Question

Use the LCD to determine which fraction is greater.

$\frac{3}{4},\frac{7}{9}$

Short answer

The fraction $\frac{7}{9}$ is greater than fraction $\frac{3}{4}$.

Step-by-step solution

Step 1. Given information

Consider, the fraction $\frac{3}{4},\frac{7}{9}$provided in the question.

Step 2. Calculation 

To evaluate the greater fraction in $\frac{3}{4},\frac{7}{9}$, it is needed to calculate the least common multiple of $4,9$

Therefore, the least common multiple of $4,9$is $36$ and this will be least common denominator of fraction $\frac{3}{4},\frac{7}{9}$

Make equivalent fraction of each fraction by least common denominator

$\begin{array}{l}\frac{3}{4}=\frac{3\times 9}{4\times 9};\frac{7}{9}=\frac{7\times 4}{9\times 4}\\ \frac{3}{4}=\frac{27}{36}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}};\frac{7}{9}=\frac{28}{36}\end{array}$

As the equivalent fractional of $\frac{3}{4},\frac{7}{9}$have same denominator so compare the numerator

$28>27$

$\frac{7}{9}>\frac{3}{4}$

Hence,

The fraction $\frac{7}{9}$ is greater than fraction $\frac{3}{4}$