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 =
Similarly,
4 × 3 = 12 gives 12 ÷ 4 =
We can thus, 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?
| 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 ÷ (-8) = |
| (-3) × (-7) = 21 | 21 ÷ (–3) = |
| (-8) × 4 = (-32) | –32 ÷ (–8) = |
| 5 × (-9) = (-45) | –45 ÷ 5 = |
| (-10) × (-5) = 50 | 50 ÷ (–10) = |
Find:
(a) (–100) ÷ 5 =
(b) (–81) ÷ 9 =
(c) (–75) ÷ 5 =
(d) (–32) ÷ 2 =
From the above we observe that :
(–12) ÷ 2 = (– 6)
(–20) ÷ 5 =
(–32) ÷ 4 =
(– 45) ÷ 5 =
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 also observe that:
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
Lastly, we observe that:
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
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)
Find:
(a) 125 ÷ (–25) =
(b) 80 ÷ (–5) =
(c) 64 ÷ (–16) =
Find:
(a) (–36) ÷ (– 4) =
(b) (–201) ÷ (–3) =
(c) (–325) ÷ (–13) =