Shortcut Division Method
a) Division by 10, 100, 1000, etc.:-
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…
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