Question

Use the LCD to determine which fraction is greater.

$\frac{7}{8},\frac{5}{6}$

Short answer

The fraction $\frac{\mathbf{7}}{\mathbf{8}}$ is greater than fraction $\frac{5}{6}$.

Step-by-step solution

Step 1. Given information

Consider, the fraction $\frac{7}{8},\frac{5}{6}$ provided in the question

Step 2. Calculation 

To evaluate the greater fraction in $\frac{7}{8},\frac{5}{6}$, it is needed to calculate the least common multiple of 8,6.

Therefore, the least common multiple of 8,6 is 24 and this will be least common denominator of fraction $\frac{7}{8},\frac{5}{6}$

Make equivalent fraction of each fraction by least common denominator

$\begin{array}{l}\frac{7}{8}=\frac{7\times 3}{8\times 3};\frac{5}{6}=\frac{5\times 4}{6\times 4}\\ \frac{7}{8}=\frac{21}{24}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}};\frac{5}{6}=\frac{20}{24}\end{array}$

As the equivalent fractional of $\frac{7}{8},\frac{5}{6}$have same denominator so compare the numerator

$21>20$

$\frac{7}{8}>\frac{5}{6}$

Hence, the fraction $\frac{7}{8}$ is greater than fraction $\frac{5}{6}$.