**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.

**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

aaaaaaaaaaaaaaaaaaaa- 05aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

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

aaaaaaaaaaaaaaaaaaaa+ 09aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

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

**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".

Apart from the stuff given above, if you want to know more about "Add subtract multiply divide integers", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**