Principles of Mathematics

Mental Conversion from Fraction to Decimal - the fast way

In maths, while doing division of numbers, sometimes we arrived at fraction, be it improper or proper form. We may need to have the answer in decimal.

Mentally how do we get the answer fast and simple?

To have this fast conversion from fraction to decimal, we first need to memorise some simple basic fractions. This is to speed up the process of mentally computing the conversion.

We can do mental division using any of the method presented in this blog (refer to links at the end of this post). But the answer is in fraction form.

Example is 40 / 7 = 5 5/7, a mixed numer format.

We like to have this 5/7 in decimal (sometimes).

• Firstly, we need to know (memorise) the below basic fractions/decimal numbers:
  1/2 = 5
  1/3 = 0.333
  1/4 = 0.25
  1/5 = 0.2
  1/6 = 0.1667
  1/7 = 0.1429
  1/8 = 0.125
  1/9 = 0.111
  1/10 = 0.1

You can see that these basic fraction/decimal conversions are not difficult to memorise.
In fact some of them are sub-product of others.

Example: 1/ 6 =(1/2) x (1/3) = 0.5 x 0.333 or 5 x 0.333 / 10
You can choose to memorise 1/2 and 1/3 and do simple mental multiplication later for 1/6.

Another example is 1/8. This can be achieved with (1/2) x (1/4).

After memorising the above basic numbers, we can straight away use them in the computation. Let’s see an example.

Example: 42 / 5 ==>  8 2/5

We know that 8 2/5 = 8 + 2/5.

Mentally converting, 8 + 2/5 ==> 8 + (2 x 0.2) = 8.4 (the answer)
This is with the use of the memorised number of 1/5 = 0.2.

Another example: 37 / 8

Mental division produces 37 / 8 = [(8 x 4) / 8] + ( 5 / 8 )  = 4 + (  5/8  )

We need only to convert the (  5 / 8  ) into decimal.

5 / 8 =  5 x 1/8  =  5 x 0.125 ==> 0.625 using Mental Multiplicaton method (from left to right approach).

Therefore  37 / 8 =  4 + 0.625 =   4.625  done mentally!

From the above examples, we can see the effectiveness of the memorised fractions/decimals numbers simplifying the mental conversion process.

Practice with this method and it will get easier with times.

Links for mental division:
Mental Division

Mental Division - denominator approach

Mental Division - Inflation method

Mental Division - Deflation method