1. 4-5 Equivalent Fractions Course 1 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up List the factors of each number. 1. 8 2. 10 3. 16 4. 20 5. 30 1, 2, 4, 8 1, 2, 5, 10 1, 2, 4, 8, 16 Course 1 4-5 Equivalent Fractions 1, 2, 4, 5, 10, 20 1, 2, 3, 5, 6, 10, 15, 30

3. Problem of the Day John has 3 coins, 2 of which are the same. Ellen has 1 fewer coin than John, and Anna has 2 more coins than John. Each girl has only 1 kind of coin. Who has coins that could equal the value of a half-dollar? Ellen and Anna Course 1 4-5 Equivalent Fractions

4. Learn to write equivalent fractions. Course 1 4-5 Equivalent Fractions

5. Vocabulary equivalent fractions simplest form Insert Lesson Title Here Course 1 4-5 Equivalent Fractions

6. Course 1 4-5 Equivalent Fractions Fractions that represent the same value are equivalent fractions. So,, and are equivalent fractions. = = 1 2 __ 2 4 4 8 1212 2424 4848

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

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

9. Course 1 4-5 Equivalent Fractions Additional Example 2A: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. 3 5 __ 20 ___ = 3 5 ______ In the denominator, 5 is multiplied by 4 to get 20. 4 4 Multiply the numerator, 3, by the same number, 4. = 12 20 ____ So is equivalent to. 3 5 __ 12 20 ___ 3 5 __ 12 20 ___ =

10. Course 1 4-5 Equivalent Fractions Additional Example 2B: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. 4 5 __ 80 ___ = 4 5 ______ In the numerator, 4 is multiplied by 20 to get 80. 20 Multiply the denominator by the same number, 20. = 80 100 ____ So is equivalent to. 4 5 __ 80 100 ___ 4 5 __ 80 100 ___ =

11. Course 1 4-5 Equivalent Fractions Check It Out: Example 2A Find the missing number that makes the fraction equivalent. 3 9 __ 27 ___ = 3 9 ______ In the denominator, 9 is multiplied by 3 to get 27. 3 3 Multiply the numerator, 3, by the same number, 3. = 9 27 ____ So is equivalent to. 3 9 __ 9 27 ___ 3 9 __ 9 27 ___ =

12. Course 1 4-5 Equivalent Fractions Check It Out: Example 2B Find the missing number that makes the fraction equivalent. 2 4 __ 40 ___ = 2 4 ______ In the numerator, 2 is multiplied by 20 to get 40. 20 Multiply the denominator by the same number, 20. = 40 80 ____ So is equivalent to. 2 4 __ 40 80 ___ 2 4 __ 40 80 ___ =

13. Course 1 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.

14. Course 1 4-5 Equivalent Fractions 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. 20 48 ___ Method 1: Use the GCF. 20 48 _______ ÷ 4 Divide 20 and 48 by their GCF, 4. = 5 12 __

15. Course 1 4-5 Equivalent Fractions Additional Example 3A Continued Method 2: Use prime factorization. Write the prime factors of 20 and 48. Simplify. 20 48 ___ 5 12 ___ So written in simplest form is. Method 2 is useful when you know that the numerator and denominator have common factors, but you are not sure what the GCF is. Helpful Hint 20 48 ___ = 2 2 2 2 3 _________________ 2 2 5 = 5 12 ___

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

17. Course 1 4-5 Equivalent Fractions 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. 12 16 ___ Method 1: Use the GCF. 12 16 _______ ÷ 4 Divide 12 and 16 by their GCF, 4. = 3 4 __

18. Course 1 4-5 Equivalent Fractions Check It Out: Example 3A Continued Method 2: Use prime factorization. Write the prime factors of 12 and 16. Simplify. 12 16 ___ 3 4 So written in simplest form is. 12 16 ___ = 2 2 2 2 _____________ 2 2 3 = 3 4 ___

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

20. Lesson Quiz Find two equivalent fractions for each given fraction. Possible Answers: 1. 2. Find the missing number that makes the fractions equivalent. 3. 4. Write each fraction in simplest form. 5.6. Insert Lesson Title Here 6 Course 1 4-5 Equivalent Fractions 4 10 ___ 7 14 ___ 2 7 __ ___ 21 = 4 15 __ ___ 20 = 4 8 __ 7 49 ___ 1 7 1 2 __ 75 1 2 ___ 14 28 ___, 8 20 ___ 2 5,