Dividing Fractions and Mixed Numbers LESSON 3-5 Problem of the Day Trent bought 2 CDs one week, 6 the following week, and 10 in the third week. If he continues this pattern, how many CDs will he buy in the seventh week? 26 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Check Skills You’ll Need (For help, go to Lesson 3-4.) 1. Vocabulary Review Which operation do you use to find a product? Find each product. 2. • 3. • 4. 50 • 5. 2 • 1 3 7 2 3 5 9 1 2 9 10 2 9 4 5 Check Skills You’ll Need 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Check Skills You’ll Need Solutions 1. multiplication 2 7 3 1 • 2 7 • 1 1 • = • = 5 • 1 9 • 2 5 18 9 1 2 = • = 2. 3. 9 10 50 1 5 5 • 9 1 • 1 50 • = • = = 45 1 2 9 4 5 20 4 • 1 1 • 1 1 = 4. 5. 2 • = • 1 1 4 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Definition – new terms – concepts to know Reciprocal – Two numbers are reciprocals if their product is 1. To find the reciprocal of a fraction, interchange the numerator and denominator To divide by a fraction, multiply by its reciprocal 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Steps to follow Follow these steps to divide fractions and mixed numbers Re-write mixed numbers as improper fractions as needed Multiply by the reciprocal of the divisor Multiply numerators Multiply denominators Simplify } } OR cross-cancel } common factors Algebra: 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Additional Examples – dividing by a fraction Find ÷ 3 10 2 5 3 10 2 5 ÷ = • 3 10 5 2 Multiply the reciprocal of , which is . = 3 • 5 10 • 2 2 1 Divide 5 and 10 by their GCF, which is 5. = 3 4 Simplify. Quick Check 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Additional Examples – Dividing by mixed numbers Find 4 ÷ 1 . 2 3 4 = ÷ 14 3 7 4 Write the mixed numbers as improper fractions. 2 3 4 ÷ 1 Multiply by the reciprocal of , which is . = • 14 3 4 7 = 14 • 4 3 • 7 2 1 Divide 14 and 7 by their GCF, which is 7. = 8 3 Multiply. = 2 2 3 Write as a mixed number. Quick Check 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Additional Examples – word problems You have a piece of yarn that is 12 ft long. You need to cut it into strips that are 1 ft long. How many strips will you have? 1 2 4 1 4 2 To find how many 1 -ft long strips are in 12 ft, divide 12 by 1 . 1 2 4 ÷ 12 ÷ 1, or 12 Estimate 12 Write the mixed numbers as improper fractions. 1 2 4 ÷ = ÷ 12 25 5 Multiply the reciprocal of , which is . 25 2 4 5 = • = 25 • 4 2 • 5 Divide 25 and 5 by their GCF, 5. Divide 4 and 2 by their GCF, 2. 1 2 5 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Additional Examples (continued) = = 10 10 1 Simplify. There are ten 1 -ft strips of yarn in 12 ft. 1 4 2 Check for Reasonableness The answer, 10, is close to the estimate, 12. The answer is reasonable. Quick Check 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Lesson Quiz Find each quotient. 1. ÷ 2. ÷ 3. 1 ÷ 2 4. 3 ÷ 1 8 3 4 2 3 3 8 1 6 1 7 9 5 6 2 5 2 7 1 5 55 72 16 3 7 3-5

Dividing Fractions and Mixed Numbers LESSON 3-5 Homework Lesson 3-5: p. 144 – 145: # 10 – 48 e Quiz tomorrow on Lessons 3-1 to 3-4 3-5