OPERATIONS WITH NEGATIVE NUMBERS

Addition

Example 1 :

Evaluate : -3 + 8.

Solution :

First number is -3 ----> start at -3.

A positive number 8 is added ----> move 8 units to the right of -3.

So, -3 + 8 = 5.

Example 2 :

Evaluate : 4 + (-2).

Solution :

First number is 4 ----> start at 4.

A negative number -2 is added ----> move 2 units to the left of 4.

So, 4 + (-2) = 2.

Example 3 :

Evaluate : -8 + 5.

Solution :

First number is -8 ----> start at -8.

A positive number 5 is added ----> move 5 units to the right of -8.

So, -8 + 5 = -3.

Example 4 :

Evaluate : -1 + (-3).

Solution :

First number is -1 ----> start at -1.

A negative number -3 is added ----> move 3 units to the left of -1.

So, -1 + (-3) = -4.

Subtraction

Example 5 :

Evaluate : 5 - 7

Solution :

First number is 5 ----> start at 5.

A positive number 7 is subtracted ----> move 7 units to the left of 5.

So, 5 - 7 = -2.

Example 6 :

Evaluate : 4 - (-2).

Solution :

First number is 4 ----> start at 4.

A negative number -2 is subtracted ----> move 2 units to the right of 4.

So, 4 - (-2) = 6.

Example 7 :

Evaluate : -2 - 3.

Solution :

First number is -2 ----> start at -2.

A positive number 3 is subtracted ----> move 3 units to the left of -2.

So, -2 - 3 = -5.

Example 8 :

Evaluate : -5 - (-3).

Solution :

First number is -5 ----> start at -5.

A negative number -3 is subtracted ----> move 3 units to the right of -5.

So, -5 - (-3) = -2.

Multiplication

Example 9 :

Evaluate : 5 x (-7)

Solution :

5 times 7 is equal to 35.

Since a positive number is multiplied by a negative number, the answer is negative.

So, 5 x (-7) = -35.

Example 10 :

Evaluate : (-4) x 9.

Solution :

4 times 9 is equal to 36.

Since a negative number is multiplied by a positive number, the answer is negative.

So, (-4) x 9 = -36.

Example 11 :

Evaluate : (-3) x (-6).

Solution :

3 times 6 is equal to 18.

Since a negative number is multiplied by a negative number, the answer is positive.

So, (-3) x (-6) = 18.

Division

Example 12 :

Evaluate : 15 ÷ (-3).

Solution :

15 divided by 3 is equal to 5.

Since a positive number is divided by a negative number, the answer is negative.

So, 15 ÷ (-3) = -5.

Example 13 :

Evaluate : (-20) ÷ 5.

Solution :

20 divided by 5 is equal to 4.

Since a negative number is divided by a positive number, the answer is negative.

So, (-20) ÷ 5 = -4.

Example 14 :

Evaluate : (-28) ÷ (-4).

Solution :

28 divided by 4 is equal to 7.

Since a negative number is divided by a negative number, the answer is positive.

So, (-28) ÷ (-4) = 7.

Example 15 :

8 - 2 x (-1)³

Solution :

= 8 - 2 x (-1)³

= 8 - 2 x (-1)

= 8 + 2

= 10

Example 16 :

15 - 6 x (-3)

Solution :

= 15 - 6 x (-3)

= 15 + 18

= 33

Example 17 :

-2 x (3 - 5)²

Solution :

= -2 x (3 - 5)²

= -2 x (-2)²

= -2 x 4

= -8

Example 18 :

5 - 14 ÷ (-2) + 1

Solution :

= 5 - 14 ÷ (-2) + 1

Performing division, we get

= 5 + 7 + 1

= 13

Example 19 :

6 - 7 - (-2)²

Solution :

= 6 - 7 - (-2)²

= 6 - 7 - 4

= 6 - 11

= -5

Example 20 :

(-2)² - -2²

Solution :

= (-2)² - -2²

= 4 - (-4)

= 4 + 4

= 8

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