Remember that 25 is 100 divided by 4, so dividing by 25 is the same as dividing by 100 and multiplying by 4:

1. move the decimal point two places to the left then
2. multiply by 4 ( or double twice)

Of course, the multiplication can be done first, but using the recommended procedure has the advantage of providing us the magnitude of the answer first.

Example 14.1:    Find 700 ÷ 25 = (7 x 100) ÷ 25 = 7 x (100 ÷ 25) = 7 x 4 = 28

This example shows the basis of our shortcut. There are 4  25s  in every 100, so there are 7 x 4 or 28  25s in 7 hundreds.

 Example 14.2:    Find 3,400÷ 25

1.   Move the decimal point two places to the left to get 34.00.
2.   Double it to get 68.
3.   Double it again to get 136.

Example 14.3:    Find 3562÷ 250

1.   250 is 1/4 of 1000 or 10³ so we move the decimal point three places to the left giving us 3.562.
2.   Multiplying it by 4 gives us 14.248.

To divide a number by 125,

1. Move the decimal point three places to the left then
2. Multiply it by 8 (or double thrice)

 Example 14.4:    Find 20,400÷ 125

Moving the decimal point three places to the left gives 20.4

20.4 x 8 = 40.8 x 4 = 81.6 x 2 = 163.2

Example 14.5:    Find 758 ÷ 12.5

1.   This time 12.5 is 1/8 of 100 so we have to shift the decimal point two places to the left making it 7.58.
2.   Multiplying it by 8 gives us 60.64

Exercise 14:

1. ) 1050 ÷ 25 =
2. ) 6025÷ 25 =
3. ) 8375 ÷ 25 =
4. ) 12,400 ÷ 250 =
5. ) 71000÷ 125 =
6. ) 5,125÷ 125 =
7. ) 3,475÷ 250 =
8. ) 830÷ 12.5 =
9. ) 2475÷ 2.5 =
10. ) 5264÷ 0.25 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!