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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.

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Review

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. More Practice • Find the missing Number. • 67 81 = 81 • 56 + = 72 + 56 • 12 + 35 = + 12 • 13 6 = 6 ? • 67 • 72 • 35 • 13 ? ? ?

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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 ? ?

  13. 11) __ + 23 = 23 + 87 12) 13 + __ = 34 + 13 13) 9 12 = __ 9 14 ) 4 45 = 45 ___ 15) 3 ( 4 + 9 ) = 3 ( 9 + __)

  14. 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

  15. 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

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