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Comparing Fractions


Sometimes if fractions have a different denominator (the number below the line), it can be difficult to work out which is larger.

For example, which of the following three fractions is largest:

23 rac{2}{3} or 45 rac{4}{5} or 67 rac{6}{7}?

To work out the correct order, you'll need to do some calculations to make them easier to compare.



If you are comparing two fractions with the same denominator, you can just look at which numerator is larger.

For example, if you are comparing the following two fractions:

25 rac{2}{5} and 35 rac{3}{5}

Both have the same denominator (5) and so you can see that 35 rac{3}{5} is larger than 25 rac{2}{5}.

If you have two numbers with different denominators, you'll need to make them the same in order to compare.

In order to make the denominators the same, you need to find the lowest common denominator of the two numbers.

If we want to compare 35 rac{3}{5} and 46 rac{4}{6}, we need to find the lowest common denominator of 5 and 6. To do this, we can write out the multiples of 5 and 6.

Multiples of 5Multiples of 6

30 is the lowest common denominator of 5 and 6. Therefore, we need to convert both 35 rac{3}{5} and 46 rac{4}{6} to have 30 as a denominator.

To convert 35 rac{3}{5} to have a denominator of 30, we need to multiply 5 by 6. However, we need to multiply both the numerator and the denominator by the same value or we will change the fraction's value. Therefore, we can multiply it by 66 rac{6}{6}.

35 rac{3}{5} x 66 rac{6}{6} = 1830 rac{18}{30}

Then we repeat the process with 46 rac{4}{6}. To make the denominator 30, we need to multiply by 55 rac{5}{5}.

46 rac{4}{6} x 55 rac{5}{5} = 2030 rac{20}{30}

Now we have both numbers with a common denominator, we can easily compare them.

2030 rac{20}{30} is larger than 1830 rac{18}{30}

Therefore 46 rac{4}{6} is larger than 35 rac{3}{5}.


57\dfrac{5}{7} ? 47\dfrac{4}{7}
57\dfrac{5}{7} ? 47\dfrac{4}{7}
57>47\dfrac{5}{7} > \dfrac{4}{7}

56\dfrac{5}{6} ? 35\dfrac{3}{5}
5565\dfrac{5*5}{6*5} ? 3656\dfrac{3*6}{5*6}
2530\dfrac{25}{30} ? 1830\dfrac{18}{30}
2530>1830\dfrac{25}{30} > \dfrac{18}{30}

1571\dfrac{5}{7} ? 2172\dfrac{1}{7}
127\dfrac{12}{7} ? 157\dfrac{15}{7}
127<157\dfrac{12}{7} < \dfrac{15}{7}

Comparing Fractions Worksheets (PDF)

Comparing Fractions Worksheet 1

Comparing Fractions Worksheet 2

Comparing Fractions Worksheet 3