Question

Replace each with <, > or = to make a true sentence.

$\frac{7}{20}\cdot \frac{2}{5}$

Short answer

The true sentence is $\frac{7}{20}<\frac{2}{5}$.

Step-by-step solution

Step 1. Take L.C.M of the denominators of each fraction.

$\text{L.C.Mof20and5}=20$

Step 2. Write all fractions with the same denominator.

To compare the given fractions, first, make the denominator of all fractions equal to L.C.M. by multiplying numerator and denominator with some number.

$\begin{array}{c}\frac{7}{20}\cdot \frac{2}{5}=\frac{7}{20}\cdot \frac{2\times 4}{5\times 4}\\ =\frac{7}{20}\cdot \frac{8}{20}\end{array}$

Step 3. Compare the numerator of both fractions.

Now compare the numerators over the same denominator. The fraction with a larger numerator will be the greater fraction.

$\because 7<8$

Therefore, the true statement is $\frac{7}{20}<\frac{2}{5}$.