Dividing Fractions and Mixed Numbers 3-11 Dividing Fractions and Mixed Numbers Course 2 Warm Up Problem of the Day Lesson Presentation

Dividing Fractions and Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers Warm Up Multiply. 7 9 3 6 7 18 1. · 9 8 6 5 27 20 7 or 1 2. · 2 77 5 or 15 1 5 3. 2 · 7 1 2 1 4 25 8 or 3 1 4. 2 · 1

Dividing Fractions and Mixed Numbers Course 2 3-11 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

Learn to divide fractions and mixed numbers. Course 2 3-11 Dividing Fractions and Mixed Numbers Learn to divide fractions and mixed numbers.

Insert Lesson Title Here Course 2 3-11 Dividing Fractions and Mixed Numbers Insert Lesson Title Here Vocabulary reciprocal

Dividing Fractions and Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers When you divide 8 by 4 you find how many 4’s there are in 8. Similarly, when you divide 2 by , you find how many ’s there are in 2. 1 3 There are six ’s in 2. 1 3

Dividing Fractions and Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1. The reciprocal of is 3 because 1 3 1 3 · 3 = · 1. To divide by a fraction, find its reciprocal and then multiply. 2 ÷ 1 3 = 2 · 3 = 6

Additional Example 1: Dividing Fractions Course 2 3-11 Dividing Fractions and Mixed Numbers Additional Example 1: Dividing Fractions Divide. Write each answer in simplest form. 3 7 2 5 ÷ A. 3 7 2 5 3 7 5 2 2 5 ÷ = · Multiply by the reciprocal of . 3 7 · 5 = · 2 15 14 14 1 = or 1 3 8 B. ÷ 12 3 8 1 3 8 Multiply by the reciprocal of 12. ÷ 12 = · 12 1 3 8 1 · Simplify. = 12 4 1 = 32

Dividing Fractions and Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 1 Divide. Write each answer in simplest form. 3 5 1 2 ÷ A. 3 5 1 2 3 5 2 1 1 2 ÷ = · Multiply by the reciprocal of . 3 5 · 2 = · 1 6 5 1 = or 1 5 3 4 B. ÷ 3 3 4 1 3 4 Multiply by the reciprocal of 3. ÷ 3 = · 3 1 3 4 1 · Simplify. = 3 1 1 = 4

Insert Lesson Title Here Course 2 3-11 Dividing Fractions and Mixed Numbers Insert Lesson Title Here Additional Example 2: Dividing Mixed Numbers Divide. Write each answer in simplest form. 2 3 1 4 A. 5 ÷ 1 Write mixed numbers as improper fractions. 2 3 17 3 5 4 5 1 4 ÷ 1 = ÷ 17 3 4 5 5 4 = · Multiply by the reciprocal of . 68 15 = or 4 8 15 3 4 1 2 B. ÷ 2 Write 2 as an improper fraction. 1 2 3 4 1 2 3 4 5 2 ÷ 2 = ÷ 5 2 3 4 2 5 = · Multiply by the reciprocal of . 1 3 · 2 Simplify. = 4 · 5 2 3 10 =

Additional Example 2: Dividing Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers Additional Example 2: Dividing Mixed Numbers Divide. Write the answer in simplest form. 2 3 13 27 C. 8 ÷ 8 2 3 ÷ 13 27 = 26 3 ÷ 13 27 Write 8 as an improper fraction. 2 3 = 26 3 · 27 13 Multiply by the reciprocal of . 13 27 2 9 = 26 3 · 27 13 1 1 = 18 1 or 18

Insert Lesson Title Here Course 2 3-11 Dividing Fractions and Mixed Numbers Insert Lesson Title Here Check It Out: Example 2 Divide. Write each answer in simplest form. 2 3 1 2 A. 3 ÷ 1 Write mixed numbers as improper fractions. 2 3 11 3 3 2 3 1 2 ÷ 1 = ÷ 11 3 2 3 3 2 = · Multiply by the reciprocal of . 22 9 = or 2 4 9 3 5 2 5 B. ÷ 1 Write 1 as an improper fraction. 2 5 3 5 2 5 3 5 7 5 ÷ 1 = ÷ 7 5 3 5 5 7 = · Multiply by the reciprocal of . 1 3 · 5 Simplify. = 5 · 7 1 3 7 =

Dividing Fractions and Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2 Divide. Write the answer in simplest form. 1 5 18 5 C. 7 ÷ 7 1 5 ÷ 18 = 36 5 ÷ 18 Write 7 as an improper fraction. 1 5 = 36 5 · 5_ 18 Multiply by the reciprocal of . 18 5 2 1 = 36 5 · 18 1 1 = 2 1 or 2

Additional Example 3: Social Studies Application Course 2 3-11 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 1 2 times longer will the golden dollar stay in circulation? 1 2 30 1 3 2 30 ÷ 1 = ÷ Write the number as an improper fraction. 30 1 2 3 3 2 · = Multiply by the reciprocal of . 10 30 · 2 = Simplify. 1 · 3 1 20 1 = or 20 The golden dollar will stay in circulation about 20 times longer than paper currency.

Dividing Fractions and Mixed Numbers Course 2 3-11 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 3 7 times longer will the queen ant live? 3 7 3 1 3 7 3 ÷ = ÷ Write the number as an improper fraction. 3 1 7 3 3 7 · = Multiply by the reciprocal of . 1 3 · 7 = Simplify. 1 · 3 1 7 1 = or 7 The queen ant will live 7 times longer than the worker ant.

Insert Lesson Title Here Course 2 3-11 Dividing Fractions and Mixed Numbers Insert Lesson Title Here Lesson Quiz Divide. Write each answer in simplest form. 4 5 1. 8 ÷ 10 5 9 4 9 40 or 2. 1 8 ÷ 1 10 3. 3 5 ÷ 6 3 4. 2 1 ÷ 7 35 44 1 4 3 4 5. There are 5 yards of silk in a roll. If it takes of a yard to make one designer scarf, how many scarves can be made from the roll? 7