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1-6 Multiplying and Dividing Real Numbers Vocabulary Review 1. How is a product different from a quotient? ____________________________________________________________________________ _______________________________________________________________________ 2. Circle the product of 12 and 4. Underline the quotient of 12 and 4. 3 8 16 48 Vocabulary Builder Related Term: multiplicative inverse Definition: Two numbers are reciprocals if their product is 1. Main Idea: To write the reciprocal of a fraction, switch the numerator and denominator of the fraction. 5 7 8 2 Examples: 45 and 4 , 28 and 27 , 5 and 15 , 112 and 3 Use Your Vocabulary 3. Draw a line from each expression in Column A to its reciprocal in Column B. Column A Column B 3 4 1 2 25 22 212 3 4 3 4 7 14 5 23 Chapter 1 2 3 22 Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. reciprocals b a and , where a b a lj0 and b lj0 reciprocal (noun) rih SIP ruh kul Key Concept Multiplying and Dividing Real Numbers The product or quotient of two real numbers with different signs is negative. The product or quotient of two real numbers with the same sign is positive. The quotient of 0 and any nonzero real number is 0. The quotient of any real number and 0 is undefined. ART 4. Write negative, positive, undefined, or zero for each result. 28(22) 5(29) FPO 049 940 5. Write 4 or (24) to make each equation true. 6? 5 24 6? 5 224 24 4 5 26 24 4 56 Problem 1 Multiplying Real Numbers Got It? What is each product? 6(215) 7 3 210 Q 5 R 12(0.2) (24) 2 7 3 6. In 6(215) and 210 Q 5 R , the signs of the numbers are the same / different . 7 3 So, the product of 6 and (215) and the product of 210 and 5 will be positive / negative . 7. Multiply. Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 6(215) 5 7 3 210 Q 5 R 5 8. In 12(0.2) and (24)(24) , the signs of the numbers are the same / different . 9. Multiply. 12(0.2) 5 (24) 2 5 (24) (24) 5 Problem 2 Simplifying Square Root Expressions Got It? What is the simplified form of !100? 10. Circle the equation that uses the positive square root of 100. 2 ? 50 5 100 4 ? 25 5 100 10 ? 10 5 100 11. Will the simplified form of !100 be positive or negative? Explain. ____________________________________________________________________________ _______________________________________________________________________ 12. The simplified form of !100 is . 23 Lesson 1-6 Problem 3 Dividing Real Numbers Got It? You make five withdrawals of equal amounts from your bank account. The total amount you withdraw is $360. What is the change in your account balance each time you make a withdrawal? 13. Complete the model. total amount divided by withdrawn Relate Write number of change in account is withdrawals balance each time â 5 14. The change in the account balance per withdrawal is 2$ . Property Inverse Property of Multiplication For every nonzero real number a, there is a multiplicative inverse a1 such that a Q a1 R 5 1. a b The reciprocal of a nonzero number of the form b is a . The product of a number and its reciprocal is 1, so the reciprocal of a number is its multiplicative inverse. Dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction. In a c a d Problem 4 Dividing Fractions Got It? What is the value of 34 4 Q 252 R ? Underline the correct word to complete each sentence. 15. The expression shows multiplication / division . 16. To divide fractions, multiply the first / second fraction by the reciprocal of the first / second fraction. 17. Simplify the expression below. 3 5 3 4 4 Q 22 R 5 4 ? ° 2 52 ¢ 5 Multiply by the reciprocal of 22 . Multiply. 20 5 Simplify. Got It? Reasoning Is 34 4 Q 252 R equivalent to 2 Q 34 4 52 R ? Explain. 5 18. Dividing a number by 2 is equivalent to multiplying the number by Chapter 1 24 . Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. general, b 4 d 5 b ? c for b, c, and d 2 0. 3 5 19. Simplify 2Q 4 4 2 R . 3 5 3 5 20. Is 4 4 Q2 2 R equivalent to 2Q 4 4 2 R ? Explain. ____________________________________________________________________________ _______________________________________________________________________ Lesson Check • Do you UNDERSTAND? Reasoning Use a number line to explain why 215 4 3 5 25. 21. In words, 215 4 3 means dividing 215 into equal groups. Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 22. To model 215 4 3 on a number line, start at 215. Then use arrows to show three equal groups. The first equal group is shown. Ľ15 Ľ14 Ľ13 Ľ12 Ľ11 Ľ10 Ľ9 Ľ8 Ľ7 Ľ6 Ľ5 Ľ4 Ľ3 Ľ2 Ľ1 0 23. What do the three arrows showing the equal groups represent? ____________________________________________________________________________ _______________________________________________________________________ 24. Divide: 215 4 3 5 . Math Success Check off the vocabulary words that you understand. Inverse Property of Multiplication multiplicative inverse reciprocal Rate how well you can multiply and divide real numbers. Need to review 0 2 4 6 8 Now I get it! 10 25 Lesson 1-6