2. Preview
Warm Up
California Standards
Lesson Presentation

3. 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

4. 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)

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 .
Additional Example 1: Finding Equivalent Fractions 5 7
Find two fractions equivalent to .
5  2 10 14 =
Multiply the numerator and denominator by 2.
7  2
5  3 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

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

11. Additional Example 2: Writing Fractions in Simplest Form18 24
Write the fraction in simplest form.
Find the GCD of 18 and 24.
18 = 2 • 3 • 3
The GCD is 6 = 2 • 3.
24 = 2 • 2 • 2 • 3 18 24
18 ÷ 6
24 ÷ 6 3 4 = =
Divide the numerator and denominator by 6.

12. Write the fraction in simplest form.
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 = =
Divide the numerator and denominator by 15.

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

14. 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 2 3 = = 28 42
28 ÷ 14
42 ÷ 14 2 3 = = 4 6 28 42 2 3
and
are equivalent because both are equal to .

15. 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 3 5 = = 20 25
20 ÷ 5
25 ÷ 5 4 5 = =
are not equivalent because their simplest
and 20 25 6 10
forms are not equal.

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 = = 6 18
6 ÷ 6
18 ÷ 6 1 3 = = 3 9 6 18 1 3
and
are equivalent because both are equal to .

17. Check It Out! Example 3B
Determine whether the fractions in each pair are equivalent. 4 12 9 48
and
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 their simplest
and 9 48 4 12
forms are not equal.

18. 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

19.  (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. + 2 3
3  7 + 2 23 3 =
Use the result to write the improper fraction. = 7 3 

20. 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
= 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 

21. 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