Page 144 - ICSE Math 7

We can verify the result of division by using the formula:
Dividend = Divisor × Quotient + Remainder

2
Example 10: Divide x – 75 + 10x by x – 5 and verify the result.
x + 15
2
Solution: x – 5 x + 10x – 75
2
2
x – 5x [ x(x – 5) = x – 5x]
– + (Changing the sign)
15x – 75
15x – 75 [ 15(x – 5) = 15x – 75]
– + (Changing the sign)
0

Verification:

Divisor × Quotient + Remainder = (x – 5) × (x + 15) + 0
= x(x + 15) – 5(x + 15)
2
2
= x + 15x – 5x – 75 = x + 10x – 75
= Dividend
2
Example 11: Divide 2p + 14 – 11p by p – 4 and verify the result.
2p – 3
2
Solution: p – 4 2p – 11p + 14
2
2
2p – 8p [ 2p(p – 4) = 2p – 8p]
– + (Changing the sign)
– 3p + 14
– 3p + 12 [ –3(p – 4) = – 3p + 12]
+ – (Changing the sign)
2

Verification:
Divisor × Quotient + Remainder = (p – 4) × (2p – 3) + 2
= p(2p – 3) – 4(2p – 3) + 2
2
2
= 2p – 3p – 8p + 12 + 2 = 2p – 11p + 14
= Dividend

2
2
Example 12: The area of a rectangle is 4a – 4ab – 3b sq. unit and its length is 2a – 3b units. Find
the breadth of the rectangle.
2a + b
Solution: Area of a rectangle = Length × Breadth 2a – 3b 4a – 4ab – 3b 2
2
2
2
\ 4a – 4ab – 3b = (2a – 3b) × Breadth 4a – 6ab [ 2a(2a – 3b)
2
2
2
4a – 4ab – 3b 2 – + = 4a – 6ab]
⇒ Breadth = 2a – 3b 2ab – 3b 2
\ Breadth of the rectangle is 2a + b units. 2ab – 3b 2 [ b(2a – 3b)
2
– + = 2ab – 3b ]
0

130