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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