1. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Problem of the Day
(For help, go to Lesson 2-4.)
1. Vocabulary Review In an improper fraction, how does
the numerator compare to the denominator?
Write each mixed number as an improper fraction. 3 5 1 2 2 3 3 4
Check Skills You’ll Need
3-4

2. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Problem of the Day
Solutions
1. The numerator is greater than the denominator.
= = = =
= = = = 3 5
(5  2) + 3 13 1 2
(2  6) + 1 13 2 3
(3  1) + 2 5 3 4
(4  4) + 3 19
3-4

3. Any questions about the homework?
Lesson 3-4, page 138, #s 1-10
Confused about question 4? See the next slide!

4. Another explanation of area models
Source:

5. Follow these steps to multiply fractions and mixed numbers
Multiplying Fractions and Mixed Numbers
LESSON 3-4
Steps to follow
Follow these steps to multiply fractions and mixed numbers
Write the mixed numbers as improper fractions, if necessary
Multiply numerator and denominators
Simplify, if necessary }
} OR cross-cancel
} common factors
Algebra:

6. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Additional Examples – Multiplying fractions
Find • . 1 9 3 4 1 9 3 4 •
0 • , or 0
Estimate
Multiply the numerators.
Multiply the denominators. 1 9 3 4 • =
1 • 3
9 • 4
Find the two products. = 3 36 =
Simplify. 1 12
Check for Reasonableness The answer, , is close to the estimate, 0.
The answer is reasonable. 1 12
Quick Check
3-4

7. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Additional Examples – Multiplying by a whole number
What is of 12? 2 3
Write 12 as (Why?) 2 3 12 1
= • 2 3
• 12
= • 2 3 12 1 4
Simplify before multiplying. 8 1 =
Multiply the numerators. Multiply the denominators.
= 8
Simplify.
Quick Check
3-4

8. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Problem of the Day – Multiplying by a whole number 1 2
In 2002, a disc jockey broadcast her show for 27 h each week.
How many hours did she broadcast that year?
1,430 h
3-4

9. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Additional Examples – Multiplying mixed numbers
Quick Check
Find 5 • 1 2 1 3
5 • • 3, or 18 1 2 3
Estimate
Write the mixed numbers as improper fractions.
5 • 3 = • 1 2 3 11 10 =
11 • 10
2 • 3
Multiply the numerators. Multiply the denominators. =
110 6 55 3
Simplify.
= 18 1 3
Write as a mixed number.
Check for Reasonableness The answer, 18 , is close to the estimate, 18.
The answer is reasonable. 1 3
3-4

10. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Lesson Quiz
Find each product.
• of 48
• • 5 3 5 10 12 5 8 1 2 30 1 2 2 10 1 4 1 3 9 10 17 1 3
3-4

11. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Additional Examples – Word problems
The length of a track around a field is ¼ mi. You jog 3½ times around the track. How far did you jog?
A poster measures 38 cm across. If a photocopy machine is used to make a copy that is 3/5 of the original size, what is the width of the copy?
The population of Sweden is about times as great as the population of Denmark. Find the population of Sweden if the population of Denmark is about 5,190,000.
7/8 mi
22 and 4/5ths cm
About 8,760,000

12. Multiplying Fractions and Mixed Numbers
LESSON 3-4
Homework
Lesson 3-4: p. 138 – 139: #s 15-43, odds
Checkpoint Quiz 1: p. 134: # 1 – 10 all
Friday: Quiz on 3-1 to 3-4