1. Course 2, Lesson 4-6
Use the draw a diagram strategy to solve Exercises 1-4
1. The Rockwells have driven 180 miles, which is about of the way to their
family reunion. How far is the total distance to their family reunion?
2. Tomi is eating a candy bar that is 12 inches long. She has already eaten
of the candy bar. How many inches of the candy bar does she have
left?
3. Toki has filled or 12 ounces of his glass. Find the total capacity of his
glass.
4. If an 8-ounce serving of yogurt provides 10% of the daily requirement for
calcium, what percent of the calcium requirement would a 20-ounce
serving provide?
2
3
5
8
3
4

2. Course 2, Lesson 4-6
Answers
1. 270 miles
2.
3. 16
4. 25%
1
4
2

3. WHAT happens when you add,
subtract, multiply, and divide
fractions?
The Number System
Course 2, Lesson 4-6

4. Course 2, Lesson 4-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.NS.2 Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
• 7.NS.2a Understand that multiplication is extended from fractions to
rational numbers by requiring that operations continue to satisfy the
properties of operations, particularly the distributive property, leading to
products such as (–1)(–1) = 1 and the rules for multiplying signed
numbers. Interpret products of rational numbers by describing real-
world contexts.
• 7.NS.2c Apply properties of operations as strategies to multiply and
divide rational numbers.
• 7.NS.3 Solve real-world and mathematical problems involving the four
operations with rational numbers.

5. Course 2, Lesson 4-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.EE.3 Solve multi-step real-life and mathematical problems posed
with positive and negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools strategically. Apply
properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of
answers using mental computation and estimation strategies.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

6. • To multiply fractions
• To multiply mixed numbers
Course 2, Lesson 4-6
The Number System

7. Course 2, Lesson 4-6
The Number System
Words To multiply fractions, multiply the numerator and multiply the
denominators.
Examples Numbers
Algebra
1 2 1 x 2 2
x or
2 3 2 x 3 6

or , where , 0
d
a c a c ac
b d
b d b bd
 

8. 1
Need Another Example?
2
Step-by-Step Example
1. Multiply × . Write in simplest form.
Simplify.
Multiply the numerators.
= Multiply the denominators.
=

9. Answer
Need Another Example?
Find × . Write in simplest form.

10. 1
Need Another Example?
2
3
Step-by-Step Example
2. Multiply 2 × – . Write in simplest form.
Simplify.
Write 2 as and – as .=
Multiply the numerators.
= Multiply the denominators.
= or –1

11. Answer
Need Another Example?
Find 6 × – . Write in simplest form.
–2

12. 1
Need Another Example?
2
Step-by-Step Example
3. Multiply × – . Write in simplest form.
Divide 2 and 8 by their GCF, 2.=
Multiply.= or –
4
1

13. Answer
Need Another Example?
Find × – . Write in simplest form.

14. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
4. Find × 4 . Write in simplest form.
Rename 4 as an improper fraction, .
=
× 4 = 2
7
Estimate
Rename the mixed number.
Think Half of 4 is 2 and half of 2 fifths is 1 fifth.
11
1
=
=
=
Multiply.
Simplify.
Simplify.
Use mental math.
The mixed number 4 is equal to 4 + .
So, × 4 = 4 + . Use the Distributive Property to multiply, then add mentally.
Rewrite the sum as a mixed number.
Check for Reasonableness
Divide 2 and 22 by their GCF, 2.
Using either method, the answer is 2 .

15. Answer
Need Another Example?
Find × 6 . Write in simplest form.

16. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
5. Humans sleep about of each day. Let each year
equal 365 days. Determine the number of days in
a year the average human sleeps.
Rename the mixed number as an improper fraction.
× 360 = 120Estimate
Divide 3 and 1,461 by their GCF, 3.
Multiply. Then rename as a mixed number.
121 ≈ 120Check for Reasonableness
Find × 365 .
× 365 = ×
7
×=
487
1
= or 121
The average human sleeps 121 days each year.

17. Answer
Need Another Example?
In a 48-hour bike race, Mel rode 289 miles.
His father rode as far as Mel did. Find the
number of miles his father rode.
217 mi

18. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-6
The Number System

19. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-6
The Number System
Sample answers:
• When you multiply fractions, multiply the numerators
and multiply the denominators.
• When you multiply mixed numbers, rename the mixed
numbers as improper fractions.

20. Find .
Write your answer in
simplest form.
Course 2, Lesson 4-6
Ratios and Proportional RelationshipsThe Number System
 
 
 
 
 
2 6- × -
3 8