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Now, to find (–2) × 4, we observe the following pattern:

2 × 4 = 8
1 × 4 = 4 = 8 – 4
0 × 4 = 0 = 4 – 4
–1 × 4 = –4 = 0 – 4 Quick Check
Complete the square integer grid and
– 2 × 4 = –8 = –4 –4 observe the multiplication patterns of
Since, 2 × (–4) = – 8 integers. What do you observe?

Therefore, (–2) × 4 = –8 = 2 × (–4) x –3 –2 –1 0 1 2 3
–3
Now, observe the following pattern to find (–2) × (–4).
(–2) × 4 = –8 –2
(–2) × 3 = –6 = –8 – (–2) –1
(–2) × 2 = –4 = (–6) – (–2) 0
(–2) × 1 = –2 = (–4) – (–2) 1
(–2) × 0 = 0 = (–2) – (–2) 2
(–2) × (–1) = 0 – (–2) = 0 + 2 = 2 3
(–2) × (–2) = 2 – (–2) = 2 + 2 = 4 Find the product of the following from

(–2) × (–3) = 4 – (–2) = 4 + 2 = 6 the above grid:
(–2) × (–4) = 6 – (–2) = 6 + 2 = 8 (a) (–2) × 3 (b) 3 × (–3)
Thus, (–2) × (–4) = 8 = 2 × 4
From these patterns, we observe that the product of integers with the same sign is positive and
the product of integers with the opposite sign is negative.
Multiplication of Integers Using Rules

There are certain rules for multiplication of integers.
Multiplication of two integers with the Same Sign

To find the product of the two integers with the same sign, multiply their absolute values and put
the positive sign (+ve) before the product obtained.
For example: (a) (+7) × (+3) = + (7 × 3) = +21 or 21
(b) (–5) × (–4) = + (5 × 4) = +20 or 20

In general, (+ve) integer × (+ve) integer = (+ve) integer

(–ve) integer × (–ve) integer = (+ve) integer

Example 1: Find the product.
(a) 7 × 5 (b) (–6) × (–7) (c) (+12) × (+11)
Solution: (a) 7 × 5 = 35
(b) (–6) × (–7) = + (6 × 7) = +42 or 42
(c) (+12) × (+11) = + (12 × 11) = +132 = 132

Multiplication of two Integers with Opposite Signs

To find the product of two integers with opposite signs, obtain the product of their absolute value
and put a minus sign before the product obtained.

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