4 5 Equivalent Fractions Learn to write equivalent

4 -5 Equivalent Fractions Learn to write equivalent fractions.

4 -5 Equivalent Fractions Vocabulary equivalent fractions simplest form

4 -5 Equivalent Fractions that represent the same value are equivalent fractions. So are equivalent fractions. 1 2 = 2 4 = 4 8

4 -5 Equivalent Fractions Additional Example 1: Finding Equivalent Fractions Find two equivalent fractions for 10 ___ 12 = 15 ___ 18 = 10 ___. 12 5 __ 6 The same area is shaded when the rectangle is divided into 12 parts, 18 parts, and 6 parts. 10 ___ 15 ___ 5 __ So 12 , 18 , and 6 are all equivalent fractions.

4 -5 Equivalent Fractions Check It Out: Example 1 Find two equivalent fractions for 4 __ 6 = 8 ___ 12 = 4 __ 6 . 2 __ 3 The same area is shaded when the rectangle is divided into 6 parts, 12 parts, and 3 parts. 4 , ___ 8 , and __ 2 are all equivalent fractions. So __ 6 12 3

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

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

4 -5 Equivalent Fractions Check It Out: Example 2 A Find the missing number that makes the fraction equivalent. 3 __ 9 = ___ 27 3 • 3 ______ 9 = ____ 9 • 3 27 3 __ So 9 In the denominator, 9 is multiplied by 3 to get 27. Multiply the numerator, 3, by the same number, 3. 9 ___ is equivalent to 27. 3 __ 9 = 9 ___ 27

4 -5 Equivalent Fractions Check It Out: Example 2 B Find the missing number that makes the fraction equivalent. 2 __ 4 = 40 ___ 2 • 20 ____ 40 ______ = 4 • 20 80 2 __ So 4 In the numerator, 2 is multiplied by 20 to get 40. Multiply the denominator by the same number, 20. 40 ___ is equivalent to 80. 2 __ 4 = 40 ___ 80

4 -5 Equivalent Fractions 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.

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

4 -5 Equivalent Fractions Additional Example 3 A Continued Method 2: Use prime factorization. 20 ___ 48 = 2 • 5 _________ 5 = ___ 2 • 2 • 3 12 So 20 ___ 48 Write the prime factors of 20 and 48. Simplify. 5 ___ written in simplest form is 12. 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.

4 -5 Equivalent Fractions Additional Example 3 B: Writing Fractions in Simplest Form Write the fraction in simplest form. 7 ___ 10 7 is already The GCF of 7 and 10 is 1 so ___ 10 in simplest form.

4 -5 Equivalent Fractions Check It Out: Example 3 A Write each fraction in simplest form. 12 ___ 16 12 ___ The GCF of 12 and 16 is 4, so 16 is not in simplest form. Method 1: Use the GCF. 12 ÷ 4 _______ 16 ÷ 4 = 3 __ 4 Divide 12 and 16 by their GCF, 4.

4 -5 Equivalent Fractions Check It Out: Example 3 A Continued Method 2: Use prime factorization. 12 ___ 16 = 2 • 3 _______ 2 • 2 • 2 3 = ___ 4 Write the prime factors of 12 and 16. Simplify. 12 written in simplest form is ___ 3. So ___ 16 4

4 -5 Equivalent Fractions Check It Out: Example 3 B Write the fraction in simplest form. 3 ___ 10 3 The GCF of 3 and 10 is 1, so ___ is already in 10 simplest form.