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Multiplying and Dividing Integers - Patterns and Rules

Learn about the patterns and rules when multiplying and dividing integers. Understand the relationships between positive and negative numbers. Helpful hints included.

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Multiplying and Dividing Integers - Patterns and Rules

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  1. Multiplying and Dividing Integers 2.4

  2. Multiplying Integers Consider the following pattern of products. 3  5 = 15 First factor decreases by 1 each time. Product decreases by 5 each time. 2  5 = 10 1  5 = 5 0  5 = 0 This pattern continues as follows. –1  5 = -5 –2  5 = -10 –3  5 = -15 This suggests that the product of a negative number and a positive number is a negative number.

  3. Multiplying Integers Observe the following pattern. 2  (–5) = –10 Product increases by 5 each time. 1  (–5) = –5 0  (–5) = 0 This pattern continues as follows. –1  (–5) = 5 –2  (–5) = 10 –3  (–5) = 15 This suggests that the product of two negative numbers is a positive number.

  4. Multiplying Integers The product of two numbers having the same sign is a positive number. 2  4 = 8 –2  (–4) = 8 • The product of two numbers having different signs is a negative number. 2  (–4) = –8 –2  4 = –8

  5. Multiplying Integers Product of Like Signs ( + )( + ) = + (–)(–) = + Product of Different Signs (–)( + ) = – ( + )(–) = –

  6. Helpful Hint If we let ( – ) represent a negative number and ( + ) represent a positive number, then ( – ) ( – ) = ( + ) The product of an even number of negative numbers is a positive result. ( – ) ( – ) ( – ) = ( – ) The product of an odd number of negative numbers is a negative result. ( – ) ( – ) ( – ) ( – ) = ( + ) ( – ) ( – ) ( – ) ( – ) ( – ) = ( – )

  7. Division of integers is related to multiplication of integers. Dividing Integers 6 = = 3 because 3 2 6 · 2 –6 = = –3 because –3 2 –6 · 2 6 = –3 because – 3 (–2) = 6 · – 2 (–2) = – 6 3 · –6 = 3 because – 2

  8. Dividing Integers The quotient of two numbers having the same sign is a positive number. –12 ÷ (–4 ) = 3 12 ÷ 4 = 3 The quotient of two numbers having different signs is a negative number. –12 ÷ 4 = –3 12 ÷ (–4) = –3

  9. Dividing Numbers Quotient of Like Signs Quotient of DifferentSigns

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