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