Remember that 25 is 100 divided by 4, so dividing by 25 is the same as dividing by 100 and multiplying by 4:
- move the decimal point two places to the left then
- 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,
- Move the decimal point three places to the left then
- 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:
- ) 1050 ÷ 25 =
- ) 6025÷ 25 =
- ) 8375 ÷ 25 =
- ) 12,400 ÷ 250 =
- ) 71000÷ 125 =
- ) 5,125÷ 125 =
- ) 3,475÷ 250 =
- ) 830÷ 12.5 =
- ) 2475÷ 2.5 =
- ) 5264÷ 0.25 =
Answers to all exercises are found in the answer key.
Discover the 25 Math Short Cuts ( 25 MSC )!
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