Comparing Fraction Products to 1

Property To compare the product of two fractions to 1 without calculating, examine each fraction. If both fractions are less than 1, their product will also be less than 1. If one fraction is greater than 1 and the other is less than 1, their product could be greater than, less than, or equal to 1.

Examples Is $\frac{3}{4} \times \frac{7}{8}$ greater than or less than 1? Since $\frac{3}{4} < 1$ and $\frac{7}{8} < 1$, their product is less than 1. Is $\frac{2}{5} \times \frac{4}{3}$ greater than or less than 1? We cannot tell without calculating because $\frac{2}{5} < 1$ and $\frac{4}{3} 1$. In this case, $\frac{2}{5} \times \frac{4}{3} = \frac{8}{15}$, which is less than 1. Is $\frac{5}{2} \times \frac{3}{4}$ greater than or less than 1? We cannot tell without calculating because $\frac{5}{2} 1$ and $\frac{3}{4} < 1$. In this case, $\frac{5}{2} \times \frac{3}{4} = \frac{15}{8}$, which is greater than 1.

Explanation This skill helps you estimate the size of a product involving fractions by comparing it to the benchmark of 1. When you multiply a number by a fraction less than 1, the result is smaller than the original number. Therefore, multiplying two fractions that are both less than 1 will always result in a product that is even smaller and thus less than 1. However, if one factor is greater than 1 and the other is less than 1, you must perform the calculation to determine how the product compares to 1.