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# Multiplication and Division of Integers

Go back to  'Integers'

## Introduction to Multiplication and Division of Integers

Multiplication is nothing but repetitive addition. Division, on the other hand, is nothing but a process of repetitive subtraction. But what happens when there are negative integers involved?

## The idea behind multiplication and division of integers

Multiplication of whole or natural numbers involves adding a particular number a given number of times. For example, 4 x 3 is nothing but adding 4 3 times.

Dividing whole or natural numbers is distributing a quantity into equal groups.  With division, you start with a larger number and break it down multiple times till you are left with the smallest number possible

### An integer by definition is a whole number that can be either positive, negative or zero (but cannot be a fraction). Integers are represented by Z and are written as;

$$\text{Z} = \text{{…, –3, –2, –1, 0, 1, 2, 3, …}}$$

Integers cannot be $$-1.25,$$ $${2 \over 3},$$ $$-589.332$$

### Rules for Multiplying Integers

When you multiply two integers the same sign;

Positive x positive = positive = 2 x 5 = 10

When you multiply two integers with two negative signs;

Negative x Negative = Positive = –2 x –3 = 6

When you multiply two integers with one negative sign and one positive sign;

Negative x positive = negative = –2 x 5 = –10

### Rules for Dividing Integers

When you divide two integers with the same sign;

Positive ÷ positive = positive 16 ÷ 8 = 2

When you divide two integers with two negative signs;

Negative ÷ negative = positive = –16 ÷ –8 = 2

When you divide two integers with one negative sign and one positive sign;

Negative ÷ positive = negative = –16 ÷ 8 = –2

To sum it all up to make everything easy, the two most important things to remember whether you are multiplying or dividing integers;

1. When the signs are different, the answer is always negative.
2. When the signs are the same, the answer is always positive.

## Problems faced during multiplication and division of integers

Most students are confused when there are more than 2 integers with different signs that have to be either multiplied or divided. The confusion of what the resultant sign is is the big question. To make it easier the rules of multiplication and division of integers is of utmost importance. Working the equation from left to right, applying the rules to each sign makes sure that mistakes will not be made. For example;

### Division

(–20) ÷ (–5) ÷ (–2) =?

The solution

Step 1: (–20 ÷ –5) ÷ (–2)
Step 2: (10) ÷ (–2)
10 is positive as negative ÷ negative = positive
Step 3: –5
Positive ÷ negative = negative
Hence (–20) ÷ (–5) ÷ (–2) = –5

### Multiplication

(–6) x (–4) x (3) =?

The solution

Step 1: (–6 x –4) x (3)
Step 2: 24 x 3
24 is positive as negative x negative is positive
Step 3: 72
Hence (–6) x (–4) x (3) = 72