Comparing Fractions with Unlike Denominators

A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).

Comparing fractions involves determining which fraction is larger, smaller, or if they are equal.

Unlike denominators are denominators that are not the same in two or more fractions.

To compare fractions with unlike denominators, convert them to equivalent fractions with a common denominator.

A common denominator is a shared multiple of the denominators of two or more fractions.

The least common multiple (LCM) of 5 and 7 is 35, so the common denominator is 35.

$$\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$$ .

$$\frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35}$$ .

$$\frac{14}{35} < \frac{15}{35}$$ , so $$\frac{2}{5} < \frac{3}{7}$$ .

When comparing negative fractions, the fraction with the smaller absolute value is larger.