I CAN write equivalent fractions I CAN write equivalent fractions. I CAN write a fraction in simplest form.

Vocabulary equivalent fractions simplest form

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 = =

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.

Find two equivalent fractions for . You Try! 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.

Example 2: Multiplying and Dividing to Find Equivalent Fractions A. 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 ___ =

Example 2: Multiplying and Dividing to Find Equivalent Fractions B. 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, 5, by the same number, 20. = • 20 100 4 5 __ 80 100 ___ So is equivalent to . 4 5 __ 80 100 ___ =

is equivalent to is equivalent to You Try! Example 2 Find the missing number that makes the fraction equivalent. 3 9 __ A. ___ 3 9 __ 9 27 ___ = is equivalent to 27 B. 2 4 __ ___ 40 = 2 4 __ 40 80 ___ is equivalent to

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

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

Write each fraction in simplest form. You Try! Example 3 Write each fraction in simplest form. A. 12 12 16 _______ ÷ 4 3 4 __ ___ = 16 ÷ 4 ÷ 5 2 7 __ B. 10 10 35 _______ ___ = 35 ÷ 5

Reflection CAN YOU write equivalent fractions? CAN YOU write a fraction in simplest form?

Find two equivalent fractions for each given fraction. 1. 2. Lesson Quiz Find two equivalent fractions for each given fraction. 1. 2. Find the missing number that makes the fractions equivalent. 3. 4. Write each fraction in simplest form. 5. 6. 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 ___

HOMEWORK p. 170: 1-16,29-36