Comparing Fractions: Which One Is Bigger?

$\tfrac{5}{7}$

The bottom numbers match, so compare the tops. Five sevenths is five parts and two sevenths is two, so $\tfrac{5}{7}$ is bigger.

Which cuts the bar into bigger pieces?

$\tfrac{1}{4}$

Quarters are bigger than sixths, because four cuts make fatter parts than six. One quarter beats one sixth.

$\tfrac{5}{6}$

Rewrite $\tfrac{2}{3}$ as $\tfrac{4}{6}$. Then $\tfrac{5}{6} > \tfrac{4}{6}$.

Cross multiply.

$\tfrac{2}{5}$

$3 \times 5 = 15$ and $2 \times 8 = 16$. The $16$ belongs to $\tfrac{2}{5}$, so $\tfrac{2}{5}$ is bigger.

Less.

Half of $11$ is $5.5$, and the top number $5$ is under that. So $\tfrac{5}{11}$ is less than a half.

$\tfrac{1}{4} < \tfrac{3}{8} < \tfrac{1}{2}$

Rewrite all three in eighths: $\tfrac{2}{8}$, $\tfrac{3}{8}$ and $\tfrac{4}{8}$.

The tops now sort themselves: $2 < 3 < 4$.

$\tfrac{7}{10}$

Cross multiply: $7 \times 3 = 21$ and $2 \times 10 = 20$. The $21$ belongs to $\tfrac{7}{10}$, so it is the bigger one.

Both are over a half, so the half check will not settle it.

Lena.

Cross multiply: $3 \times 8 = 24$ and $5 \times 5 = 25$. The $25$ belongs to $\tfrac{5}{8}$, so Lena ate more — but only a little.

$>$

$\tfrac{4}{4}$ is four parts out of four, which is the whole bar, or $1$.

$\tfrac{7}{8}$ is one eighth short of the whole bar. So $\tfrac{4}{4} > \tfrac{7}{8}$.

Draw both bars, or think about sharing.

She has it backwards. $\tfrac{2}{5}$ is bigger.

The bottom number counts how many parts the whole was cut into. Nine parts are thinner than five parts, so two ninths is less bar than two fifths.

Sharing shows it: two slices from a pizza cut for nine people is less food than two slices from a pizza cut for five.