1. 3-10 Dividing Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes Objective: students divide fractions and mixed numbers

2. 3-10 Dividing Fractions and Mixed Numbers Warm Up Multiply. 1. 7979 · 3636 2. 9898 · 6565 3. 1515 2 · 7 4. 2 1212 · 1 1414 7 18 27 20 7 or 1 2 77 5 5 or 15 25 8 8 or 3 1

3. 3-10 Dividing Fractions and Mixed Numbers Problem of the Day The Jeffers family is putting in a new fence around their yard. The yard is in the shape of a square. If they put nine fence posts on each side of the square, how many posts will be used? 32

4. 3-10 Dividing Fractions and Mixed Numbers Learn to divide fractions and mixed numbers.

5. 3-10 Dividing Fractions and Mixed Numbers Vocabulary reciprocal

6. 3-10 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1. The reciprocal of is 3 because 1313 1313 · 3 = 1313 · 3131 = 3333 = 1. Dividing by a number is the same as multiplying by its reciprocal. 2 ÷ 1313 = 2 · 3 = 6

7. 3-10 Dividing Fractions and Mixed Numbers Additional Example 1: Dividing Fractions Divide. Write each answer in simplest form. A. 3737 ÷ 2525 3737 ÷ 2525 = 3737 · 5252 = 3737 · 5 · 2 = 15 14 or 1 14 1 Multiply by the reciprocal of. 2525 B. 3838 ÷ 12 3838 ÷ = 3838 · 1 = 3838 · 1 1 4 = Multiply by the reciprocal of 12. 1 32 Simplify.

8. 3-10 Dividing Fractions and Mixed Numbers Check It Out: Example 1 Divide. Write each answer in simplest form. A. 3535 ÷ 1212 3535 ÷ 1212 = 3535 · 2121 = 3535 · 2 · 1 = 6565 or 1 5 1 Multiply by the reciprocal of. 1212 B. 3434 ÷ 3 3434 ÷ 3 = 3434 · 1 3 = 3434 · 1 3 1 1 = Multiply by the reciprocal of 3. 1 4 Simplify.

9. 3-10 Dividing Fractions and Mixed Numbers Divide. Write each answer in simplest form. A.5 2323 ÷ 1 1414 5 2323 ÷ 1 1414 = 17 3 ÷ 5454 = 17 3 · 4545 = 68 15 or 4 8 15 Write mixed numbers as improper fractions. Multiply by the reciprocal of 5454 B. 3434 ÷ 2 1212 3434 ÷ 2 1212 = 3434 ÷ 5252 = 3 4 · 2525 = 3·2 4·5 1 2 = 3 10 Write 2 as an improper fraction. 1212 Multiply by the reciprocal of. 5252 Simplify.. Additional Example 2: Dividing Mixed Numbers

10. 3-10 Dividing Fractions and Mixed Numbers Divide. Write the answer in simplest form. Additional Example 2: Dividing Mixed Numbers C. 8 2323 ÷ 13 27 8 2323 ÷ 13 27 = 26 3 ÷ 13 27 = 26 3 · 27 13 9 1 2 1 = 18 1 or 18 Write 8 as an improper fraction. 2323 Multiply by the reciprocal of. 13 27 = 26 3 · 27 13 ·

11. 3-10 Dividing Fractions and Mixed Numbers Divide. Write each answer in simplest form. A.3 2323 ÷ 1 1212 3 2323 ÷ 1 1212 = 11 3 ÷ 3232 = 11 3 · 2323 = 22 9 or 2 4 9 Write mixed numbers as improper fractions. Multiply by the reciprocal of 3232 B. 3535 ÷ 1 2525 3535 ÷ 1 2525 = 3535 ÷ 7575 = 3 5 · 5757 = 3·5 5·7 1 1 = 3 7 Write 1 as an improper fraction. 2525 Multiply by the reciprocal of. 7575 Simplify.. Check It Out: Example 2

12. 3-10 Dividing Fractions and Mixed Numbers Divide. Write the answer in simplest form. Check It Out: Example 2 C. 7 1515 ÷ 18 5 7 1515 ÷ 18 5 = 36 5 ÷ 18 5 = 36 5 · 5_ 18 1 1 2 1 = 2121 or 2 Write 7 as an improper fraction. 1515 Multiply by the reciprocal of. 18 5 = 36 5 · 18 ·

13. 3-10 Dividing Fractions and Mixed Numbers Additional Example 3: Social Studies Application The life span of a golden dollar coin is 30 years, while paper currency lasts an average of 1 years. How many 1212 times longer will the golden dollar stay in circulation? 30 ÷ 1 1212 = 30 1 ÷ 3232 Write the number as an improper fraction. = 30 1 · 2323 Multiply by the reciprocal of. 3232 = · Simplify. 30 2 1 3 10 1 = 20 1 or 20 The golden dollar will stay in circulation about 20 times longer than paper currency. ·

14. 3-10 Dividing Fractions and Mixed Numbers Check It Out: Example 3 The average life of a queen ant is approximately 3 years. The life span of a worker ant is year. How many 3737 times longer will the queen ant live? 3 ÷ 3737 = 3131 ÷ 3737 Write the number as an improper fraction. = 3131 · 7373 Multiply by the reciprocal of. 3737 = · Simplify. 3 7 1 3 1 1 = 7171 or 7 The queen ant will live 7 times longer than the worker ant. ·

15. 3-10 Dividing Fractions and Mixed Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

16. 3-10 Dividing Fractions and Mixed Numbers Lesson Quiz 10 Divide. Write each answer in simplest form. 1. 2. 8 ÷ 4545 5959 ÷ 1818 3. 3535 ÷6 5. There are 5 1414 yards of silk in a roll. If it takes 3434 of a yard to make one designer scarf, how many scarves can be made from the roll? 7 4 4949 40 9 or 1 10 3 4. 2 1212 ÷ 1717 35 44

17. 3-10 Dividing Fractions and Mixed Numbers 1. Divide. Write your answer in simplest form. 10 ÷ A. 6 B. 18 C. 12 D. 24 Lesson Quiz for Student Response Systems 5656

18. 3-10 Dividing Fractions and Mixed Numbers 2. Divide. Write your answer in simplest form. ÷ A. or 4 C. B.or 2D. Lesson Quiz for Student Response Systems 20 5 20 7 4 35 3 35 4747 1515 6767

19. 3-10 Dividing Fractions and Mixed Numbers 3. Divide. Write your answer in simplest form. ÷ 15 A. or 9C. B.24 D. or Lesson Quiz for Student Response Systems 75 8 1 24 3 15 5858 3838 1515

20. 3-10 Dividing Fractions and Mixed Numbers 4. Multiply. Write your answer in simplest form. 3 ÷ 5 A. C. or 1 B. D. 27 Lesson Quiz for Student Response Systems 50 81 23 27 81 50 1313 2525 31 50

21. 3-10 Dividing Fractions and Mixed Numbers 5. A blacksmith has 6 pounds of iron with him. If it takes of a pound to make one lock, how many locks can he make from the iron? A. 9 locks B. 11 locks C. 12 locks D. 13 locks Lesson Quiz for Student Response Systems 1212 1212