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Maths help: Conversion chart for fractions, percentages and decimals. numerator denominator

Updated on October 23, 2015

Remember what these words are for:

Fraction = a number 'out of' something else. It is represented as a number over another number.

Numerator = the top number on a fraction

Denominator = the bottom number on a fraction

percent = per 100

Decimal = a number which is smaller than a unit and is represented as a number/numbers past the decimal place.

If you start with a fraction ...

If you start with a fraction and want to convert to a percentage or decimal then there are plenty of methods which you can use to help you:

How do you convert a fraction to a percentage?

1. Using a calculator is the simpliest way ...

How do I do this?

  • Divide the fraction to convert it to a decimal - divide the numerator by the denominator.
  • Then multiply the result by 100 - make sure you add the % sign.

Example:

What is 5/8 as a percent?

  • Punch into your calculator '5'. Then Punch in the '÷' sign , then the '8' and last of all the '=' sign.
  • The answer should read off 0.625.
  • Punch into your calculator the 'x' sign and then '100' before punching the '=' sign.
  • The answer on your screen should read '62.5'.
  • When writing this as an answer you must always write % after it though.


2. Paper method:

A lot of the time we do not allow our students the use of a calculator because we want them to understand the maths behind the problem and be able to solve it using their greatest tool - their mind.

If the students understand the concept behind percentage then this step should become a lot easier. They must know that percent = per 100. Therefore if we change our decimal into an equivalent decimal with 100 as the denominator then that would mean the numberator value will also be equivalent to the percentage.

  • Find a number you can multiply the denominator by to get 100.
  • (This can be done by dividing 100 by the denominator.)
  • Multiply the top and bottom of the fraction by that number.
  • The numerator value = the percentage.
  • Write this down adding the % sign in after.

Example 1:

3/4 as a percent.

  • 100 ÷ 4 = 25.
  • So 4 x 25 = 100
  • Multiply both 3 and 4 by 25 and write this as a fraction:
  • 3 x 25 = 75 4 x 25 = 100 Fraction = 75/100
  • So 3/4 expressed as a percentage = 75%

Example 2:

4/10 as a percent

  • 100 ÷ 10 = 10
  • So 10 x 10 = 100
  • Multiply both 4 and 10 by 10 and write this as a fraction:
  • 4 x 10 = 40 10 x 10 = 100 Fraction = 40/100
  • So 4/10

How do I convert from a fraction to a decimal?

Method 1: Using a caluculator is the simpliest way again:

I have always taught the children that fractions are in essence a division that you haven't solved because sometimes it's a nicer number that way. So in order to convert a fraction to a decimal all we need to do is divide the numerator by the denominator:

Example 1:

5/8 as a decimal

  • Punch into your calculator ' 5 ÷ 8 = '
  • The answer is then on the screen for them to copy down. (0.625)

Example 2:

(This is a common fraction to decimal conversion they should know from the top of their head but it is always good to prove this method works by using this example as they know the answer already.)

1/4 as a decimal

  • Punch into your calculator '1 ÷ 4 ='
  • The answer on their screen should read 0.25

Method 2: Written method (1)

The bus stop method.

A video is included below to remind you of what the bus stop method is all about. I found one that works past the decimal point and I thought it was good because it shows you how I would teach such a method.

  • Start off using the bus stop method with divisions that won't result in any remainders.
  • Next go onto results that will result in remainders.
  • Last of all, use these remainders to carry on past the decimal point. Once they have this method grasped then they can do any division quickly and easily.

Anyway, if a calculator isn't available then they can still divide the numerator by the denominator using this method. Make sure the denominator is on the outside of the bus stop and away you go. Straight away you will notice that there are no whole numbers and we are dealing with decimals (unless you work with a top heavy fraction).

Example 1:

1/5 as a decimal

5 ⁄¯¯1 =

   0

5⁄¯¯1

( There are no 5's that go into 1 so you write 0 above it)

  0.2 

5⁄ 1.¹0

(That would leave us with 1 remainder which you would then move to the next column to the right to create 10 tenths.)


The answer would then be 0.2.


(Sorry about how this looks but writing on here doesn't allow you to write it very nice! I will only do one example here because of how difficult it is to create the bus stop using this text program. )

Method 3: Written method (2)

This step will follow a similar way to converting a fraction to a percentage. You follow the same rules to make the numerator the same value as the percent. Then you divide the fraction; divide the numberator by 100 to find the decimal:

  • Find a number you can multiply the denominator by to get 100.
  • (This can be done by dividing 100 by the denominator.)
  • Multiply the top and bottom of the fraction by that number.
  • Then you divide the numerator by 100 to make the decimal.

Example 1:

3/4 as a decimal.

  • 100 ÷ 4 = 25.
  • So 4 x 25 = 100
  • Multiply both 3 and 4 by 25 and write this as a fraction:
  • 3 x 25 = 75 4 x 25 = 100 Fraction = 75/100
  • You can now divide the numerator by 100. (75 ÷ 100 = 0.75)
  • 3/4 as a decimal = 0.75

Example 2:

4/10 as a percent

  • 100 ÷ 10 = 10
  • So 10 x 10 = 100
  • Multiply both 4 and 10 by 10 and write this as a fraction:
  • 4 x 10 = 40 10 x 10 = 100 Fraction = 40/100
  • You can now divide the numerator by 100. (40 ÷ 100 = 0.4)
  • 4/10 as a decimal = 0.4
  • This one of course could easily be done as 4 ÷ 10 but I wanted to show you how similar the methods are.


To convert a decimal to a percentage, follow these simple steps;

This is the easiest one of all because a percent mean out of 100. So all you need to do is multiply!

  • Multiply the decimal by 100 to get the percent.

Example:

0.25 as a percent

  • 0.25 x 100 = 25%

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