Understanding How to Compare Fractions

Comparing fractions helps us figure out which fraction represents a larger or smaller amount. In third grade, we usually compare fractions by looking at two special cases: when the denominators are the same, and when the numerators are the same.

Comparing Fractions with the Same Denominator

The denominator (the bottom number) tells us how many equal pieces make up the whole. If two fractions have the same denominator, the pieces are the exact same size.

To compare them, just look at the numerator (the top number). The fraction with the bigger numerator is larger because you have more of those pieces.

Example: Compare $\frac{2}{5}$ and $\frac{4}{5}$.

Since both fractions are cut into fifths, we just compare $2$ and $4$. Four pieces are more than two pieces, so: $\frac{4}{5} > \frac{2}{5}$

Comparing Fractions with the Same Numerator

If two fractions have the same numerator, it means you have the exact same number of pieces.

To compare them, look at the denominator. A smaller denominator means the whole was cut into fewer pieces, which makes each individual piece bigger.

Example: Compare $\frac{1}{3}$ and $\frac{1}{6}$.

Both fractions give you $1$ piece. However, a third ($\frac{1}{3}$) is much bigger than a sixth ($\frac{1}{6}$) because sharing a pizza among $3$ people gives you a bigger slice than sharing it among $6$ people. Therefore: $\frac{1}{3} > \frac{1}{6}$

Ordering Fractions

You can use these same rules to put multiple fractions in order from least to greatest.

Example: Order $\frac{3}{8}$, $\frac{3}{4}$, and $\frac{3}{6}$ from least to greatest.

Notice that all the numerators are $3$. We need to look at the denominators: $8$, $4$, and $6$. Remember, the larger the denominator, the smaller the pieces.

• Eighths are the smallest pieces.
• Sixths are medium pieces.
• Fourths are the largest pieces.

So, the correct order from least to greatest is: $\frac{3}{8} < \frac{3}{6} < \frac{3}{4}$