Multiplying and dividing integers
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The document summarizes rules for multiplying and dividing integers: - The product of integers with like signs is positive, while the product of integers with unlike signs is negative. - The product of integers with an even number of negative factors is positive, while the product of integers with an odd number of negative factors is negative. - The quotient of integers with like signs is positive, while the quotient of integers with unlike signs is negative.
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2) The Quotient of Powers Property allows you to divide one power by another by subtracting the exponents.
3) The Power of a Power Property allows you to raise a power to another exponent by multiplying the exponents.
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Refresh on Distributive Property. Lecture given on Sept. 22nd, 2008. Adaptation of previously created power point.
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Multiplying and dividing integers
- 2. Let’s Remember The product of two integers with like signs is positive. The product of two integers with unlike signs is negative. The product of integers with even number of negative factors is positive. The product of integers with odd number of negative factors is negative.
- 3. Multiplying Integers with Like Signs Multiplying Integers with Unlike Signs 1. (3)(4) = 12 2. (-3)(-4) = 12 3. (-4)(-6) = 24 4. (4)(6) = 24 5. (-5)(-5) = 25 1. (-3)(4) = -12 2. (6)(-1) = -6 3. (3)(-6) = -18 4. (-2)(5) = -10 5. (-8)(2) = -16
- 4. Multiplying Integers with Even Number of Negative Factors Multiplying Integers with Odd Number of Negative Factors 1. (-4)(2)(-3) = 24 2. (-4)(3)(-2)(5) = 120 3. (-4)(-2)(2)(-3)(-1) = 48 4. (2)(-1)(4)(-5)(-3)(-2) = 240 5. (-1)(1)(-1)(-1)(-1)(1)(-1)(-1) = 1 1. (4)(2)(-3) = -24 2. (-4)(3)(2)(5) = -120 3. (-4)(-2)(2)(3)(-1) = -48 4. (-2)(-2)(-2) = -8 5. (-1)(-1)(-1)(-1)(-1) = -1
- 5. Let’s Remember The quotient of two integers with like signs is positive. The quotient of two integers with unlike signs is negative.
- 6. Dividing Integers with Like Sign Dividing Integers with Unlike Sign 1. 8 ÷ 4 = 2 2. (-8) ÷ (-4) = 2 3. 12 ÷ 4 = 3 4. −12 −4 = 3 5. −5 −7 = 5 7 1. -8 ÷ 4 = -2 2. 8 ÷ (-4) = -2 3. 15 ÷ (-5) = -3 4. 30 −6 = -5 5. −24 18 (6) = - 4 3 or -1 1 3
- 8. Let’s Apply Simplify the following. 1. (2)(9) = 18 2. (-8)(2) = -16 3. (-3)(-9) = 27 4. (-1)(-3) = 3 5. (-9)(-1)(5) = 45 6. (-24) ÷ 6 = -4 7. (8) ÷ 1 = 8 8. 15 −3 = -5 9. −6 −48 (6) = 1 8 10. 10 −10 = -1