Shortcut Division Method

a) Division by 10, 100, 1000, etc.:- 

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Separate 1, 2, 3, 4 digits respectively from the right. The number formed by the left digit is the quotient and number formed by the right digits is the remainder.

Example:- a) 123 ÷ 10 = 12.3

b) 564321 ÷ 1000 = 564.321

c) 78654 ÷ 100 = 786.54

d) 344678 ÷ 1000000 = 0.344678

b) Division by 5:-

Division by 5 is simple-merely multiply numerator by 2 and divide the product obtained by 10.

Example:- Divide 65432 by 5

Solution:- 65432 ÷ 5 = (65432 × 2) ÷ 10 =130864 ÷ 10 = 13086.4

Example:- Divide 1234 by 5

Solution:- 1234 ÷ 5 = (1234 × 2) ÷ 10 = 2468 ÷ 10 = 246.8

c) Division by 25:-

Remember the multiplication of a number by 25? Division of a number by 25 also works on the same principle. Multiply the dividend by 4 and move decimal two places left which will give you the correct answer.

Example:- 641 ÷ 25 = ?

Solution:- Multiply 641 by 4  = 641  × 4  = 2564 Multiplication of any number by 4 can be done in breaks.

First multiply the number by 2 and then multiply the product again by 2. It works better.

641 × 2 = 1200 + 82 = 1282

1282 × 2 = 1200 × 2 + 80 × 2 + 2 × 2 = 2400 + 160 + 4 = 2564

Now move decimal places 2 digits left = 25.64 Hence, 641 ÷ 25 = 25.64

Example:- 12652 ÷ 25=?

Solution:- 12652 × 4 = 12000 × 4 + 600 × 4 + 50 × 4 + 2 × 4

= 48000 + 2400 + 200 + 8 = 50608

Move decimal point 2 digits left = 506.08

d) Division by 35:-

A number of 2 – 3 digits can be divided  by 35 by simply multiplying the number by 2 and dividing the result by 7. Finally move the decimal one place to the left.

Example:- 61 ÷ 35 =?

Solution:- Multiply 61 by 2 = 61 × 2 = 122

Divide it by 7 = 122 ÷ 7 = 17.428… Move decimal one point left = 1.7428…

Example:- 4521 ÷ 35 = ?

Solution:- Multiply 4521 by 2 = 4521 × 2 = 9042

Divide it by 7 = 9042 ÷ 7 = 1291.71428…

Move decimal one point left = 1291.71428…