When you want to show a fraction as a percentage the most important thing to remember is that 100% is a whole amount, and in decimal terms it can be shown as the number 1. When you divide one into quarters you split the whole amount (1) into four parts. So when you show 100% as quarters you just split 100 into four equal parts and multiply this number by the number of quarters in your fraction.
- The bottom number (the denominator) in all quarter fractions is 4.
- Imagine you have a cake and you cut it into four pieces – each piece is one quarter of the cake.
- One cake is 100% of the cake – so let’s cut the percentage value for a whole (100) into four pieces as well!
- 100 ÷ 4 = 25
- Every top number in the fraction (the numerator) represents one quarter of 100%.
- Multiply the numerator by the percentage value of each piece to show the fraction as a percent.
With the above in mind, here are each of the quarter fractions shown as a percentage and the workings behind the answer.
1/4 as a percent
- Divide 100 by the denominator: 100 ÷ 4 = 25
- Multiply this number by the nominator: 25 × 1 = 25
So what is 1/4 as a percentage? The answer is 25%.
2/4 as a percent
Before we go into the usual conversion routine we can examine another practice you should use before you look at converting to a percentage – check to see if the fraction can be simplified. One way to check if a fraction can be simplified is to divide the top and bottom numbers of the fraction by two – if the result of both divisions is a whole number then replace your fraction with the result of the division. 2/4 is a great example to start with:
- 2 ÷ 2 = 1
- 4 ÷ 2 = 2
This shows that 2/4 is the same as 1/2. If you have two quarters of the cake it is the same as having had one half of it. When you look at fractions with a larger denominators it makes sense to try and reduce the fraction first – if you have
Now let’s use the standard method to produce our percentage.
- Divide 100 by the denominator: 100 ÷ 4 = 25
- Multiply this number by the nominator: 25 × 2 = 50
So what is 2/4 as a percentage? The answer is 50%.
3/4 as a percent
- Divide 100 by the denominator: 100 ÷ 4 = 25
- Multiply this number by the nominator: 25 × 3 = 75
So what is 3/4 as a percentage? The answer is 75%.
4/4 as a percent
- Divide 100 by the denominator: 100 ÷ 4 = 25
- Multiply this number by the nominator: 25 × 4 = 100
So what is 4/4 as a percentage? The answer is 100%.
Remember this point about four quarters – if the numerator can be divided by the denominator where the result is a whole number, you can reduce the fraction.
4 ÷ 4 = 1
So the fraction could also be expressed as 1/1 – 1 part of 1 is 1 – it is all of it, the whole amount – it is 100%!