EVALUATING EXPRESSIONS WITH POSITIVE AND NEGATIVE NUMBERS

All real numbers are either positive or negative. Number lines can be used to show the positions of positive and negative numbers.

When adding and subtracting positive and negative numbers, we use the following the rules.

Adding and Subtracting

+ + + = Add

- + - = Add

+ + - = Subtract

- + + = Subtract

Multiplying

+ ⋅ + = +

-   - = +

-   + = -

+   - = -

Note :

  • If the numbers are having the same signs like positive or negative, we add them and use the greater number sign for the answer.
  • If the numbers are having different signs, we subtract them and put the greater number sign for the answer.
  • When we multiply two numbers, we have to follow the multiplication rules.

Find :

Example 1 :

8 + - 5

Solution :

We use parentheses().

= 8 + (- 5)

By rule (+) . (-) = -, we get

= 8 - 3

= 3

Example 2 :

8 - - 5

Solution :

We use parentheses().

8 - (- 5)

By rule (-) . (-) = +, we get

= 8 + 5

= 13

Example 3 :

- 8 + - 5

Solution :

We use parentheses().

= (- 8) + (- 5)

Since the given numbers are having the same negative signs, we have to add them and put the negative sign.

= -13

Example 4 :

- 8 - - 5

Solution :

We use parentheses().

= (- 8) - (- 5)

By rule (-) . (-) = +, we get

= - 8 + 5

Since the given numbers are having the less positive and more negative signs, we have to subtract them and put the more negative sign.

= -3

Example 5 :

4 + - 9

Solution :

We use parentheses().

= 4 + (- 9)

By rule (+) . (-) = -, we get

= 4 - 9

= - 5

Example 6 :

4 - - 9

Solution :

We use parentheses().

= 4 - (- 9)

By rule (-) . (-) = +, we get

= 4 + 9

= 13

Example 7 :

- 4 + - 9

Solution :

We use parentheses().

= (- 4) + (- 9)

Since the given numbers are having the same negative signs, we have to add them and put the negative sign.

= -13

Example 8 :

- 4 - - 9

Solution :

We use parentheses ().

= (- 4) - (- 9)

By rule (-) . (-) = +, we get

= - 4 + 9

Since the given numbers are having the more positive and less negative signs, we have to subtract them and put the more positive sign.

= 5

Find :

Example 9 :

3 - - 2 + 4

Solution :

We use parentheses ().

= 3 - (- 2) + 4

Here the signs are multiplied.

By rule (-) . (-) = +, we get

= 3 + 2 + 4

= 9

Example 10 :

13 + - 5 - - 2

Solution :

We use parentheses ().

= 13 + (- 5) - (- 2)

Here the signs are multiplied.

By rule (-) . (-) = +, we get

= 13 + (- 5) + 2

By rule (+) . (-) = -, we get

13 - 5 + 2

= 8 + 2

= 10

Example 11 :

- 6 - - 4 + - 5

Solution :

We use parentheses ().

= (- 6) - (- 4) + (- 5)

Here the signs are multiplied.

By rule (-) . (-) = +, we get

= (- 6) + 4 + (- 5)

By rule (+) . (-) = -, we get

= (-6) + 4 - 5

= - 2 - 5

Since the negative signs, we have to add them and put the negative sign.

= - 7

Example 12 :

- 6 + - 1 - - 8

Solution :

We use parentheses ().

= (- 6) + (- 1) - (- 8)

= (- 6) + (- 1) + 8

= - 7 + 8

= 1

Example 13 :

5 - 12 - - 4

Solution :

We use parentheses ().

5 - 12 - (- 4)

= 5 - 12 + 4

= - 7 + 4

= - 3

Example 14 :

8 - 15 + - 11

Solution :

We use parentheses ().

8 - 15 + (- 11)

= 8 - 15 - 11

= 8 - 26

= - 18

Example 15 :

3 - - 1 - - 5

Solution :

We use parentheses ().

3 - (- 1) - (- 5)

= 3 + 1 + 5

= 9

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