2.4 Multiply Real Numbers

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1 24 Multiply Real Numbers Goal p Multiply real numbers Your Notes VOCABULARY Multiplicative identity THE SIGN OF A PRODUCT The product of two real numbers with the same sign is Examples: 5(2) 5 24(25) 5 The product of two real numbers with different signs is Examples: 5(23) 5 28(4) 5 Example 1 Find the product Multiply real numbers a 27(23) 5 Same signs: product is b 3(4)(22) 5 (22) Multiply 3 and 4 5 Different signs: product is c } 1 4 (216)(23) 5 (23) Multiply } 1 and Same signs: product is 38 Lesson 24 Algebra 1 Notetaking Guide Copyright Holt McDougal All rights reserved

2 24 Multiply Real Numbers Goal p Multiply real numbers Your Notes VOCABULARY Multiplicative identity The number 1; The identity property states the product of a and 1 is a THE SIGN OF A PRODUCT The product of two real numbers with the same sign is positive Examples: 5(2) (25) 5 20 The product of two real numbers with different signs is negative Examples: 5(23) (4) Example 1 Find the product Multiply real numbers a 27(23) 5 21 Same signs: product is positive b 3(4)(22) 5 12 (22) Multiply 3 and Different signs: product is negative c } 1 4 (216)(23) 5 24 (23) Multiply } 1 and Same signs: product is positive 38 Lesson 24 Algebra 1 Notetaking Guide Copyright Holt McDougal All rights reserved

3 Checkpoint Find the product 1 24(26) 2 23(22)(27) PROPERTIES OF MULTIPLICATION Commutative Property The order in which two numbers are multiplied does not change the product a p b 5 p Example: 3 p 4 5 p Associative Property The way you group three numbers when multiplying does not change the product (a p b) p c 5 p ( p ) Example: (2 p 3) p 4 5 p ( p ) Identity Property The product of a number and 1 is that number a p 1 5 p 5 Example: (22) p 1 5 Property of Zero The product of a number and 0 is 0 a p 0 5 p 5 Example: 4 p 5 0 Property of 21 The product of a number and 21 is the opposite of the number a p (21) 5 p 5 Example: 25 p (21) 5 Copyright Holt McDougal All rights reserved Lesson 24 Algebra 1 Notetaking Guide 39

4 Checkpoint Find the product 1 24(26) 2 23(22)(27) PROPERTIES OF MULTIPLICATION Commutative Property The order in which two numbers are multiplied does not change the product a p b 5 b p a Example: 3 p p 3 Associative Property The way you group three numbers when multiplying does not change the product (a p b) p c 5 a p ( b p c ) Example: (2 p 3) p p ( 3 p 4 ) Identity Property The product of a number and 1 is that number a p p a 5 a Example: (22) p Property of Zero The product of a number and 0 is 0 a p p a 5 0 Example: 4 p Property of 21 The product of a number and 21 is the opposite of the number a p (21) 5 21 p a 5 2a Example: 25 p (21) 5 5 Copyright Holt McDougal All rights reserved Lesson 24 Algebra 1 Notetaking Guide 39

5 Example 2 Identify properties Identify the property illustrated by each expression Statement a 3 p Property Illustrated b t p 1 5 t c a p p a d n p (3 p 5) 5 (n p 3) p 5 e 27(21) 5 7 Checkpoint Identify the property illustrated 3 24 p p p 6 5 (4 p 5) p p (5 p 6) 6 4 p (21) Lesson 24 Algebra 1 Notetaking Guide Copyright Holt McDougal All rights reserved

6 Example 2 Identify properties Identify the property illustrated by each expression Statement Property Illustrated a 3 p Multiplicative property of zero b t p 1 5 t Identity property c a p p a Commutative property d n p (3 p 5) 5 (n p 3) p 5 Associative property e 27(21) 5 7 Multiplicative property of 21 Checkpoint Identify the property illustrated 3 24 p Multiplicative property of zero 4 6 p p 6 Commutative property 5 (4 p 5) p p (5 p 6) Associative property 6 4 p (21) 5 24 Multiplicative property of ]1 40 Lesson 24 Algebra 1 Notetaking Guide Copyright Holt McDougal All rights reserved

7 Example 3 Use properties Find the product (05)(22x)(6) Justify your steps (05)(22x)(6) 5 (22x)(05)(6) 5 (22x)(05 p 6) 5 (22x)(3) 5 3 p (22x) 5 [3 p (22)]x 5 26x Checkpoint Find the product Justify your steps } 2 (2)(3y) 8 (22)(a)(25) Homework Copyright Holt McDougal All rights reserved Lesson 24 Algebra 1 Notetaking Guide 41

8 Example 3 Use properties Find the product (05)(22x)(6) Justify your steps (05)(22x)(6) 5 (22x)(05)(6) Commutative property 5 (22x)(05 p 6) Associative property 5 (22x)(3) Product of 05 and 6 is p (22x) Commutative property multiplication 5 [3 p (22)]x Associative property 5 26x Product of 3 and 22 is 26 Checkpoint Find the product Justify your steps } 2 (2)(3y) 2 1 } 2 (2)(3y) 5 (21)(3y) Product of 2 } 1 and 2 is [(21) p 3]y Associative property 5 23y Multiplicative property of 21 Homework 8 (22)(a)(25) (22)(a)(25) 5 (a)(22)(25) Commutative property 5 a p 10 Product of 22 and 25 is a Commutative property Copyright Holt McDougal All rights reserved Lesson 24 Algebra 1 Notetaking Guide 41

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