Multiplying integers is the third operations on integers, among the four fundamental operations on integers and it is the short process of finding the sum if a given number of repetitions of the same number. The sign or symbol of multiplication is ‘×’.

**For example:**

(i) 5 + 5 + 5 + ……….. 15 times = 5 multiplied by 15 = 5 × 15.

(ii) (-4) + (-4) + (-4) +……….. 12 times = (-4) multiplied by 12 = (-4) × 12.

The repeating number is called the multiplicand and the number which indicates how often the multiplicand is to be repeated is called the multiplier.

Thus, in 3 + 3 + 3 + ……….. 14 times i.e. in 3 × 14; 3 is the multiplicand and 14 is the multiplier.

Adopt the following rules for the multiplying integers.

1. When the integers have same sign:

The multiplication of two integers, both positive or both negative, is always a positive integer equal to the product of their absolute values.

And in other words when both the numbers have same (like) signs, the result of the multiplication is always positive.

**For example:**

(i) (+5) × (+4) = 5 × 4 = 20

(ii) (-6) × (-3) = 6 × 3 = 18

(iii) (+12) × (+12) = 12 × 12 = 144

(iv) (-16) × (-5) = 16 × 5 = 80

(v) (-20) × (-10) = 20 × 10 = 200

2. When the integers have unlike sign:

The multiplication of a positive integer and a negative integer is always negative.

And in other words when both the numbers have different (unlike) signs, the result of the multiplication is always negative.

**For example:**

(i) (-15) × (+8) = - (15 × 8) = -120

(ii) (+12) × (-9) = - (12 × 9) = -108

(iii) (-10) × (+5) = - (10 × 5) = -50

(iv) (+20) × (-8) = - (20 × 8) = -160

(v) (-8) × (+7) = - (8 × 7) = -56

**Note:** (+) × (+) = (+)

(+) × (-) = (-)

(-) × (+) = (-)

(-) × (-) = (+)

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