Page 22 - pdf N.C.E.R.T INTEGERS CH 1

22 MATHEMATICS

(b) What is the number of white cement bags it must sell to have neither profit
nor loss, if the number of grey bags sold is 6,400 bags.

9. Replace the blank with an integer to make it a true statement.
(a) (–3) × _____ = 27 (b) 5 × _____ = –35

(c) _____ × (– 8) = –56 (d) _____ × (–12) = 132

1.6 DIVISION OF INTEGERS

We know that division is the inverse operation of multiplication. Let us see an example
for whole numbers.

Since 3 × 5 = 15
So 15 ÷ 5 = 3 and 15 ÷ 3 = 5
Similarly, 4 × 3 = 12 gives 12 ÷ 4 = 3 and 12 ÷ 3 = 4
We can say for each multiplication statement of whole numbers there are two
division statements.
Can you write multiplication statement and its corresponding divison statements
for integers?
Observe the following and complete it.

Multiplication Statement Corresponding Division Statements

2 × (– 6) = (–12) (–12) ÷ (– 6) = 2 , (–12) ÷ 2 = (– 6)

(– 4) × 5 = (–20) (–20) ÷ (5) = (– 4) , (–20) ÷ (– 4) = 5

(– 8) × (–9) = 72 72 ÷ _____ = _____ , 72 ÷ _____ = _____
_____ ÷ (–3) = ____ , _____________
(–3) × (–7) = _____
_____________ , _____________
(– 8) × 4 = ____
_____________ , _____________
5 × (– 9) = _____
_____________ , _____________
(–10) × (–5) =

From the above we observe that : TRY THESE
(–12) ÷ 2 = (– 6)
Find:
(–20) ÷ (5) = (– 4)
(a) (–100) ÷ 5 (b) (–81) ÷ 9
(–32) ÷ 4 = – 8
(c) (–75) ÷ 5 (d) (–32) ÷ 2
(– 45) ÷ 5 = – 9
We observe that when we divide a negative integer by a positive integer, we divide
them as whole numbers and then put a minus sign (–) before the quotient. We, thus,
get a negative integer.