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(7) lesson 4.6 - Multiply Fractions

• 1. Course 2, Lesson 4-6 Use the draw a diagram strategy to solve Exercises 1-4 1. The Rockwells have driven 180 miles, which is about of the way to their family reunion. How far is the total distance to their family reunion? 2. Tomi is eating a candy bar that is 12 inches long. She has already eaten of the candy bar. How many inches of the candy bar does she have left? 3. Toki has filled or 12 ounces of his glass. Find the total capacity of his glass. 4. If an 8-ounce serving of yogurt provides 10% of the daily requirement for calcium, what percent of the calcium requirement would a 20-ounce serving provide? 2 3 5 8 3 4
• 2. Course 2, Lesson 4-6 Answers 1. 270 miles 2. 3. 16 4. 25% 1 4 2
• 3. WHAT happens when you add, subtract, multiply, and divide fractions? The Number System Course 2, Lesson 4-6
• 4. Course 2, Lesson 4-6 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.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real- world contexts. • 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.
• 5. Course 2, Lesson 4-6 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.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. 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.
• 6. • To multiply fractions • To multiply mixed numbers Course 2, Lesson 4-6 The Number System
• 7. Course 2, Lesson 4-6 The Number System Words To multiply fractions, multiply the numerator and multiply the denominators. Examples Numbers Algebra 1 2 1 x 2 2 x or 2 3 2 x 3 6  or , where , 0 d a c a c ac b d b d b bd  
• 8. 1 Need Another Example? 2 Step-by-Step Example 1. Multiply × . Write in simplest form. Simplify. Multiply the numerators. = Multiply the denominators. =
• 9. Answer Need Another Example? Find × . Write in simplest form.
• 10. 1 Need Another Example? 2 3 Step-by-Step Example 2. Multiply 2 × – . Write in simplest form. Simplify. Write 2 as and – as .= Multiply the numerators. = Multiply the denominators. = or –1
• 11. Answer Need Another Example? Find 6 × – . Write in simplest form. –2
• 12. 1 Need Another Example? 2 Step-by-Step Example 3. Multiply × – . Write in simplest form. Divide 2 and 8 by their GCF, 2.= Multiply.= or – 4 1
• 13. Answer Need Another Example? Find × – . Write in simplest form.
• 14. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 4. Find × 4 . Write in simplest form. Rename 4 as an improper fraction, . = × 4 = 2 7 Estimate Rename the mixed number. Think Half of 4 is 2 and half of 2 fifths is 1 fifth. 11 1 = = = Multiply. Simplify. Simplify. Use mental math. The mixed number 4 is equal to 4 + . So, × 4 = 4 + . Use the Distributive Property to multiply, then add mentally. Rewrite the sum as a mixed number. Check for Reasonableness Divide 2 and 22 by their GCF, 2. Using either method, the answer is 2 .
• 15. Answer Need Another Example? Find × 6 . Write in simplest form.
• 16. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 5. Humans sleep about of each day. Let each year equal 365 days. Determine the number of days in a year the average human sleeps. Rename the mixed number as an improper fraction. × 360 = 120Estimate Divide 3 and 1,461 by their GCF, 3. Multiply. Then rename as a mixed number. 121 ≈ 120Check for Reasonableness Find × 365 . × 365 = × 7 ×= 487 1 = or 121 The average human sleeps 121 days each year.
• 17. Answer Need Another Example? In a 48-hour bike race, Mel rode 289 miles. His father rode as far as Mel did. Find the number of miles his father rode. 217 mi
• 18. How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide fractions? Course 2, Lesson 4-6 The Number System
• 19. How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide fractions? Course 2, Lesson 4-6 The Number System Sample answers: • When you multiply fractions, multiply the numerators and multiply the denominators. • When you multiply mixed numbers, rename the mixed numbers as improper fractions.
• 20. Find . Write your answer in simplest form. Course 2, Lesson 4-6 Ratios and Proportional RelationshipsThe Number System           2 6- × - 3 8
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