# ADD SUBTRACT MULTIPLY AND DIVIDE INTEGERS

## About "Add subtract multiply divide integers"

Add subtract multiply divide integers :

We have to simplify two or more numbers according to their signs.

• If we have same signs for two or more numbers, we have to add those numbers.
• If we have different signs for two numbers, we have to subtract the smaller number from greater number.

Always put greater number sign for the answer.

Multiplying integers :

The product of two integers with opposite signs is negative. The product of two integers with the same sign is positive. The product of 0 and any other integer is 0.

Dividing integers :

We used the relationship between multiplication and division to make conjectures about the signs of quotients of integers.

The division of two integers with opposite signs is negative. The division of two integers with the same sign is positive.

We can use multiplication to understand why division by zero is not possible.

Think about the division problem below and its related multiplication problem.

5 ÷ 0  =  ?   0 × ?  =  5

The multiplication sentence says that there is some number times 0 that equals 5. We already know that 0 times any number equals 0. This means division by 0 is not possible, so we say that division by 0 is undefined.

Let us see some example problems based on the above concept.

## Add subtract multiply divide integers - Examples

Example 1 :

Find the sum of (-34) + 50

Solution :

Since the signs are different, we have to subtract the smaller number from greater number and put greater number sign.

aaaaaaaaaaaaaaaaaaaa+ 50aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa- 34aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa------aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaa16aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa------aaaaaaaaaaaaaaaaaaaaaaaaaaa

Example 2 :

Find the sum of 38 + (-5)

Solution :

Since the signs are different, we have to subtract the smaller number from greater number and put greater number sign.

aaaaaaaaaaaaaaaaaaaa+ 38aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa05aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa------aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaa33aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa------aaaaaaaaaaaaaaaaaaaaaaaaaaa

Example 3 :

Find the sum of -45 + 9

Solution :

Since the signs are different, we have to subtract the smaller number from greater number and put greater number sign.

aaaaaaaaaaaaaaaaaaaa- 45aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa09aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa------aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa-36aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa------aaaaaaaaaaaaaaaaaaaaaaaaaaa

Example 4 :

Find the difference of -8 - (-6)

Solution :

=  -8 + 6

Since the signs are different, we have to subtract smaller number from greater number and and put greater number sign.

aaaaaaaaaaaaaaaaaaaaa- 8aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaa+ 6aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa----aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa-02aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaa------aaaaaaaaaaaaaaaaaaaaaaaaaaa

## Multiply and divide integers

Example 5 :

Multiply : (13)(-3).

Solution :

Step 1 :

Determine the sign of the product.

13 is positive and -3 is negative. Since the numbers have opposite signs, the product will be negative.

Step 2 :

Find the absolute values of the numbers and multiply them.

|13|  =  13 and |-3|  =  3

13 x 3  =  39

Step 3 :

Assign the correct sign to the product.

13(-3)  =  -39

Hence, the product is -39.

Example 6 :

Multiply : (-5)(-8).

Solution :

Step 1 :

Determine the sign of the product.

-5 is negative and -8 is negative. Since the numbers have the same sign, the product will be positive.

Step 2 :

Find the absolute values of the numbers and multiply them.

|-5|  =  5 and |-8|  =  8

5 x 8  =  40

Step 3 :

Assign the correct sign to the product.

(-5)(-8)  =  40

Hence, the product is 40.

Example 7 :

Divide: 24 ÷ (-3)

Solution :

Step 1 :

Determine the sign of the quotient.

24 is positive and -3 is negative. Since the numbers have opposite signs, the quotient will be negative.

Step 2 :

Divide.

24 ÷ (-3)  =  -8

Example 8 :

Divide: -6 ÷ (-2)

Solution :

Step 1 :

Determine the sign of the quotient.

-6 is negative and -2 is negative. Since the numbers have the same sign, the quotient will be positive.

Step 2 :

Divide.

-6 ÷ (-2)  =  3

Example 9 :

Divide: 0 ÷ (-2)

Solution :

Step 1 :

Determine the sign of the quotient.

The dividend is 0 and the divisor is not 0. So, the quotient is 0.

Step 2 :

Divide.

0 ÷ (-2)  =  0

After having gone through the stuff given above, we hope that the students would have understood "Add subtract multiply divide integers".

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