Maths
How do you compare fractions?
Quick answer
To compare fractions, check whether they share a denominator or a numerator, or rewrite them with a common denominator. The bigger fraction is the one with more of the whole.
In one sentence
To compare fractions, make the pieces the same size or look at how close each is to a half or a whole, then decide which is greater.
Explained
A fraction is a part of a whole, so comparing is about deciding which part is larger. There are three easy tricks.
Same denominator. The pieces are the same size, so the one with more pieces is bigger. 5/8 is greater than 3/8.
Same numerator. You have the same number of pieces, so look at the size. The bigger the denominator, the smaller each piece. So 1/5 is greater than 1/8, and 3/4 is greater than 3/10.
pie
pizza
cake
Different numerators and denominators. Turn both into equivalent fractions with the same denominator, then compare the numerators. To compare 3/4 and 2/3, use 12 as the common denominator. Then 3/4 = 9/12 and 2/3 = 8/12. Nine twelfths is more than eight twelfths, so 3/4 > 2/3.
Another shortcut is to use benchmarks like 0, 1/2 and 1. Is the fraction less than a half, or more? 2/5 is less than a half, because half of 5 is 2.5. Meanwhile 5/8 is more than a half, because 4/8 would be exactly half. So 5/8 > 2/5, with no further working.
You can also put fractions on a number line from 0 to 1. The fraction that sits further to the right is the larger one. Use the symbols > (greater than), < (less than) and = (equal to) to write the comparison: 2/5 < 1/2.
Examples
| Compare | Method | Result |
|---|---|---|
| 5/8 and 3/8 | same denominator | 5/8 > 3/8 |
| 1/5 and 1/8 | same numerator | 1/5 > 1/8 |
| 3/4 and 2/3 | common denominator 12 | 3/4 > 2/3 |
| 2/5 and 5/8 | half as a benchmark | 2/5 < 5/8 |
Common mistakes
- "A bigger denominator means a bigger fraction." It means smaller pieces. 1/10 is less than 1/2.
- Comparing only the top numbers. 3/10 is not larger than 2/3.
- Drawing pictures of different sizes. Wholes must be the same size to compare.
Quick quiz
Comparing fractions
Check what you know with 4 quick questions.
Question 1 of 4
Which is bigger: 3/8 or 5/8?
Practise it
Try it
Fractions practice
Practise it step by step in a full course: Grade 4 Maths
For grown-ups
Related topics
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Equivalent fractions
Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.
Number line
A number line is a straight line with numbers marked at equal steps, smallest on the left and biggest on the right. It helps you count, compare, add and subtract.
Adding and subtracting fractions
To add or subtract fractions, first give them the same denominator. Then add or subtract only the numerators and keep the denominator. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Improper fractions and mixed numbers
An improper fraction has a numerator bigger than its denominator, like 7/4. A mixed number shows the same amount as a whole number plus a fraction, like 1 3/4.
Simplifying fractions
To simplify a fraction, divide the top and bottom by the same number until you cannot go any further. For example, 12/18 simplifies to 2/3 when you divide both by 6.