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Multiplying & Dividing Integers

Mathematics, Grade 9

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• Multiplication is repeated addition. • Multiplication with integers is commutative • Division is the inverse of multiplication • The same sign rules apply to multiplication and division of integers. – 5 – 4 – 3 – 2 – 1 – 10 – 12 – 11 – 9 – 8 – 7 – 6 5 4 3 2 1 10 11 12 9 8 6 0 7 4 x 3 means to add 3 four times: • Similarly, the product of 4 and – 3 means to add – 3 four times: Multiplying Integers Dividing Integers (-3) (-3) (-3) (-3) 4 groups of -3 = -12 3 + 3 + 3 + 3 –3 + (–3) + (–3) + (–3) –3 x (–2) = 6 5 x (–3) = –15 –15 ÷ (–3) = 5 –5 x (–3) = 15 15 ÷ (–3) = –5 6 ÷ (–3) = –2 –3 x 4 = –4 x (3) Example Rule You multiply integers just as you do whole numbers, except that you determine the sign of the product using these rules. If the factors have different signs, the product is negative. If the factors have the same signs, the product is positive. If one factor is zero, the product is zero. – 7 x 4 = – 28 – 4 x 0 = 0 – 8 x – 9 = 72 6 x 2 = 12 5 x – 3 = – 15 Example Rule • You cannot divide an integer by 0. If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals 0. – 12 ÷ 4 = – 3 32 ÷ 4 = 8 15 ÷ (– 3) = – 5 – 21 ÷ (– 3) = 7 0 9 = 0 0 = 0 – 8 same signs product is positive different signs quotient is negative © C opyright NewPath Learning. All Rights Reserved. 93-4606 www.newpathlearning.com Multiplying & Dividing Integers

• Multiplication is • Multiplication with integers is commutative • Division is the inverse of multiplication • The same sign rules apply to multiplication and division of integers. – 5 – 4 – 3 – 2 – 1 – 10 – 12 – 11 – 9 – 8 – 7 – 6 5 4 3 2 1 10 11 12 9 8 6 0 7 4 x 3 means to times: • Similarly, the product of 4 and -3 means to times: Multiplying Integers Dividing Integers 4 groups of -3 = -12 3 + 3 + 3 + 3 –3 + (–3) + (–3) + (–3) –3 x (–2) = 6 5 x (–3) = –15 –15 ÷ (–3) = 5 –5 x (–3) = 15 15 ÷ (–3) = –5 6 ÷ (–3) = –2 –3 x 4 = –4 x ( –3 ) Example Rule You multiply integers just as you do whole numbers, except that you determine the sign of the product using these rules. If the factors have different signs, the product is negative. If the factors have the same signs, the product is positive. If one factor is zero, the product is zero. Example Rule • You cannot divide an integer by 0. If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals 0. Key Vocabulary Terms • commutative • dividend • divisor • factor • integer • product • quotient • repeated addition © Copyright NewPath Learning. All Rights Reserved. 93-4606 www.newpathlearning.com Multiplying & Dividing Integers \|xiBAHBDy01674ozX

Multiplying & Dividing Integers

Mathematics, Grade 9

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