mi)12 in.3 ft.5,280 ft.

Customary Units of Mass

\begin{align*}& \text{ounce} \ (oz)\\ & \text{pound} \ (lb) && 16 \ oz.\end{align*}ounce (oz)pound (lb)16 oz.

Customary Units of Volume

\begin{align*}& \text{ounce} \ (oz)\\ & \text{cup} \ (c) && 8 \ oz.\\ & \text{pint} \ (pt) && 16 \ oz.\\ & \text{quart} \ (qt) && 32 \ oz.\\ & \text{gallon} \ (gal) && 4 \ qt.\end{align*}ounce (oz)cup (c)pint (pt)quart (qt)gallon (gal)8 oz.16 oz.32 oz.4 qt.

Customary Units of Volume Used in Cooking

\begin{align*}& \text{teaspoon} \ (tsp)\\ & \text{tablespoon} \ (tbsp) && 3 \ tsp.\\ & \text{cup} \ (c) && 16 \ tbsp.\end{align*}teaspoon (tsp)tablespoon (tbsp)cup (c)3 tsp.16 tbsp.

Do you notice a relationship between the various units of volume? If we have 8 ounces of a liquid, we have 1 cup of it. If we have 16 ounces of a liquid, we have 1 pint of it, or 2 cups of it. If we have 2 pints of a liquid, we have 1 quart, or 4 cups, or 32 ounces of it.

We just looked at volume relationships by going from ounces to quarts, let’s look at a larger quantity and break it down to smaller parts. If we have 1 cup, how many teaspoons do we have? 1 cup is 16 tablespoons and 1 tablespoon is 3 teaspoons, so 1 cup is \begin{align*}16 \cdot 3\end{align*}163 teaspoons. 1 cup is 48 teaspoons.

Once we know how the different units of measurement relate to each other it is easy to convert among them. Don’t forget that 12 inches is equal to 1 foot. As you work more with measurements, it will be helpful for you to learn many of these relationships by heart.

Convert 374 inches into feet.

There are 12 inches in 1 foot, so to go from inches to feet we divide 374 by 12.

Our answer is \begin{align*}31 \frac{1}{6}\end{align*}3116 feet.

Notice this rule again.

If you go from a smaller unit to a larger unit, we divide. If we go from a larger unit to a smaller unit, we multiply.

Dividing and multiplying any units always has to do with factors and multiples of different numbers.

Studying measurement is particularly helpful because you learn to estimate more accurately what things around you measure. You catch a bass that weighs about 10 pounds, or your book bag filled with books weighs about 25 pounds. Maybe your good friend is about \begin{align*}5 \frac{1}{2}\end{align*}512 feet tall or your bicycle is 4 feet long.

Once you start measuring things, you can compare different quantities. Is the distance from your house to school farther than the distance from your house to the grocery store? Does your math book weigh more than your history book?

To be accurate in comparing and ordering with measurements, it is essential that you are comparing using the same unit. So, if you compare pounds and ounces, you should convert ounces to pounds and then compare pounds to pounds. Or, you can convert pounds to ounces and compare ounces to ounces.

Compare \begin{align*}4 \frac{1}{2}\end{align*}412 lbs ___ 74 oz.

First, notice that we have two different units of measurement. To accurately compare these two quantities, we need to make them both into the same unit. We can do this by multiplying. Multiply the pounds by 16 to get ounces.

\begin{align*}4 \frac{1}{2} \cdot 16 = 72 \ oz.\end{align*}41216=72 oz.

Our answer is that \begin{align*}4 \frac{1}{2} \ lbs < 74 \ oz\end{align*}412 lbs<74 oz.

Compare 62 ft. ___ 744 in.

First, we need to convert the units so that they are both the same. We can do this by converting inches to feet. The inches measurement is so large, that it is difficult to get an idea the exact size. Divide inches by 12 to get feet.

\begin{align*}744 \div 12 = 62 \ feet\end{align*}744÷12=62 feet

Our answer is that 62 ft. = 744 inches.

You can also use this information when ordering units of measurement from least to greatest and from greatest to least.

Now it's time for you to practice. Convert these measurements into quarts.

