1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Name a common factor for each pair.
1. 5 and and 12
3. 20 and and 14
5. 6 and and 15
Possible answers: 5 3 4 2 2 1

3. California
Standards
Number Sense (NS2.4) - Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction).
Also covered: Number Sense (NS1.1)

4. Objective: You will learn how to identify, write, and convert between equivalent fractions and mixed numbers.

5. Vocabulary
equivalent fractions
improper fraction
mixed number

6. Different fractions can name the same number.3 5 6 10 15 25 = =

7. In the diagram = . These are called
equivalent fractions because they are different expressions for the same nonzero number. =
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.

8. Find two fractions equivalent to .
Example 1: Finding Equivalent Fractions 57
Find two fractions equivalent to .
5  2 10 14 =
Using “Cake”
7  2
5  3 15 21 =
7  3
Remember!
A fraction with the same numerator and
denominator, such as is equal to 1.
2 2

9. 5 7 10 14 15 21
The fractions , , and are equivalent,
but only is in simplest form. A fraction is in
simplest form when the greatest common divisor
of its numerator and denominator is 1.
5 7

10. Check It Out! Example 2 6 12
Find two fractions equivalent to .
Using “Cake”
6  2 12 24 =
12  2
6 ÷ 2
12 ÷ 2 3 6 =

11. Example 3: Writing Fractions in Simplest Form18 24
Write the fraction in simplest form.
Using Factors
Using “Cake”

12. Check It Out! Example 4 15 45
Write the fraction in simplest form.
Using Factors
Using “Cake”

13. To determine if two fractions are equivalent, simplify the fractions.

14. Example 5: Determining Whether Fractions are Equivalent
Determine whether the fractions in each pair are equivalent. 4 6 28 42
and
Simplify both fractions and compare.
Using “Cake” 4 6
4 ÷ 2
6 ÷ 2 2 3 = = 28 42
28 ÷ 14
42 ÷ 14 2 3 = = 4 6 28 42
and
are equivalent because both are equal to . 2 3

15. Example 5: Comparing Using Cross-Products
Determine whether the fractions in each pair are equivalent. 4 6 28 42
and

16. Example 6: Determining Whether Fractions are Equivalent
Determine whether the fractions in each pair are equivalent. 6 10 20 25
and
Using “Cake”
Simplify both fractions and compare. 6 10
6 ÷ 2
10 ÷ 2 3 5 = = 20 25
20 ÷ 5
25 ÷ 5 4 5 = =
are not equivalent because
and 20 25 6 10
their simplest forms are not equal.

17. Example 6: Comparing Using Cross-Products
Determine whether the fractions in each pair are equivalent. 6 10 20 25
and

18. Check It Out! Example 7
Determine whether the fractions in each pair are equivalent.
and 3 9 6 18
Simplify both fractions and compare.
Using “Cake” 3 9
3 ÷ 3
9 ÷ 3 1 3 = = 6 18
6 ÷ 6
18 ÷ 6 1 3 = = 3 9 6 18
and
are equivalent because both are equal to . 1 3

19. Example 7: Comparing Using Cross-Products
Determine whether the fractions in each pair are equivalent.
and 3 9 6 18 19

20. Check It Out! Example 8
Determine whether the fractions in each pair are equivalent. 4 12 9 48
and
Using “Cake”
Simplify both fractions and compare. 4 12
4 ÷ 4
12 ÷ 4 1 3 = = 9 48
9 ÷ 3
48 ÷ 3 3 16 = =
are not equivalent because
and 9 48 4 12
their simplest forms are not equal.

21. Example 8: Comparing Using Cross-Products
Determine whether the fractions in each pair are equivalent. 4 12 9 48
and 21

22. 8 3 = 1 5 5 8 5 3 5 is an improper 1 is a mixed fraction. Its
numerator is
greater than its
denominator. 8 5 3 5
number. It
contains both a
whole number
and a fraction.
= 1

23. Example 9: Converting Between Improper Fractions and Mixed Numbers
(A) Write 13 5
as a mixed number.
First divide the numerator by the denominator. 13 5 3 5
Use the quotient and remainder to write the mixed number.
= 2 2 3
(B) Write 7
as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator. + 2 3
3  7 + 2 23 3 =
Use the result to write the improper fraction. = 7 3 

24. 8  Check It Out! Example 10 (A) Write as a mixed number.15 6
(A) Write
as a mixed number.
First divide the numerator by the denominator. 15 6 3 6
= 2 1 2
= 2
Use the quotient and remainder to write the mixed number. 1 3
(B) Write 8
as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator. + 1 3
3  8 + 1
Use the result to
write the improper
fraction. 25 3 8 = = 3 

25. Home Learning
On-Line Tutoring
Melvin’s Dilemma
Equivalent Fractions?

26. 1. Write two fractions equivalent to .
Lesson Quiz 1 2 3 6 , 12 24
1. Write two fractions equivalent to
2. Determine if and are equivalent.
3. Write the fraction in simplest form.
4. Write as a mixed number.
5. Write 4 as an improper fraction.
5 12
4 10 no 16 48 1 3 17 8 1 8 2 3 7 31 7