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
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: NS1.1

4. Vocabulary
equivalent fractions
improper fraction
mixed number

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

6. In the diagram = . These are called
equivalent fractions because they are different expressions for the same nonzero number. 3 5 6 10 15 25 =
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.

7. 8 5 3 5 = 1 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

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

9. Additional Example 1: Finding Equivalent Fractions5 7
Find two fractions equivalent to .
5  2 1 10 14 =
Multiply the numerator and
denominator by 2.
7  2
5  3 1 15 21
Multiply the numerator and
denominator by 3. =
7  3
Remember!
A fraction with the same numerator and
denominator, such as is equal to 1.
2 2

10. 5 7
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 14 15 21

11. Additional Example 3A: Determining Whether Fractions are Equivalent
Determine whether the fractions in each pair are equivalent. 4 6 28 42
and
Simplify both fractions and compare. 4 6
4 ÷ 2
6 ÷ 2 1 2 3 = = 28 42
28 ÷ 14
42 ÷ 14 2 3 = 1 =
are equivalent because both are equal to .
and 4 6 28 42 2 3

12. Additional Example 3B: Determining Whether Fractions are Equivalent
Determine whether the fractions in each pair are equivalent. 6 10 20 25
and
Simplify both fractions and compare. 6 10
6 ÷ 2
10 ÷ 2 1 3 5 = = 20 25
20 ÷ 5
25 ÷ 5 4 5 1 = =
are not equivalent because their simplest
and 20 25 6 10
forms are not equal.

13.  A. Write as a mixed number.
Additional Example 4: 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. +
Use the result to
write the improper
fraction. 2 3
3  7 + 2 23 3 = = 7 3 

14. 1 1 Check It Out! Example 1 6 12 Find two fractions equivalent to .
6  2 1 12 24 =
Multiply the numerator and
denominator by 2.
12  2
6 ÷ 2
12 ÷ 2 3 6
Divide the numerator and
denominator by 2. 1 =

15. 1 Check It Out! Example 2 15 45 Write the fraction in simplest form.
Find the GCD of 15 and 45.
15 = 3 • 5
The GCD is 15 = 3 • 5.
45 = 3 • 3 • 5 15 45
15 ÷ 15
45 ÷ 15 1 3 1
Divide the numerator and
denominator by 15. = =

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

17. 8  Check It Out! Example 4 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 1 2
= 2
Use the quotient and remainder to write the mixed number.
= 2 1 3
B. Write 8
as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator. +
Use the result to
write the improper
fraction. 1 3
3  8 + 1 25 3 8 = = 3 

18. 1. Write two fractions equivalent to .
Lesson Quiz 12 24 1 2 3 6 ,
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