1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
List the factors of each number.
1. 8
2. 10
3. 16
4. 20
5. 30
1, 2, 4, 8
1, 2, 5, 10
1, 2, 4, 8, 16
1, 2, 4, 5, 10, 20
1, 2, 3, 5, 6, 10, 15, 30

3. Problem of the Day
John has 3 coins, 2 of which are the same. Ellen has 1 fewer coin than John, and Anna has 2 more coins than John. Each girl has only 1 kind of coin. Who has coins that could equal the value of a half dollar?
Ellen and Anna

4. Learn to write equivalent fractions.

5. Vocabulary
equivalent fractions
simplest form

6. Fractions that represent the same value are equivalent fractions
Fractions that represent the same value are equivalent fractions. So are equivalent fractions.
1 2
2 4
4 8 = =

7. Additional Example 1: Finding Equivalent Fractions
Find two equivalent fractions for . 10
___ 12 10 12
___ 15 18
___ 5 6 __ = =
The same area is shaded when the rectangle is divided into 12 parts, 18 parts, and 6 parts. 10 12
___ 15 18
___ 5 6 __
So , , and are all equivalent fractions.

8. Find two equivalent fractions for .
Check It Out: Example 1
Find two equivalent fractions for . 4 __ 6 4 6 __ 8 12
___ 2 3 __ = =
The same area is shaded when the rectangle is divided into 6 parts, 12 parts, and 3 parts. 4 6 __ 8 12
___ 2 3 __
So , , and are all equivalent fractions.

9. Find the missing number that makes the fractions equivalent.
Additional Example 2A: Multiplying and Dividing to Find Equivalent Fractions
Find the missing number that makes the fractions equivalent. 3 5 __
___
In the denominator, 5 is multiplied by 4 to get 20. = 20 3 5
______
• 4 12
____
Multiply the numerator, 3, by the same number, 4. =
• 4 20 3 5 __ 12 20
___
So is equivalent to 3 5 __ 12 20
___ =

10. Find the missing number that makes the fractions equivalent.
Additional Example 2B: Multiplying and Dividing to Find Equivalent Fractions
Find the missing number that makes the fractions equivalent. 4 5 __
___ 80 =
In the numerator, 4 is multiplied by 20 to get 80. 4 5
______
• 20 80
____
Multiply the denominator by the same number, 20. =
• 20
100 4 5 __ 80
100
___
So is equivalent to 4 5 __ 80
100
___ =

11. Find the missing number that makes the fraction equivalent.
Check It Out: Example 2A
Find the missing number that makes the fraction equivalent. 3 9 __
___
In the denominator, 9 is multiplied by 3 to get 27. = 27 3 9
______
• 3 9
____
Multiply the numerator, 3, by the same number, 3. =
• 3 27 3 9 __ 9 27
___
So is equivalent to 3 9 __ 9 27
___ =

12. Find the missing number that makes the fraction equivalent.
Check It Out: Example 2B
Find the missing number that makes the fraction equivalent. 2 4 __
___ 40
In the numerator, 2 is multiplied by 20 to get 40. = 2 4
______
• 20 40
____
Multiply the denominator by the same number, 20. =
• 20 80 2 4 __ 40 80
___
So is equivalent to 2 4 __ 40 80
___ =

13. Every fraction has one equivalent fraction that is called the simplest form of the fraction. A fraction is in simplest form when the GCF of the numerator and the denominator is 1.
Example 3 shows two methods for writing a fraction in simplest form.

14. Additional Example 3A: Writing Fractions in Simplest Form
Write each fraction in simplest form. 20
___ 48 20 48
___
The GCF of 20 and 48 is 4, so is not in simplest form.
Method 1: Use the GCF. 20 48
_______
÷ 4 5 12 __ =
Divide 20 and 48 by their GCF, 4.
÷ 4

15. So written in simplest form is .
Additional Example 3A Continued
Method 2: Use prime factorization. 20 48
___
_________________
2 • 2 • 5 5 12
___
Write the prime factors of 20 and 48. Simplify. = =
2 • 2 • 2 • 2 • 3 20 48
___ 5 12
___
So written in simplest form is
Helpful Hint
Method 2 is useful when you know that the numerator and denominator have common factors, but you are not sure what the GCF is.

16. Additional Example 3B: Writing Fractions in Simplest Form
Write the fraction in simplest form. 7 10
___ 7 10
___
The GCF of 7 and 10 is 1 so is already in simplest form.

17. Write each fraction in simplest form.
Check It Out: Example 3A
Write each fraction in simplest form. 12
___ 16 12 16
___
The GCF of 12 and 16 is 4, so is not in simplest form.
Method 1: Use the GCF. 12 16
_______
÷ 4 3 4 __
Divide 12 and 16 by their GCF, 4. =
÷ 4

18. Check It Out: Example 3A Continued
Method 2: Use prime factorization. 12 16
___
_____________
2 • 2 • 3 3 4
___
Write the prime factors of 12 and 16. Simplify. = =
2 • 2 • 2 • 2 12 16
___ 3 4
___
So written in simplest form is

19. Write the fraction in simplest form.
Check It Out: Example 3B
Write the fraction in simplest form. 3 10
___ 3 10
___
The GCF of 3 and 10 is 1, so is already in simplest form.

20. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

21. Find two equivalent fractions for each given fraction. 1. 2.
Lesson Quiz
Find two equivalent fractions for each given fraction.
Find the missing number that makes the fractions equivalent.
Write each fraction in simplest form.
Possible answers: 4 10
___ 8 20
___ 2 5 , 7 14
___ 1 2
___ 14 28 , 2 7 __ 4 15 __ 20
___
___ = 6 = 75 21 4 8 __ 1 2 __ 7 49
___ 1 7
___

22. Lesson Quiz for Student Response Systems
1. Identify two equivalent fractions for
A C.
B D.

23. Lesson Quiz for Student Response Systems
2. Identify two equivalent fractions for .
A C.
B D.

24. Lesson Quiz for Student Response Systems
3. Identify the missing number that makes the given fractions equivalent.
A C. 6
B D. 9

25. Lesson Quiz for Student Response Systems
4. Identify the missing number that makes the given fractions equivalent.
A C. 40
B D. 48

26. Lesson Quiz for Student Response Systems
5. Identify the simplest form of the fraction
A C.
B D.