7.7: Converting Customary Units
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 \begin{align*}\times\end{align*} 12 \begin{align*}=\end{align*} 120 inches
Our answer is 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 \begin{align*}\times\end{align*} 8 \begin{align*}=\end{align*} 24
Our answer is 24 fluid ounces.
Try a few of these conversions on your own.
- 4 tons = ____ pounds
- 5 feet = ____ inches
- 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 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} 50 dollars
Our answer is 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 \begin{align*}\div\end{align*} 2000 = 2.75 or \begin{align*}2\frac{3}{4}\end{align*} tons
Our answer is 2.75 or \begin{align*}2 \frac{3}{4}\end{align*} tons.
Take this information and apply it when converting the following units of measure.
- 84 inches = ____ feet
- 40 cups = ____ pints
- 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.
Let’s think about this by using an example.
Example
Jeff’s van can hold 2000 pounds. He wants to move \begin{align*}\frac{1}{2}\end{align*} 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 \begin{align*}\frac{1}{2}\end{align*} 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 \begin{align*}\times\end{align*} 5,280 \begin{align*}=\end{align*} 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 \begin{align*}\times\end{align*} 5,280 \begin{align*}=\end{align*} 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.
http://en.wikipedia.org/wiki/Amazon_River
http://www.extremescience.com/zoom/index.php/earth-records/3-greatest-river
Technology Integration
Khan Academy Converting Pounds to Ounces
James Sousa Converting Customary Units
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
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