1. Multiplying Fractions
5-7
Multiplying Fractions
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up 1. What is of 12? 6 2. What is of 100? 3. What is of 120? 50__ 6 1 2 __ 50 1 2 __ 60 1 4 __ 25 1 4 __
120

3. Problem of the Day
Your favorite uncle left one-fifth of his estate to each of his three children and the rest to his favorite charity. If his estate was worth $105,000, how much was given to charity?
$42,000

4. Learn to multiply fractions.

5. On average, people spend of their lives asleep. About 1 3 __
On average, people spend of their lives asleep. About
of the time they sleep, they dream. What fraction of
a lifetime does a person typically spend dreaming? 1 4 __ 1 4 __ 1 3 __
One way to find of is to make a model.
Find of . 1 4 __ 1 3 __ 1 4 __ 1 3 __ 1 12 __ • =

6. You can also multiply fractions without making a model.1 4 __ 1 3 __
_____
1 • 1
Multiply the numerators. • =
4 • 3
Multiply the denominators. 1 12 __
The answer is in simplest form. = 1 12 __
A person typically spends of his or her lifetime dreaming.

7. Multiply. Write each answer in simplest form.
Additional Example 1A: Multiplying Fractions
Multiply. Write each answer in simplest form. 1 4 __ 2 5 __ • 1 4 __ 2 5 __
_____
1 • 2 • =
Multiply numerators. Multiply denominators.
4 • 5 2 20 __ =
The GCF of 2 and 20 is 2. 1 10 __ =
The answer is in simplest form.

8. Multiply. Write each answer in simplest form.
Additional Example 1B: Multiplying Fractions
Multiply. Write each answer in simplest form. 5 7 __ 4 15 __ •
Use the GCF to simplify the fractions before multiplying. The greatest common factor of 5 and 15 is 5. 5 7 __ 1 4 15 __ 1 7 __ 4 3 __ • = • 3
_____
1 • 4
Multiply numerators. Multiply denominators. =
7 • 3 4 21 __ =
The answer is in simplest form.

9. Multiply. Write each answer in simplest form.
Additional Example 1C: Multiplying Fractions
Multiply. Write each answer in simplest form. 4 9 __ 6 10 __ • 4 9 __ 6 10 __
______
4 • 6 • =
Multiply numerators. Multiply denominators.
9 • 10 24 90 __ =
The GCF of 24 and 90 is 6. 4 15 __ =
The answer is in simplest form.

10. Multiply. Write each answer in simplest form.
Check It Out: Example 1A
Multiply. Write each answer in simplest form. 1 2 __ 3 6 __ • 1 2 __ 3 6 __
_____
1 • 3 • =
Multiply numerators. Multiply denominators.
2 • 6 3 12 __ =
The GCF of 3 and 12 is 3. 1 4 __
The answer is in simplest form. =

11. Multiply. Write each answer in simplest form.
Check It Out: Example 1B
Multiply. Write each answer in simplest form. 3 7 __ 5 9 __ •
Use the GCF to simplify the fractions before multiplying. The greatest common factor of 3 and 9 is 3. 3 7 __ 1 5 9 __ 1 7 __ 5 3 __ • = • 3
_____
1 • 5
Multiply numerators. Multiply denominators. =
7 • 3 5 21 __ =
The answer is in simplest form.

12. Multiply. Write each answer in simplest form.
Check It Out: Example 1C
Multiply. Write each answer in simplest form. 3 7 __ 5 15 __ • 3 7 __ 5 15 __
______
3 • 5 • =
Multiply numerators. Multiply denominators.
7 • 15 15
105
____ =
The GCF of 15 and 105 is 15. 1 7 __ =
The answer is in simplest form.

13. Additional Example 2A: Evaluating Fraction Expressions5 __
Evaluate the expression b • for each value of b.
Write each answer in simplest form. 1 3 __ 2 5 __
b =
b • 1 3 __ 1 3 __ 2 5 __ •
Substitute for b.
_____
1 • 2
3 • 5
Multiply. 2 15 __
The answer is in simplest form.

14. You can look for a common factor in a numerator and a denominator to determine whether you can simplify before multiplying.
Helpful Hint

15. Additional Example 2B: Evaluating Fraction Expressions3 8 __ 2 5 __
b • 3 8 __ 3 8 __ 2 5 __ •
Substitute for b. 1 3 8 __ 2 5 __ •
Use the GCF to simplify. 4
_____
3 • 1
4 • 5
Multiply. 3 20 __
The answer is in simplest form.

16. Additional Example 2C: Evaluating Fraction Expressions
b = 5 7 __ 2 5 __
b • 5 7 __ 2 5 __ 5 7 __ •
Substitute for b.
_____
5 • 2
7 • 5
Multiply. 10 35 __
The GCF of 10 and 35 is 5. 2 7 __
The answer is in simplest form.

17. Check It Out: Example 2A
Evaluate the expression c • for each value of c.
Write each answer in simplest form.
c = 1 4 __ 1 7 __ 1 4 __
c • 1 7 __ 1 4 __ 1 7 __ •
Substitute for c.
_____
1 • 1
7 • 4
Multiply. 1 28 __
The answer is in simplest form.

18. Check It Out: Example 2B c = 2 __ 7 2 __ Substitute for c. • 71 4 __
c • 2 7 __ 2 7 __ 1 4 __
Substitute for c. • 1 2 7 __ 1 4 __ •
Use the GCF to simplify. 2
_____
1 • 1
7 • 2
Multiply. 1 14 __
The answer is in simplest form.

19. Check It Out: Example 2C c = 4 7 __ 1 4 __ c • 4 7 __ 1 4 __ 4 7 __ •
Substitute for c.
_____
4 • 1
7 • 4
Multiply. 4 28 __
The GCF of 4 and 28 is 4. 1 7 __
The answer is in simplest form.

20. Multiply. Write each answer in simplest form. 1. 2.
Lesson Quiz
Multiply. Write each answer in simplest form.
Evaluate the expression x • for each value of x. Write the answer in simplest form.
3. x = x =
5. At a particular college of the students take a math class. Of these students, take basic algebra. What fraction of all students take basic algebra? 1 4 __ 3 5 __ 3 20 __ 3 10 __ 5 7 __ 3 14 __ • • 1 8 __ 4 5 __ 1 10 __ 1 8 __ 1 64 __ 2 5 __ 1 4 __ 1 10 __