Multiplying and Dividing Integers 2.4 Multiplying and Dividing Integers

Consider the following pattern of products. Chapter 1 / Whole Numbers and Introduction to Algebra Multiplying Integers Consider the following pattern of products. First factor decreases by 1 each time. 3  5 = 15 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.

Chapter 1 / Whole Numbers and Introduction to Algebra 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.

Chapter 1 / Whole Numbers and Introduction to Algebra 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

Chapter 1 / Whole Numbers and Introduction to Algebra Multiplying Integers Product of Like Signs ( + )( + ) = + (–)(–) = + Product of Different Signs (–)( + ) = – ( + )(–) = –

Chapter 1 / Whole Numbers and Introduction to Algebra 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. ( – ) ( – ) ( – ) ( – ) = ( + ) ( – ) ( – ) ( – ) ( – ) ( – ) = ( – )

Division of integers is related to multiplication of integers. Chapter 1 / Whole Numbers and Introduction to Algebra Dividing Integers Division of integers is related to multiplication of integers. 3 2 6 = · because = · – 3 2 – 6 because – 3 (– 2) 6 = · because – 2 = 3 – 6 because (– 2) · – 6 – 2

Chapter 1 / Whole Numbers and Introduction to Algebra Dividing Integers Chapter 1 / Whole Numbers and Introduction to Algebra 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

Chapter 1 / Whole Numbers and Introduction to Algebra Dividing Numbers Chapter 1 / Whole Numbers and Introduction to Algebra Quotient of Like Signs Quotient of Different Signs