3.8: Converting Customary Units
Introduction
Comparing Tables
Tyrone has his first measurement done when he meets Mr. Potter in the auditorium. He has written the measurement of the first table on paper.
The first table is \begin{align*}8' \times 4'\end{align*}.
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*}.”
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*}
To figure out which table is larger, Tyrone will need to convert between customary units of measurement. Then he will need to compare them.
This lesson 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.
What You Will Learn
By the end of this lesson, you will be able to demonstrate the following:
- Convert between customary units of measure using factors and multiples.
- Compare and order given customary units of measure.
- Estimate equivalence between customary and metric units of measure.
- Solve real-world problems involving conversion of customary units of measure.
Teaching Time
I. Convert among Customary Units of Measure using Factors and Multiples
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*}
Customary Units of Mass
\begin{align*}& \text{ounce} \ (oz)\\ & \text{pound} \ (lb) && 16 \ oz.\end{align*}
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*}
Customary Units of Volume Used in Cooking
\begin{align*}& \text{teaspoon} \ (tsp)\\ & \text{tablespoon} \ (tbsp) && 3 \ tsp.\\ & \text{cup} \ (c) && 16 \ tbsp.\end{align*}
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*} teaspoons. 1 cup is 48 teaspoons.
Once we know how the different units of measurement relate to each other it is easy to convert between them. As you work more with measurements, it will be helpful for you to commit many of these relationships to memory.
Example
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*} feet.
Remember;
If we go from a smaller unit to a larger unit, divide. If we go from a larger unit to a smaller unit, multiply.
3U. Lesson Exercises
Convert these measurements into quarts.
- 82 pints
- 476 ounces
- \begin{align*}8 \frac{1}{2}\end{align*} gallons
Now take a few minutes to check your answers with a peer.
II. Compare and Order Given Customary Units of Measure
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 measurements, it is essential that you are comparing using the same unit of measurement. 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.
Let’s look at an example.
Example
Compare \begin{align*}4 \frac{1}{2}\end{align*} 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*}
Now we can find our answer, which is that \begin{align*}4 \frac{1}{2} \ lbs < 74 \ oz\end{align*}.
Example
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*}
Our answer is 62 ft. = 744 inches.
You can also use this information when ordering units of measurement from least to greatest and from greatest to least.
Remember the key!!
3V. Lesson Exercises
Compare.
- 11 qt. ___ 64 c
- 12 tbsp ___ 35 tsp
Compare your answers with a partner. Is your work accurate and correct?
III. Estimate Equivalence Between Customary and Metric Units of Measure
While you encounter the Customary System of measurement all of the time in your everyday life, there is another system of measurement that is also widely used. This system is known as the Metric System. In other countries people use the metric system for the same things that we use the customary system for. We might weigh grapes using pounds, but in France they use grams to weigh grapes. You may measure the length of one side of your backyard in feet, but in Beijing they use meters. Even in the United States, the metric system is frequently used especially in science.
You may find yourself in a situation where you need to convert between the metric system and the customary system. Take a look at the chart below. It shows the estimated customary equivalent to common metric units.
Customary Units | Metric Units |
---|---|
1 centimeter | 0.39 inches |
1 meter | 3.28 feet |
1 kilometer | 0.62 miles |
1 milliliter | 0.2 teaspoons |
1 liter | 4.23 cups |
1 gram | 0.04 ounces |
1 kilogram | 2.2 pounds |
Using this chart can help us to estimate the equivalence between metric units of measurement and customary units of measurement. Let’s look at an example.
Example
Estimate the equivalent measurement, converting from 14 centimeters to inches.
A centimeter is equal to about 0.39 inches, so we multiply \begin{align*}14 \cdot 0.39 = 5.46 \ inches\end{align*}
Example
Estimate the equivalent measurement, converting from 7.7 pounds to kilograms.
There are 2.2 pounds in 1 kilogram, so we divide the number of pounds by the number of pounds in 1 kilogram. \begin{align*}7.7 \div 2.2 = 3.5\end{align*}
The answer is 3.5 kilograms.
