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Name_____________________________________ Class____________________________ Date________________ Lesson 2-3 Multiplying and Dividing Rational Numbers 1 Multiply real numbers NAEP 2005 Strand: Number Properties and Operations Topic: Number Operations 2 Divide real numbers Local Standards: ____________________________________ Lesson Objectives All rights reserved. Vocabulary and Key Concepts. Identity Property of Multiplication For every real number n, Examples 1 ? 5 1 ? (5) Multiplication Property of 1 For every real number n, Examples 1 ? 5 . Multiplication Property of Zero For every real number n, Examples 35 ? 0 35 ? 0 . –1 ? (5) Multiplying Numbers With the Same Sign The product of two positive numbers or two negative numbers is Examples 5 ? 2 . . 5(2) © Pearson Education, Inc., publishing as Pearson Prentice Hall. Multiplying Numbers With Different Signs The product of a positive number and a negative number, or a negative number and a positive number, is Examples 3(6) . 3 ? 6 Dividing Numbers With the Same Sign The quotient of two positive numbers or two negative numbers is Examples 6 3 . 6 (3) Dividing Numbers With Different Signs The quotient of a positive number and a negative number, or a negative number and a positive number, is Examples 6 3 = . 6 (3) = Inverse Property of Multiplication For every nonzero real number a, there is a multiplicative inverse 1a such that . Examples 5(15) –5(15) The multiplicative inverse of a nonzero rational number ba is A reciprocal is Daily Notetaking Guide Algebra 1 Lesson 2-3 23 Name_____________________________________ Class____________________________ Date ________________ Examples. 1 Multiplying Numbers Simplify the expression 6(34). The product of a positive number and () 6 34 a negative number is Write . as a mixed number. a 2 Evaluating Expressions Use the function t 5.5(1,000 )°F to calculate the ( 1,000 5.5 ( ) Divide within parentheses. F Multiply. t 5.5 ) Substitute All rights reserved. change in temperature t for an increase in altitude a of 7,200 ft. for a. 3 Simplifying Exponential Expressions Use the order of operations to simplify each expression. ? ? ? ) b. (0.2)4 ( Write as repeated multiplication. Simplify. )?( )?( )?( ) Write as repeated multiplication. Simplify. Quick Check. 1. Simplify each expression. a. 4(6) c. 4.9(8) 24 Algebra 1 Lesson 2-3 b. 10(5) d. 23(34) Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. ( a. 0.24 Name_____________________________________ Class____________________________ Date ________________ © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 2. Use the expression in Example 2 to find the change in temperature if a balloon rises 4,500 ft from the ground. Daily Notetaking Guide Algebra 1 Lesson 2-3 25 Name_____________________________________ Class____________________________ Date ________________ Examples. 4 Dividing Numbers Simplify the expression 54 (9). 54 (9) The quotient of a negative number and a negative number is . 5 Evaluating Expressions Evaluate xy 4z2 for x 4, y 2, and z 4. ( )2 Substitute ( ) Simplify the power. 4 4 2 ( ) for x, for y, and for z. All rights reserved. ( ) ( ) xy 4z Divide and multiply. Subtract. p 6 Division Using the Reciprocal Evaluate r for p 32 and r 34. 32 ( ) ( ) Rewrite the equation. Substitute Multiply by for p and for r. , the reciprocal of 3 . 4 Simplify. Quick Check. Simplify each expression. 3. a. 43 b. (2)4 5. Evaluate each expression for x 8, y 5, and z 3. a. 3x (2z) y 10 26 Algebra 1 Lesson 2-3 b. 2z x 2y 4. a. 42 7 b. 8 (2) x 6. Evaluate y for x 8 and y 2 4 5 Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. p r

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