Understanding Properties of Addition and Multiplication
Explore Commutative and Associative Properties, learn how numbers can be added or multiplied in different orders, with helpful practice examples.
Understanding Properties of Addition and Multiplication
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Presentation Transcript
40 Review 40 Add these numbers 15 + 25 = 25 + 15 = What do you find interesting about problem #1 and #2 ? Multiply these numbers 3) 5 x 13 = 4) 13 x 5 = What do you find interesting about problem #3 and #4 ? 65 65
The Commutative Property of Addition • In a Sum, you can add terms in any order. In Algebra a + b = b + a This means you can pick any number for a or b. In Arithmetic 6 + 9 = 9 + 6 6 + 9 = 15 9 + 6 = 15 Sum means addition
Commutative Property of Multiplication In a product, you can multiply factors in any order. Product- Means Multiplication. ab = ab a times b is the same as b times a. This means that you can pick any number for a or b. 4 7 = 7 4 : 4 times 7 is the same as 7 4. 4 7 = 28 7 4 = 28
Lets Practice • Tell me which one is using commutative property. • 13 + 47 = 14 + 47 • 23 + 17 = 17 + 23 • 24 - 16 = 16 – 24 • 10 + 21 = 21 + 10 No its not 13 + 47 = 60 14 + 47 = 61 • Commutative Property Addition • + 17 = 40 • 17 + 23 = 40 No its not 24 – 16 = 8 16 – 24 = -8 Commutative Property Addition 10 + 21 = 31 21 + 10 = 31
More practice • 12 3 = 3 12 • 33 1 = 1 33 • 10 4 = 4 11 • 6 12 = 12 6 Commutative Property Multiplication 1 2 * 3 = 36 3 * 12 = 36 Commutative Property Multiplication 33 * 1 = 33 1 * 33 = 33 No its not 10 * 4 = 40 4 * 11 = 44 No its not 6 12 = ½ 12 6 = 2
More Practice • Find the missing Number. • 67 81 = 81 • 56 + = 72 + 56 • 12 + 35 = + 12 • 13 6 = 6 ? • 67 • 72 • 35 • 13 ? ? ?
Review • (2 + 4) +5 = • 2+ (4 + 5) = • (23 + 4) + 12 = • 23 +( 4 + 12) = • Tell me what you found interesting? 2 sentences 11 11 39 39
Associative Property of Addition • Changing the grouping of terms will not change the sum. • Algebra : (a + b ) + c = a + ( b + c) • Arithmetic : (9 + 5) + 6 = 9 + ( 5 +6) (9 + 5 ) = 14 14 + 6 = 20 likewise 9 + ( 5+6) = 9 + 11 = 20
Associative Property of Multiplication • Changing the grouping of factors will not change the product. • In Algebra: (a b) c = a (b c) • In Arithmetic: ( 10 5) 3 = 10 ( 5 3) True: 10 5 = 50 50 3 = 150, likewise 10 (5 3) = 10 ( 15) = 150
Lets PracticeTell me which one is associative. • 8 + ( 9 + 7 ) = ( 8 + 9 ) + 7 • 2 ( 3 11) = (2 3 ) 11 • ( 6 + 9 ) + 11 = 6 +( 9 + 11) • (25 10 ) 10 = 25 ( 10 10) Associative: 8 + ( 9+ 7 ) = 8 + ( 16 ) = 24 (8+ 9) + 7 = (17) + 7 = 24 Associative: 2 ( 3 11) = 2 ( 33) = 66 (2 3) 11 = (6) 11 = 66 Associative: (6+ 9) + 11 = (15) + 11 = 26 6+ ( 9 + 11) = 6 + 20 = 26 Associative: (25 10 ) 10 = (250) 10 = 2500 25 ( 10 10 ) = 25 100 = 2500
More Practice • (35 20 ) = ( 2 35 ) 20 • ( 89 + 67 ) + 49 = + ( 67 + 49 ) • 2 (23 20 ) = ( 2 ) 20 • ( 80 + 27 ) + 49 = 80 + ( 27 + ) ? ? ? ? • 2 • 89 • 23 • 49
Practice • Tell me which one are Commutative. • 14 + 13 = 13 + 14 • 31 - 23 = 23 – 31 • 21 + 23 = 23 + 21 • 13 + 87 = 80 + 20 • 8 7 = 7 8 • 9 11 = 11 9 • 13 4 = 4 12 • 12 3 = 3 12 • 15 + 21 = 21 + • 12 = 25 12 ? ?
11) __ + 23 = 23 + 87 12) 13 + __ = 34 + 13 13) 9 12 = __ 9 14 ) 4 45 = 45 ___ 15) 3 ( 4 + 9 ) = 3 ( 9 + __)
Practice • 32+ (___ + 21) = (32 + 8) + 21 • 11+ ( 12 + 23) = ( __ + 12 ) + 23 • 67 ( 12 __) = ( 67 12 ) 32 • 44 ( 15 __ ) = ( 44 15 ) 39 • __ ( 12 56 ) = ( 78 12) 56 • 9 ( 31 22) = ( 9 31 ) ___ • 45+ ( 87 + 91 )= ( 45 + ___) + 91 • ___ + (135 + 12) = 78 + ( 135 + 12 ) • 34 ( 12 __ ) = ( 34 12 ) 45 • 123 ( 24 ___) = ( 123 24 ) 345
11) ( __ + 123 ) + 567 = 333( 123+ 567) 12) ( 987 + ___) + 938= 987 ( 746+ 938) 13) 3* ( 23* 2 ) = ( __ * 23 ) * 2 14) 8 * ( 11 * 2 ) = ( 8 * 11 ) * __ 15) 84 * ( 2 * 11) = ( __* 2 ) 11
