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1.02 Properties Notes Name: _________________________________ Date: __________________ Period: ________ PROPERTIES OF ADDITION Properties Addition Multiplication The sum of any two real numbers is a unique real number. The product of any two real numbers is a unique real number. The order in which two numbers are added does not change the sum. The order in which two numbers are multiplied does not change the product. The way three numbers are grouped when adding does not change the sum. The way you group 3 numbers when multiplying does not change the product. The sum of a number and zero (0) is the number. The product of a number and one (1) is the number. The sum of a number and its opposite is zero (0). The product of a number and its reciprocal is 1. Closure Property Commutative Property Associative Property Identity Property Inverse Property How will I remember? How will I remember? Properties Definition Distributive Property A number outside parenthesis must be multiplied by everything inside. Practice with Properties of Addition Practice with Properties of Multiplication 1. (3 + 4) + 7 = 3 + (4 + 7) ________________ 1. a(b + c) = ab + bc ________________ 2. 7 – 0 = 7 ________________ 2. 4 ● 3 = 12 ________________ 3. 2 + 5 = 5 + 2 ________________ 3. 7(6 + 7) = 7 6 + 7 7 ________________ 4. 2 + (–2) = 0 ________________ 4. 7 ● 1 = 7 ________________ 5. 5 + (1 + 3) = (5 + 1) + 3 ________________ 5. 3 7 7 3 ________________ 6. 4 + 10 = 14 ________________ 6. 4 7. Which property is being demonstrated here? 1 1 4 7. Which property is being demonstrated here? 8●1=8 8 + (-8) = 0 A. Identity Property B. Inverse Property ________________ C. Associative Property A. B. D. Closure Property Identity Property Inverse Property C. Associative Property D. Closure Property 8. Identify which addition property is demonstrated below. 3+7=7+3 8. Identify which multiplication property is demonstrated below. A. B. A. B. commutative distributive C. D. associative inverse 9. Identify which addition property is demonstrated below. ( ab) c a (bc ) commutative distributive commutative distributive C. D. associative identity 10. Identify which addition property is demonstrated below. 5+0=5 A. B. commutative identity C. D. associative inverse associative inverse 9. Identify which multiplication property is demonstrated below. 6●5=5●6 (7 + 11) + 9 = 7 + (11 + 9) A. B. C. D. A. B. commutative distributive C. D. associative identity 10. Identify which multiplication property is demonstrated below. 1 2 1 2 1 A. B. commutative distributive C. D. associative inverse