Question

Use the inequality symbols\(<\) or \(>\) to compare the following fractions. $$\frac{3}{7} \text { and } \frac{2}{5}$$

Short answer

Question: Determine whether the inequality is true or false: \(\frac{3}{7} > \frac{2}{5}\) Answer: True

Step-by-step solution

Find the least common multiple (LCM) of the denominators

In this case, the denominators are 7 and 5. The least common multiple of 7 and 5 is 35.

Convert the fractions to have the common denominator 35

We will multiply the numerator and the denominator of each fraction by the appropriate factor to get the equivalent fraction with a denominator of 35. For the first fraction, we multiply both the numerator and the denominator by \(\frac{5}{5}\): $$ \frac{3}{7} \cdot \frac{5}{5} = \frac{15}{35} $$ For the second fraction, we multiply both the numerator and the denominator by \(\frac{7}{7}\): $$ \frac{2}{5} \cdot \frac{7}{7} = \frac{14}{35} $$ Now, the fractions are \(\frac{15}{35}\) and \(\frac{14}{35}\).

Compare the numerators

We now have the fractions \(\frac{15}{35}\) and \(\frac{14}{35}\). To compare the fractions, we can simply compare their numerators since they have the same denominator. In this case, 15 > 14.

Write the inequality

Since 15 > 14, the inequality is: $$ \frac{3}{7} > \frac{2}{5} $$