Example A

82 pints

Solution: 41 quarts

Example B

80 ounces

Solution:2.5 quarts

Example C

\begin{align*}8 \frac{1}{2}\end{align*}812 gallons

Solution:34 quarts

Here is the original problem once again.

Tyrone has his first measurement done when he meets Mr. Potter in the auditorium. He has written the measurement of the first table on the paper.

The first table is \begin{align*}8' \times 4'\end{align*}8×4.

When Tyrone arrives at the auditorium, Mr. Potter has another table all clean and set up for Tyrone to check out.

“I think this one is larger than the other one,” Mr. Potter says. “It measures \begin{align*}96'' \times 30''\end{align*}96′′×30′′.”

Tyrone looks at the table. He doesn’t think this one looks larger, but he can’t be sure.

On his paper he writes.

Table \begin{align*}2 = 96'' \times 30''\end{align*}2=96′′×30′′

To figure out which table is larger, Tyrone will need to convert customary units of measure. Then he will need to compare them.

To figure out which table is larger, Tyrone needs to convert both tables to the same unit of measure. One has been measured in inches and one has been measured in feet. Tyrone will convert both tables to inches.

He takes his measurements from table one.

\begin{align*}8' \times 4'\end{align*}8×4

There are 12 inches in 1 foot, so if he multiplies each by 12 they will be converted to inches.

\begin{align*}8 \times 12 = 96''\end{align*}8×12=96′′

The length of both tables is the same. Let’s check out the width.

\begin{align*}4 \times 12 = 48''\end{align*}4×12=48′′

The first table is \begin{align*}96'' \times 48''\end{align*}96′′×48′′.

The second table is \begin{align*}96'' \times 30''\end{align*}96′′×30′′.

Tyrone shows his math to Mr. Potter. The first table that the students already have is the larger of the two tables. Tyrone thanks Mr. Potter, but decides to stick with the first table.

Vocabulary

Here are the vocabulary words in this Concept.

Customary System
a system of measurement common in the United States. It involves units of measurement such as inches, feet, miles.
Metric System
a system of measurement developed by the French and common in Europe. It involves meters, grams, liters.

Guided Practice

Here is one for you to try on your own.

Henrietta is having her 8 best friends over for a luncheon. She wants to prepare salads on which she uses exactly 7 tablespoons of Romano cheese. If she is preparing 8 salads, how many cups of Romano cheese does Henrietta require?

Answer

We know that each salad requires 7 tablespoons and that Henrietta is making 8 salads. To find out the total amount of Romano cheese she needs in tablespoons, we multiply 7 by 8 to get 56 tablespoons. Now we need to convert 56 tablespoons to cups. There are 16 tablespoons in a cup, so we need to divide 56 by 16.

\begin{align*}56 \div 16 = 3 \frac{1}{2}\end{align*}56÷16=312

Henrietta will need \begin{align*}3 \frac{1}{2}\end{align*}312 cups of Romano cheese.

Video Review

Here are videos for review.

- This is a James Sousa video on equivalent customary units of length.

- This is a James Sousa video on equivalent customary units of capacity.

- This is a James Sousa video on equivalent customary units of mass.

Practice

Directions: Convert the following measurements into yards.

1. 195 inches

2. 0.2 miles

3. 88 feet

4. 90 feet

5. 900 feet

Directions: Convert the following measurements into pounds.

5. 2,104 ounces

6. 96 ounces

7. 3 tons

8. 15 tons

Directions: Convert the following measurements into pints.

9. 102 quarts

10. 57 ounces

11. 9.5 gallons

12. 4 quarts

13. 18 quarts

14. 67 gallons

15. 500 gallons

Directions: Compare the following measurements. Write <, >, or = for each ___.

16. 41 ounces ___ 2.5 quarts

17. 89 feet ___ 31 yards

18. 79 inches ___ 6 feet

19. 47 tablespoons ___ 144 teaspoons

20. Order the following measurements from least to greatest: 0.25 mi., 1525 ft., 18,750 in., 492 yd.

21. Order the following measurements from least to greatest: 42 pts, 282 oz., 24 gal., 64 qt.

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Difficulty Level:
At Grade
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Date Created:
Nov 30, 2012
Last Modified:
Sep 08, 2016
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