Compare fractions with related denominators
Theory
Denominators are related when one is a multiple of the other, such as \(3\) and \(12\). To compare, rename the fraction with the smaller denominator so both have the larger denominator, then compare the numerators. This Year 6 maths page shows how, including fractions that turn out to be equal.
\(3\) and \(12\) are related denominators because \(3 \times 4 = 12\). So are \(4\) and \(8\), \(5\) and \(10\), \(8\) and \(16\).
To rename \(\dfrac{2}{3}\) in twelfths, multiply the top and bottom by \(4\): \(\dfrac{2}{3} = \dfrac{8}{12}\). The size does not change.
With the same denominator, compare the numerators: \(\dfrac{8}{12} > \dfrac{7}{12}\), so \(\dfrac{2}{3} > \dfrac{7}{12}\).
If the numerators match after renaming, the fractions are equal: \(\dfrac{4}{5} = \dfrac{8}{10}\).
Renaming with a related denominator:
| Fraction | Renamed |
|---|---|
| \(\dfrac{2}{3}\) | \(\dfrac{8}{12}\) |
| \(\dfrac{1}{4}\) | \(\dfrac{3}{12}\) |
| \(\dfrac{5}{8}\) | \(\dfrac{10}{16}\) |
| \(\dfrac{1}{5}\) | \(\dfrac{2}{10}\) |
| \(\dfrac{1}{3}\) | \(\dfrac{3}{9}\) |
How to compare fractions with related denominators
- Find the larger denominator and how many times the smaller one fits into it.
- Rename the other fraction: multiply its top and bottom by that number.
- Compare the numerators and write \(>\), \(<\) or \(=\) between the original fractions.
| \(\dfrac{2}{3}\) | \(=\) | \(\dfrac{8}{12}\) |
\(8 > 7\), so \(\dfrac{2}{3} > \dfrac{7}{12}\).
| \(\dfrac{1}{4}\) | \(=\) | \(\dfrac{3}{12}\) |
\(\dfrac{1}{4} < \dfrac{5}{12}\).
| \(\dfrac{5}{8}\) | \(=\) | \(\dfrac{10}{16}\) |
\(\dfrac{11}{16}\).
(i) \(\dfrac{1}{5}\) ___ \(\dfrac{3}{10}\)
(ii) \(\dfrac{4}{5}\) ___ \(\dfrac{8}{10}\)
| \(\dfrac{1}{5}\) | \(=\) | \(\dfrac{2}{10}\) |
| \(\dfrac{4}{5}\) | \(=\) | \(\dfrac{8}{10}\) |
(i) \(\dfrac{1}{5} < \dfrac{3}{10}\)
(ii) \(\dfrac{4}{5} = \dfrac{8}{10}\)
| \(\dfrac{1}{3}\) | \(=\) | \(\dfrac{3}{9}\) |
\(\dfrac{2}{9}\).
In sixteenths: \(\dfrac{12}{16}\), \(\dfrac{5}{16}\), \(\dfrac{8}{16}\), \(\dfrac{7}{16}\).
\(\dfrac{5}{16}, \dfrac{7}{16}, \dfrac{1}{2}, \dfrac{3}{4}\).
(i) Which holds more?
(ii) By how much?
| \(\dfrac{4}{5}\) | \(=\) | \(\dfrac{8}{10}\) |
| \(\dfrac{8}{10} - \dfrac{7}{10}\) | \(=\) | \(\dfrac{1}{10}\) |
(i) The \(\dfrac{4}{5}\) L tin
(ii) \(\dfrac{1}{10}\) L more
| \(\dfrac{1}{2}\) | \(=\) | \(\dfrac{6}{12}\) |
Numerators only compare when the denominators match. In twelfths, \(5 < 6\), so \(\dfrac{1}{2}\) is larger.
Common pitfalls
Frequently asked questions
What are related denominators?
Denominators where one is a multiple of the other, such as 4 and 8 or 3 and 12.
How do I rename a fraction?
Multiply the numerator and denominator by the same number.
Which fraction do I rename?
The one with the smaller denominator, so both end up with the larger denominator.
Is 2/3 bigger than 7/12?
Yes: \(\dfrac{2}{3} = \dfrac{8}{12}\).
Can two different-looking fractions be equal?
Yes: \(\dfrac{4}{5} = \dfrac{8}{10}\).