Properties Of Integers 2eq59

Properties of integers 1. Commutative Property of Addition

Adding integers will have the same result regardless of the arrangement of the integers.

Example 1 Is 2 + 6 = 6 + 2 ? Yes

Explanation: 2+6=8 6+2=8 By Commutative Property of Addition: 2 + 6 = 6 + 2 Example 2 By Commutative Property of Addition, 3 + 4 = ? 4+3

Explanation: In Commutative Property of Addition, the integers on the other side are interchanged. 3+4=4+3

2. Commutative Property of Multiplication

Multiplying integers will have the same result regardless of the arrangement of the integers..

The sum will not change even if the integers are grouped differently.

Example 1 Is 3 x 5 = 5 x 3? Yes

Explanation: 3 x 5 = 15 5 x 3 = 15 By Commutative Property of Multiplication: 3x5=5x3 Example 2 By Commutative Property of Multiplication, 4 x 6 = ? 6x4

Explanation: In Commutative Property of Multiplication, the integers on the other side are interchanged. 4x6=6x4

3. Associative Property of Addition

Adding integers will have the same result regardless of the grouping.

The sum will not change even if the integers are grouped differently. Example 1 Is 1 + (4 + 6) = (1 + 4) + 6? Yes

Explanation: 1 + (4 + 6) = 1 + 10 = 11 (1 + 4) + 6 = 5 + 6 = 11 By Associative Property of Addition: 1 + (4 + 6) = (1 + 4) + 6 Example 2 By Associative Property of Addition, 3 + (5 + 4) = ? (3 + 5) + 4

Explanation: In Associative Property of Addition, the integers on the other side can be grouped differently. 3 + (5 + 4) = (3 + 5) + 4

4. Associative Property of Multiplication

Multiplying integers will have the same result regardless of the grouping.

The product will not change even if the integers are grouped differently.

Example 1 Is 3 x (5 x 6) = (3 x 5) x 6? Yes

Explanation: 3 x (5 x 6) = 3 x 30 = 90 (3 x 5) x 6 = 15 x 6 = 90 By Associative Property of Multiplication: 3 x (5 x 6) = (3 x 5) x 6 Example 2 By Associative Property of Multiplication, 4 x (5 x 2) = ? (4 x 5) x 2

Explanation: In Associative Property of Multiplication, the integers on the other side can be grouped differently. 4 x (5 x 2) = (4 x 5) x 2

5. Distributive Property of Addition and Multiplication

Distributive property involves the addition of integers being multiplied by another integer.

Each integer inside the parenthesis is multiplied by the integer outside the parenthesis, then the resulting products are added together.

Example 1 Is 2 x (1 + 3) = (2 x 1) + (2 x 3) ? Yes

Explanation: 2 x (1 + 3) = 2 x 4 = 8 (2 x 1) + (2 x 3) = 2 + 6 = 8 By Distributive Property of Multiplication and Addition: 2 x (1 + 3) = (2 x 1) + (2 x 3) Example 2 By Distributive Property of Addition and Multiplication, 4 x (2 + 3) = ? (4 x 2) + (4 x 3)

Explanation: In Distributive Property of Addition and Multiplication, each integer inside the parenthesis is multiplied by the integer outside the parenthesis, then the resulting products are added together.

4 x (2 + 3) = (4 x 2) + (4 x 3)

Multiplying integers Multiplying integers is just multiplying the numbers normally but there are 2 conditions to :

1. If the two integers have the same sign, then their product is positive. 2. If the two integers have different signs, then their product is negative.

Problem 1 6 x –9 = ? -54

Explanation: 6 and –9 have different signs. So the product is negative. 6 x 9 = 54 The product is –54. Problem 2 –8 x –7 = ? 56

Explanation: –8 and –7 have the same sign. So the product is positive. 8 x 7 = 56 The product is 56.

Dividing integers Similar to multiplying integers, dividing integers is just dividing the numbers normally but there are 2 conditions to :

1. If the two integers have the same sign, then their quotient is positive. 2. If the two integers have different signs, then their quotient is negative.

Parts of a Division Problem

Example 1 45 ÷ –3 = ? -15

Explanation: 45 and –3 have different signs. So the quotient is negative. 45 ÷ 3 = 15

The quotient is –15. Example 2 –72 ÷ –8 = ? 9

Explanation: –72 and –8 have the same sign. So the quotient is positive. 72 ÷ 8 = 9 The quotient is 9.