(7) Lesson 4.8 - Divide Fractions
- 1. Course 2, Lesson 4-8 Complete. Round to the nearest hundredth if necessary. 1. 16 in. ≈ cm 2. 35 g ≈ lb 3. 7 pt ≈ L 4. 15 km ≈ mi 5. Gina’s dog weighs 39 pounds. How many kilograms does it weigh? 6. Thomas ran 3.5 miles. How many kilometers did he run? 7. A recipe calls for 4 cups of milk. How many milliliters of milk are needed?
- 2. Course 2, Lesson 4-8 Answers 1. 40.64 2. 0.08 3. 3.31 4. 9.32 5. 17.69 6. 5.63 7. 946.36 mL
- 3. WHAT happens when you add, subtract, multiply, and divide fractions? The Number System Course 2, Lesson 4-8
- 4. Course 2, Lesson 4-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Number System • 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. • 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. • 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. • 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
- 5. Course 2, Lesson 4-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Number System Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 5 Use appropriate tools strategically.
- 6. • To divide fractions • To divide mixed numbers Course 2, Lesson 4-8 The Number System
- 7. Course 2, Lesson 4-8 The Number System Words To divide by a fraction, multiply by its multiplicative inverse, or reciprocal. Examples Numbers Algebra 7 7 8 8 3 4 4 3 , where , , 0 a c a d b c d b d b c
- 8. 1 Need Another Example? 2 3 Step-by-Step Example 1. Find ÷ 5. Multiply by the reciprocal of , which is . Multiply. A whole number can be written as a fraction over 1.
- 9. Answer Need Another Example? Find ÷ 4. Write in simplest form.
- 10. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 2. Find ÷ – . Write in simplest form. Divide 4 and 2 by their GCF, 2. Multiply. Estimate 1 ÷ = –2 2 1 = – or –1 Check for Reasonableness – ≈ –2 Multiply by the reciprocal of – , which is – .
- 11. Answer Need Another Example? Find ÷ – . Write in simplest form.
- 12. 1 Need Another Example? 2 3 4 Step-by-Step Example 3. Find ÷ 3 . Write in simplest form. Multiply by the reciprocal of , which is . Multiply. Rename 3 a fraction greater than one. Divide out common factors. 1 1 5 1
- 13. Answer Need Another Example? Find ÷ 2 . Write in simplest form.
- 14. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 4. The side pieces of a butterfly house are 8 inches long. How many side pieces can be cut from a board measuring 49 inches long? Rename the mixed numbers as fractions greater than one. Multiply. Use compatible numbers. 48 ÷ 8 = 6 Divide out common factors. 7 To find how many side pieces can be cut, divide 49 by 8 . Estimate Multiply by the reciprocal of , which is . 3 1 1 2 = or 6 So, 6 side pieces can be cut. Check for Reasonableness Compare to the estimate. 6 = 6
- 15. Answer Need Another Example? A bottling machine needs to be restocked with new lids every 2 hours. If the machine runs 19 hours, how many times will it have to be restocked with lids? 7 times
- 16. How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide fractions? Course 2, Lesson 4-8 The Number System
- 17. How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide fractions? Course 2, Lesson 4-8 The Number System Sample answers: • The multiplicative inverse of a fraction is its reciprocal. • When you divide by a fraction, multiply by its multiplicative inverse.
- 18. Course 2, Lesson 4-8 Ratios and Proportional RelationshipsThe Number System Explain how your work with multiplying rational numbers helped you with this lesson.