Learn to write equivalent fractions .

1. Learn to write equivalent fractions.

2. Vocabulary equivalent fractions simplest form

3. Fractions that represent the same value are equivalent fractions. So are equivalent fractions. 12 24 48 = =

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

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

6. 3 __ 5 3 ______ 5 12 3 ___ __ 20 5 3 12 __ ___ 5 20 Additional Example 2A: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. ___ In the denominator, 5 is multiplied by 4 to get 20. = 20 • 4 12 ____ Multiply the numerator, 3, by the same number, 4. = • 4 20 So is equivalent to . =

7. 4 __ 5 4 ______ 5 80 4 ___ __ 100 5 4 80 __ ___ 5 100 Additional Example 2B: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. 80 ___ In the numerator, 4 is multiplied by 20 to get 80. = • 20 80 ____ Multiply the denominator by the same number, 20. = • 20 100 So is equivalent to . =

8. 3 __ 9 3 ______ 9 9 3 ___ __ 27 9 3 9 __ ___ 9 27 Check It Out: Example 2A Find the missing number that makes the fraction equivalent. ___ In the denominator, 9 is multiplied by 3 to get 27. = 27 • 3 9 ____ Multiply the numerator, 3, by the same number, 3. = • 3 27 So is equivalent to . =

9. 2 __ 4 2 ______ 4 40 2 ___ __ 80 4 2 40 __ ___ 4 80 Check It Out: Example 2B Find the missing number that makes the fraction equivalent. 40 ___ In the numerator, 2 is multiplied by 20 to get 40. = • 20 40 ____ Multiply the denominator by the same number, 20. = • 20 80 So is equivalent to . =

10. 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.

11. 20 ___ 48 20 5 _______ __ 48 12 Additional Example 3A: Writing Fractions in Simplest Form Write each fraction in simplest form. 20 ___ 48 The GCF of 20 and 48 is 4, so is not in simplest form. Method 1: Use the GCF. ÷ 4 Divide 20 and 48 by their GCF, 4. = ÷ 4

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

13. 7 ___ 10 7 ___ 10 Additional Example 3B: Writing Fractions in Simplest Form Write the fraction in simplest form. The GCF of 7 and 10 is 1 so is already in simplest form.

14. 12 ___ 16 12 3 _______ __ 16 4 Check It Out: Example 3A Write each fraction in simplest form. 12 ___ 16 The GCF of 12 and 16 is 4, so is not in simplest form. Method 1: Use the GCF. ÷ 4 Divide 12 and 16 by their GCF, 4. = ÷ 4

15. 12 2 • 2 • 3 3 ___ ___ 16 4 12 3 ___ ___ 16 4 Check It Out: Example 3A Continued Method 2: Use prime factorization. Write the prime factors of 12 and 16. Simplify. _____________ = = 2 • 2 • 2 • 2 So written in simplest form is .

16. 3 ___ 10 3 ___ 10 Check It Out: Example 3B Write the fraction in simplest form. The GCF of 3 and 10 is 1, so is already in simplest form.