# Multiplying integers

We know that integers can be both positive or negative numbers.

The multiplication of numbers with different signs requires understanding of some basic rules.

On completing this chapter, you will learn to multiply integers with same and different signs.

## How to Multiply two integers?

Given below are possible scenarios for multiplication of integers;

(a) Both multiplying integers have same sign.
⟹ Both integers are positive
⟹ Both integers are negative

(b) Both multiplying integers have different signs.

Let us understand both the scenarios in detail.

### Multiplying integers with same sign

The multiplication of integers with same sign always results in positive integers.

There are two case possible;
( i ) Both the integers are positive
( ii ) Both the integers are negative

Multiplication of two positive sign is positive.
Multiplication of two negative sign is also positive.

Given below are some examples for your understanding.

#### Example of Multiplication of Positive Integers

Example 01

Note that the result is positive integer.

Example 02

#### Example of Multiplication of Negative Integers

Note:
The multiplication of two -ve sign results in +ve sign.
Hence, in any multiplication, if you have numbers with two negative sign, the final result will be positive.

Trick to Remember
Remember that two negative’s turns into positive.

Example 02

### Multiplication of two integer with different signs

The multiplication of positive and negative integer always results in negative integer.

Note that the multiplication of +ve and -ve sign is always -ve.

Example 01

In the above example;
One integer is negative ( i.e. -3 )
The other integer is positive (i.e. 2)
Multiplication of positive and negative integer results in negative integer (i.e. -6)

Example 02

Here the multiplication of positive integer ( i.e. 4) and negative integer ( i.e. -6) results in negative integer -24.

## Multiplication of Integers – Solved Example

(01) Multiply the following integers

Solution
(i) – 7 x 5

Multiplication of -ve integer with + ve integer results in negative integer.
⟹ -35

(ii) 3 x 2
⟹ 6

(iii) – 8 x – 8
Both integer have same sign, hence the result is positive integer.
⟹ -64

(iv) 9 x -7

Both integer have different sign, hence the result is negative integer.
⟹ -63

(v) -10 x -12
Both integers have same sign, so the result is positive integer.
⟹ 120