If you keep this chart in mind, you will always be able to estimate measurements between these two standards of measurement. If you do this enough, you will be able to convert some of them without the chart.
For example, most runners know that a 5k race is about 3.1 miles. Where as a 10k is 6.2 miles.
IV. Solve Real-World Problems Involving Conversion of Customary Units of Measure
Remember that recipe that called for 13 tablespoons of whipping cream? We needed to make 4 times what the recipe called for because we were cooking for a banquet. It is absurd to imagine that someone would stand over a mixing bowl and count out 52 little tablespoons. If we convert 52 tablespoons into cups, we get \begin{align*}3 \frac{1}{4}\end{align*} cups. It takes only a minute to measure out \begin{align*}3 \frac{1}{4}\end{align*} cups of whipping cream. We saved ourselves a lot of time by converting from tablespoons to cups.
There are many other real-world situations in which converting among customary units can be very useful. Let’s take a look at a few.
Example
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?
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*}
Henrietta will need \begin{align*}3 \frac{1}{2}\end{align*} cups of Romano cheese.
Real-Life Example Completed
Comparing Tables
Here is the original problem once again. Reread it and then underline any important information.
Tyrone has his first measurement done when he meets Mr. Potter in the auditorium. He has written the measurement of the first table on paper.
The first table is \begin{align*}8' \times 4'\end{align*}.
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*}.”
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*}
To figure out which table is larger, Tyrone will need to convert between customary units of measurement. 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 measurement. 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*}
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*}
The length of both tables is the same. Let’s check out the width.
\begin{align*}4 \times 12 = 48''\end{align*}
The first table is \begin{align*}96'' \times 48''\end{align*}.
The second table is \begin{align*}96'' \times 30''\end{align*}.
Tyrone shows his math to Mr. Potter. The 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 that are found in this lesson.
- 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.
Technology Integration
James Sousa, American Unit Conversions
James Sousa, Example of Converting Between Units of Volume in the American System
James Sousa, Example of Converting Between Units of Weight in the American System
James Sousa, Example of Converting Between Units of Length in the American System
Other Videos:
- http://www.mathplayground.com/howto_Metric.html – This is a video to help you understand the metric system.
- http://www.gamequarium.org/cgi-bin/search/linfo.cgi?id=6911 – This is a video on metric and standard or customary systems of measurement.
Time to Practice
Directions: Convert the following measurements into yards.
1. 195 inches
2. 0.2 miles
3. 88 feet
Directions: Convert the following measurements into pounds.
4. 2,104 ounces
5. 96 ounces
Directions: Convert the following measurements into pints.
6. 102 quarts
7. 57 ounces
8. 9.5 gallons
Directions: Compare the following measurements. Write <, >, or = for each ___.
9. 41 ounces ___ 2.5 quarts
10. 89 feet ___ 31 yards
11. 79 inches ___ 6 feet
12. 47 tablespoons ___ 144 teaspoons
13. Order the following measurements from least to greatest: 0.25 mi., 1525 ft., 18,750 in., 492 yd.
14. Order the following measurements from least to greatest: 42 pts, 282 oz., 24 gal., 64 qt.
Directions: Estimate a customary equivalent for the following metric measurements, round to the nearest hundredth where necessary.
15. 4 kilograms to pounds
16. 7.5 meters to feet
17. 6 liters to cups
18. 13.25 kilometers to miles
Directions: Estimate a metric equivalent for the following customary measurements, round to the nearest hundredth where necessary.
19. 4 quarts to liters
20. 34 ounces to grams
21. 52 pounds to kilograms
22. 9 inches to centimeters
23. Hillary is ready to bottle her orange drink concoction, Orange Whizzbang. She orders the first shipment of 1250 pints from the bottling company. The bottling company charges by the gallon, how many gallons did Hillary order from the bottling company?
24. Toby the turtle walked 723 feet in 10 hours. How fast did Toby walk in inches per hour? [Remember: rate = distance \begin{align*}\div\end{align*} time].