NCERT Class 7 Mathematics Textbook for low vision and blind students made Screen readable by Professor T K Bansal.

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
implies 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 table and complete it.

From the above we observe that :

( −12) ÷ 2 = ( −6)
( −20) ÷ 5 = ( −4)
( −32) ÷ 4 = ( −8)
( −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.

TRY THESE 1.12

Find:
(a) ( −100) ÷ 5
(b) ( −81) ÷ 9
(c) ( −75) ÷ 5
(d) ( −32) ÷ 2

We also observe that:
72 ÷ ( −8) = −9 and
50 ÷ ( −10) = −5
72 ÷ ( −9) = − 8
50 ÷ ( −5) = −10

So we can say that when we divide a positive integer by a negative integer, we first divide them as whole numbers and then put a minus sign (−) before the quotient.

In general, for any two positive integers a and b
a ÷ (−b) = (− a) ÷ b where b ≠ 0

Can we say that
( −48) ÷ 8 = 48 ÷ ( −8)?
Let us check.
We know that
( −48) ÷ 8 = − 6
and 48 ÷ ( −8) = −6
So ( −48) ÷ 8 = 48 ÷ ( −8)

Check this for
(i) 90 ÷ ( −45) and ( −90) ÷ 45
(ii) ( −136) ÷ 4 and 136 ÷ ( −4)

TRY THESE 1.13

Find:
(a) 125 ÷ ( −25)
(b) 80 ÷ ( −5)
(c) 64 ÷ ( −16)

Lastly, we observe that
( −12) ÷ ( −6) = 2;
( −20) ÷ ( −4) = 5;
( −32) ÷ ( −8) = 4;
( −45) ÷ ( −9) = 5

So, we can say that when we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign (+).

In general, for any two positive integers a and b
( −a) ÷ ( −b) = a ÷ b where b ≠ 0

TRY THESE 1.14

Find:
(a) ( −36) ÷ ( −4)
(b) ( −201) ÷ ( −3)
(c) ( −325) ÷ ( −13)