Properties of REAL Numbers Opposites Two real numbers

Properties of REAL Numbers

Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other. EXAMPLES -100 AND 100 2 AND -2 9/15/2020 www. numberbender. com 2

Reciprocals • 9/15/2020 www. numberbender. com 3

Absolute Value • 9/15/2020 www. numberbender. com 4

Commutative Property of Addition a+b=b+a When adding two numbers, the order of the numbers does not matter. EXAMPLES 2 + 3 = 3 + 2 (-5) + 4 = 4 + (-5) 9/15/2020 www. numberbender. com 5

Commutative Property of Multiplication a×b=b×a When multiplying two numbers, the order of the numbers does not matter. EXAMPLES 2 × 3 = 3 × 2 (-3) × 24 = 24 × (-3) 9/15/2020 www. numberbender. com 6

Associative Property of Addition a + (b + c) = (a + b) + c When three numbers are added, it makes no difference which two numbers are added first. EXAMPLES 2 + (3 + 5) = (2 + 3) + 5 (4 + 2) + 6 = 4 + (2 + 6) 9/15/2020 www. numberbender. com 7

Associative Property of Multiplication a(bc) = (ab)c When three numbers are multiplied, it makes no difference which two numbers are multiplied first. EXAMPLES 2 × (3 × 5) = (2 × 3) × 5 (4 × 2) × 6 = 4 × (2 × 6) 9/15/2020 www. numberbender. com 8

Distributive Property a(b + c) = ab + ac Multiplication distributes over addition. EXAMPLES 2 (3 + 5) = (2 × 3) + (2 × 5) (4 + 2) × 6 = (4 × 6) + (2 × 6) 9/15/2020 www. numberbender. com 9

Additive Identity Property The additive identity property states that if 0 is added to a number, the result is that number. EXAMPLE 3 + 0 = 0 + 3 = 3 9/15/2020 www. numberbender. com 10

Multiplicative Identity Property The multiplicative identity property states that if a number is multiplied by 1, the result is that number. EXAMPLE 5 × 1 = 1 × 5 = 5 9/15/2020 www. numberbender. com 11

Additive Inverse Property The additive inverse property states that opposites add to zero. EXAMPLE 7 + (-7) = 0 and -4 + 4 = 0 9/15/2020 www. numberbender. com 12

Multiplicative Inverse Property • 9/15/2020 www. numberbender. com 13

PRACTICE EXERCISES 9/15/2020 www. numberbender. com 14

Identify which property justifies each of the following: 4 × (8 × 2) = (4 × 8) × 2 9/15/2020 www. numberbender. com 15

Identify which property justifies each of the following: 6 + 8 = 8 + 6 9/15/2020 www. numberbender. com 16

Identify which property justifies each of the following: 12 + 0 = 12 9/15/2020 www. numberbender. com 17

Identify which property justifies each of the following: 5(2 + 9) = (5 × 2) + (5 × 9) 9/15/2020 www. numberbender. com 18

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Identify which property justifies each of the following: 5 × 24 = 24 × 5 9/15/2020 www. numberbender. com 20

Identify which property justifies each of the following: 18 + (-18) = 0 9/15/2020 www. numberbender. com 21

Identify which property justifies each of the following: -34 × 1 = -34 9/15/2020 www. numberbender. com 22