EVALUATING EXPRESSIONS WITH POSITIVE AND NEGATIVE NUMBERS

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

Example 16 :

The list shows four bank account transactions in July. Find the change C in the account balance.

Solution :

Change C = -40 + 50 + 75 - 50

= -90 + 125

= + 35

so, account balance is increased by $35 in July.

Example 17 :

Tell whether the sum is positive, negative, or zero without adding. Explain your reasoning.

a) −8 + 20

b)  30 + (−30)

c) −10 + (−18)

Solution :

a) −8 + 20

Since we have different signs for these two numbers, we have to subtract htem and put the greater number sign for the result. Then +12 is the result.

b)  30 + (−30)

Since we have two same numbers with different sign, then we subtract these two and get the result 0.

c) −10 + (−18)

Since we have same signs for these two numbers, we have to add them and put the greater number sign for the result. Then the answer is -28.

Example 18 :

Tell whether the statement is true or false. Explain your reasoning.

a) The sum of two negative integers is always negative.

b) An integer and its absolute value are always opposites.

Solution :

a) True, when we have two numbers of same signs we add them and put greater number sign for the result.

b) False, the result of absolute signs of negative number is also positive.