3-11 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

3-11 Dividing Fractions and Mixed Numbers Warm Up Multiply · · · · or or or 3 1

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

3-11 Dividing Fractions and Mixed Numbers MA.7.A.3.2 …Divide…fractions…including solving problems in everyday contexts. Also MA.7.A.5.2 Sunshine State Standards

3-11 Dividing Fractions and Mixed Numbers Vocabulary reciprocal multiplicative inverse

3-11 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 · 3 = 1313 · 3131 = 3333 = 1. Dividing by a number is the same as multiplying by its reciprocal.

3-11 Dividing Fractions and Mixed Numbers Additional Example 1: Dividing Fractions Divide. Write each answer in simplest form. A ÷ ÷ 2525 = 3737 · 5252 = 3737 · 5 · 2 = or Multiply by the reciprocal of B ÷ ÷ = 3838 · 1 = 3838 · = Multiply by the reciprocal of Simplify.

3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 1 Divide. Write the answer in simplest form. A ÷ 1212 B ÷ ÷ 1212 = 3535 · 2121 = 6565 = ÷ 20 = 4747 · 1 1 =

3-11 Dividing Fractions and Mixed Numbers Divide. Write each answer in simplest form. A ÷ ÷ = 17 3 ÷ 5454 = 17 3 · 4545 = or Write mixed numbers as improper fractions. Multiply by the reciprocal of 5454 B ÷ ÷ = 3434 ÷ 5252 = 3 4 · 2525 = 3·2 4·5 1 2 = 3 10 Write 2 as an improper fraction Multiply by the reciprocal of Simplify.. Additional Example 2: Dividing Mixed Numbers

3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2A Divide. Write the answer in simplest form ÷ ÷ = 3535 ÷ 7575 = · =

3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2B 1616 ÷ ÷ = 19 6 ÷ = 4949 · = = Divide. Write the answer in simplest form.

3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2C Divide. Write the answer in simplest form ÷ ÷ 5959 = 45 8 · ÷ 5959 = = 81 8 =

3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2D Divide. Write the answer in simplest form ÷ ÷ 8383 = 38 9 · ÷ 2323 = = =

3-11 Dividing Fractions and Mixed Numbers Additional Example 3: Consumer Application Anthony bought several pounds of fruit at the farmer’s market. He first purchased strawberries. Then he picked up 1 times as many pounds of bananas as strawberries. He finally selected 3 more pounds of apples than bananas. Anthony purchased 6 pounds of apples. How many pounds of strawberries did he buy? Subtract the fractions then subtract the integers. The amount of bananas purchased is 2 lb Step 1: Find the amount of bananas Anthony purchased. 6 – =5 – = = Regroup: 6 = Simplify. Work backward from the amount of apples Anthony purchased to the amount of strawberries.

3-11 Dividing Fractions and Mixed Numbers Additional Example 3: Consumer Application Write mixed numbers as improper fractions The amount of strawberries purchased is 1 lb. 2  =  or = Multiply by the reciprocal of. Simplify. Step 2: Find the amount of strawberries purchased. The amount is times as much as the amount of bananas purchased, so divide the amount of bananas by =  = 

3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 3 Hannah is putting her loose change into rolls. She has the most number of penny rolls. There are times as many dime rolls as penny rolls. There are times as many quarter rolls as dime rolls. If there are 15 quarter rolls, how many penny rolls does Hannah have? There are 15 quarter rolls There are 15 ÷ 3 10 = 15 1 · = 50 dime rolls 1 5 There are 50 ÷ 5 6 = · 6565 = 60 penny rolls 1 10

3-11 Dividing Fractions and Mixed Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

3-11 Dividing Fractions and Mixed Numbers Lesson Quiz 10 Divide. Write each answer in simplest form ÷ ÷ ÷6 5. Roy cuts yard of silk from a roll. Susan then takes of the remaining silk on the roll. If there are 5 yards of silk after Susan’s cut, how much was on the roll before Roy’s cut? or ÷ yards 3434

3-11 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

3-11 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

3-11 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

3-11 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