Compare & order fractions (denom 2,3,4,5,6,8,10)
Theory
To compare fractions, look at the size of the parts and how many parts there are. With the same denominator, more parts is larger; with the same numerator, a bigger denominator is smaller. Otherwise rewrite with a common denominator first.
With the same denominator, the parts are equal, so the fraction with more parts is larger: \(\dfrac{5}{8}>\dfrac{3}{8}\).
With the same numerator, a bigger denominator cuts smaller parts, so the fraction is smaller: \(\dfrac{2}{8}<\dfrac{2}{3}\).
When neither matches, rewrite both with a common denominator, then compare the numerators.
Two quick rules cover most comparisons before any renaming is needed.
| Situation | Rule | Example |
|---|---|---|
| Same denominator | More parts is larger | \(\dfrac{5}{8}>\dfrac{3}{8}\) |
| Same numerator | Bigger denominator is smaller | \(\dfrac{2}{8}<\dfrac{2}{3}\) |
| Compare with a half | Rewrite the half to match | \(\dfrac{3}{8}<\dfrac{4}{8}\) |
How to compare and order fractions
- Same denominator? Order by the numerator; more parts is larger.
- Same numerator? The bigger the denominator, the smaller the fraction.
- Neither? Rewrite with a common denominator, then compare numerators.
Eighths are equal parts, so more parts wins.
| \(\dfrac{5}{8}\) | \(=\) | \(\dfrac{3}{8}\) larger |
The bigger the denominator, the smaller the parts, so \(\dfrac{2}{8}<\dfrac{2}{6}<\dfrac{2}{4}\).
\(\dfrac{2}{8}\) is smallest.
Write a half in eighths: \(\dfrac{1}{2}=\dfrac{4}{8}\). Since \(\dfrac{3}{8}<\dfrac{4}{8}\), it is less than a half.
Sixths are equal, so order by numerator.
\(\dfrac{1}{6},\ \dfrac{3}{6},\ \dfrac{5}{6}\)
Common pitfalls
Frequently asked questions
How do you compare fractions with the same denominator?
The parts are equal, so the fraction with the bigger numerator is larger. \(\dfrac{5}{8}>\dfrac{3}{8}\).
How do you compare fractions with the same numerator?
The same number of parts, but a bigger denominator makes smaller parts, so that fraction is smaller. \(\dfrac{2}{8}<\dfrac{2}{3}\).
How do you compare fractions that share nothing?
Rewrite both with a common denominator so the parts match, then compare the numerators.
Is a bigger denominator always a bigger fraction?
No. A bigger denominator means the whole is cut into more, smaller parts, so each part is smaller.