Question

Use the LCD to determine which fraction is greater.

$\frac{13}{15},\frac{11}{18}$

Short answer

The fraction $\frac{\mathbf{13}}{\mathbf{15}}$ is greater than fraction $\frac{\mathbf{11}}{\mathbf{18}}$ .

Step-by-step solution

Step 1. Given information

The fraction $\frac{13}{15},\frac{11}{18}$ .

Step 2. Calculation 

To evaluate the greater fraction in $\frac{13}{15},\frac{11}{18}$, it is needed to calculate the least common multiple of 15,18.

Therefore, the least common multiple of 15, 18 is 90 and this will be least common denominator of fraction $\frac{13}{15},\frac{11}{18}$.

Make equivalent fraction of each fraction by least common denominator.

$\begin{array}{l}\frac{13}{15}=\frac{13\times 6}{15\times 6};\frac{11}{18}=\frac{11\times 5}{18\times 5}\\ \frac{13}{15}=\frac{78}{90}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}};\frac{11}{18}=\frac{55}{90}\end{array}$

As the equivalent fractional of $\frac{13}{15},\frac{11}{18}$have same denominator so compare the numerator

$78>55$

$\frac{13}{15}>\frac{11}{18}$

Hence, the fraction $\frac{13}{15}$ is greater than fraction $\frac{11}{18}$