1. Multiplying and Dividing Integers
2.4
Multiplying and Dividing Integers

2. 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.

3. 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.

4. 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

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

6. 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.
( – ) ( – ) ( – ) ( – ) = ( + )
( – ) ( – ) ( – ) ( – ) ( – ) = ( – )

7. 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

8. 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

9. 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