Properties of addition and multiplication
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This document discusses properties of addition and multiplication. It explains the commutative, associative, identity, and distributive properties for both addition and multiplication. Examples are provided to illustrate each property. Practice problems are included for students to identify which properties are being used. The document also shows how to solve equations by applying properties of operations.
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The document discusses the distributive property in algebra. It defines terms, like terms, and constant terms. It explains that the distributive property allows a number or variable outside a set of parentheses to be distributed to each term inside. Examples show using the distributive property to expand expressions like (a + b)(c), and to combine like terms. It provides mental math examples of using the distributive property to calculate total costs. Students are assigned problems applying the distributive property, with instructions to show the steps and use of the property from start to finish.
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Properties of addition and multiplication
- 1. C O L E G I O M Y R A N G 5 T H G R A D E M R S . S H I A R A A G O S T O Properties of Addition and Multiplication
- 2. Properties of Addition and Multiplication There are 4 main properties, 3 of which are used both in Addition and Multiplication. Associative (+) (×) Commutative (+) (×) Identity (+) (×) Distributive
- 3. Properties of Addition Commutative Property of Addition If you change the order of addends the sum stays the same. 12 + 24 = 24 + 12 Associative Property of Addition If you change the grouping of addends the sum stays the same. 15 + (52 + 6) = (15 + 52) + 6 Identity Property of Addition The sum of any number and zero is the same number. 28 + 0 = 28
- 4. Properties of Multiplication Commutative Property of Multiplication If you change the order of factors the product stays the same. 12 x 24 = 24 x 12 Associative Property of Multiplication If you change the grouping of factors the product stays the same. 15 x (52 x 6) = (15 x 52) x 6 Identity Property of Multiplication The product of any number and one is the same number. 28 x 1 = 28
- 5. Distributive Property The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. 5 x (17 + 8) = (5 x 17) + (5 x 8) It can also be used with subtraction: 2 x (10 – 8) = (2 x 10) – (2 x 8)
- 6. Properties Practice Identify the properties that are used in each exercise. 52 + 85 = 85 + 52 Commutative Property of Addition 65 x 3 = 3 x 65 Commutative Property of Multiplication 12 x (6 + 8) = (12 x 6) + (12 x 8) Distributive Property 5 + 0 = 5 Identity Property of Addition
- 7. Solve Using Properties What property(ies) can you use to solve the following exercises? (24 x 5) – (24 x 1) We can use the Distributive Property. 24 x (5 – 1) 24 x 4 = 96
- 8. Solve Using Properties 9 + 65 + 1 Using the Commutative Property 9 + 1 +65 10 + 65 = 75 Using the Associative Property 9 + (65 +1) 9 + 66 = 75
- 9. Solve Using Properties 12 x ___ = 12 Identity Property of Multiplication 49 + 56 = ___+ 49 Commutative Property of Addition 60 + (52 + ___)= (60+ 52) + 39 Associative Property of Multiplication 8 x 298 8 x (300 - ___ ) (8 x 300) – (8 x ___) _____ – ____ = 56 39 1 1 1 2,400 8 2,392 Distributive Property