Comparing Fractions

≈ 15 min

When two fractions have the same denominator, they are made of parts of the same size — so you only need to compare the numerators. More parts of the same size means more.

\frac{3}{5} > \frac{2}{5} \quad\text{because } 3 \text{ fifths beat } 2 \text{ fifths.}

Unit fractions behave the opposite way. $\frac{1}{4}$ is larger than $\frac{1}{8}$ : the more equal parts you cut a whole into, the smaller each single part becomes.

Worked example. Which is larger, $\frac{2}{3}$ or $\frac{1}{3}$ ?

Both are thirds — the same size of slice — so just compare the tops: $2 > 1$ . Therefore $\frac{2}{3} > \frac{1}{3}$ .

Which fraction is larger: $\frac{3}{5}$ or $\frac{2}{5}$ ?

$\frac{3}{5}$

$\frac{2}{5}$

they are equal

cannot tell

Which fraction is larger: $\frac{1}{4}$ or $\frac{1}{8}$ ?

$\frac{1}{4}$

$\frac{1}{8}$

they are equal

cannot tell

Which gives the bigger piece: $\frac{1}{3}$ of a cake or $\frac{1}{6}$ of the same cake? Write your answer as $a/b$ .

One pizza is shared equally by $2$ friends; an identical pizza is shared equally by $4$ friends. Each friend in which group gets more pizza — write how many friends are in that group.