Question

Use the LCD to determine which fraction is greater.

$\frac{2}{7},\frac{3}{5}$

Short answer

The fraction $\frac{3}{5}$is greater than fraction $\frac{2}{7}$.

Step-by-step solution

Step 1. Given information

Consider, the fraction $\frac{2}{7},\frac{3}{5}$ provided in the question.

Step 2. Calculation 

To evaluate the greater fraction in$\frac{2}{7},\frac{3}{5}$it is needed to calculate the least common multiple of $7,5$

Therefore, the least common multiple of 7, 5 is 35 and this will be least common denominator of fraction $\frac{2}{7},\frac{3}{5}$

Make equivalent fraction of each fraction by least common denominator

Make equivalent fraction of each fraction by least common denominator

$\begin{array}{l}\frac{2}{7}=\frac{2\times 5}{4\times 5};\frac{3}{5}=\frac{3\times 7}{5\times 7}\\ \frac{2}{7}=\frac{10}{35}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}};\frac{3}{5}=\frac{21}{35}\end{array}$

As the equivalent fractional of $\frac{2}{7},\frac{3}{5}$have same denominator so compare the numerator

$21>10$

$\frac{3}{5}>\frac{2}{7}$

Hence, the fraction $\frac{3}{5}$is greater than fraction $\frac{2}{7}$