Multiplying and Dividing Fractions and
Mixed Numbers Let’s Measure
ACTIVITY
2.5
LEARNING STRATEGIES: Activating Prior Knowledge, Quickwrite
My Notes
Knowing how to compute with fractions and mixed numbers is
necessary to work with the customary measurement system.
2
1 miles. LaDonna ran 1 __
During track practice, Jenna ran 2 __
4
3
times as far as Jenna. How far did LaDonna run? To find how far
LaDonna ran, multiply the mixed numbers.
1 by 1 __
2.
1. Explain each step of multiplying 2 __
4
3
Step
Explanation
The customary measurement
system is the one used by most
people in the United States.
Listed below are some
often-used units of length.
Length
1 × 1 __
2
2 __
4
3
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 ft
1 mile (mi) = 1760 yd
9 __
__
×5
4
3
3
9 × __
5
__
4
31
3 × 5 ___
15
______
=
4×1
4
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3
3 __ miles
4
For help with the abbreviations
for some measurements, use the
table of measures in the back of
your book.
2. In the third step of the multiplication above, the expression
9 × __
5 was simplified.
__
4 3
a. If the expression were not simplified, what improper fraction
would you get when you multiply?
b. Is this answer equivalent to the answer in Question 1?
Explain your answer.
10 × __
3 and ___
10 × __
5.
c. Find the products: ___
7
5
7
3
Unit 2 • Operations with Numbers
91
ACTIVITY 2.5
Multiplying and Dividing Fractions and Mixed Numbers
continued
Let’s Measure
LEARNING STRATEGIES: Quickwrite, Debriefing
My Notes
d. Could you have simplified the multiplication expressions in
Part c before you multiplied? Use the numerical expressions
to explain why or why not.
e. Why is it important to write a 1 when you simplify?
1 feet long.
Jorge will put square tiles along a wall that is 13 __
2
1 feet long. To determine the number of
The tile sides are 1 __
2
tiles needed to put along the side of the room, divide the mixed
numbers.
1 by 1 __
1.
3. Explain each step of dividing 13 __
2
2
Step
Explanation
27 ÷ __
3
___
2
2
27 × __
2
___
2
3
1
27 × __
2
___
31
1 2
9
9 × 1 = __
9
_____
1×1
1
9 floor tiles
4. Explain how common factors were used to simplify the
expression.
92
SpringBoard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
1
1 ÷ 1 __
13 __
2
2
Multiplying and Dividing Fractions and Mixed Numbers
ACTIVITY 2.5
continued
Let’s Measure
LEARNING STRATEGIES: Activating Prior Knowledge, Quickwrite
My Notes
5. For the following problems, estimate first and then calculate.
Look at the estimate for each problem to check your answers.
1 × 1 ___
11
a. 3 __
3
15
3 ÷ 2 __
1
b. 13 __
5
4
1
2
c. 5 __ ÷ 2 __
5
3
Another use for fractions and mixed numbers is converting
between measures in the customary system.
Capacity
1 cup = 8 fl oz
1 pt = 2 cups
1 qt = 2 pt
1 gal = 4 qt
Mass
1 lb = 16 oz
1 ton = 2,000 lb
EXAMPLE 1
1 cups of milk?
How many fluid ounces are in 3 __
3
Step 1: Determine the number of fluid ounces in 1 cup.
1 cup = 8 fl oz
1 cups by 8 fl oz in a cup.
Multiply 3 __
3
80 = 26 __
8 fl oz = ___
10 × __
8 = ___
1 cups × _____
2 fl oz
3 __
3
1 cup
3
3
3
1
2
1
Solution: There are 26 __ fluid ounces in 3 __ cups of milk.
3
3
Step 2:
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EXAMPLE 2
1 inches long. How long is the box in feet?
A box is 39 __
2
Step 1: Determine the number of inches in 1 foot.
1 ft = 12 in.,
1 in. by 12 in. in a foot.
Divide 39 __
2
79 ÷ ___
79 × ___
79 = 3 ___
12 in. = ___
7 ft
1 in. ÷ _____
12 = ___
1 = ___
Solution: 39 __
2
2
1
2
12 24
24
1 ft
Step 2:
TRY THESE A
1 gallons?
a. How many quarts are in 3 __
2
4 ounces. What is the weight of the package
b. A package weighs 28 __
5
in pounds?
Unit 2 • Operations with Numbers
93
ACTIVITY 2.5
Multiplying and Dividing Fractions and Mixed Numbers
continued
Let’s Measure
LEARNING STRATEGIES: Quickwrite, Debriefing
My Notes
6. Example 1 used multiplication to convert units of measure and
example 2 used division. Explain how you know when to use
multiplication and when to use division.
7. Describe the process you would use to convert a number of
miles to a number of yards. Use an example.
Write your answers on notebook paper. Show
your work.
3 × 1 __
1.
1. Estimate first, then multiply 3 __
4
3
Check your answer to see if it is close to
the estimate.
3 × 12 __
1.
2. Multiply: 5 __
5
2
1 ÷ 3 __
1.
3. Estimate first, then divide 6 __
8
2
Check your answer to see if it is close to
the estimate.
94
SpringBoard® Mathematics with Meaning™ Level 1
1
4 ÷ 5 __
4. Divide: 8 __
5
2
1 pounds?
5. How many ounces are in 7 __
3
3 gallons?
6. How many pints in 4 __
4
7. How many yards are in 261 inches?
8. MATHEMATICAL Name two customary
R E F L E C T I O N measurements that you
could convert between and write a note to
one of your classmates telling the steps
needed to do this conversion. You may
include an example in your note.
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CHECK YOUR UNDERSTANDING