Chapter 1, Problem 13MS

To determine

To rewrite: The fraction $\frac{5}{8}$ and $\frac{3}{4}$ using least common denominator.

Answer to Problem 13MS

The given fraction with least common denominator is $\frac{5}{8}\text{and }\frac{6}{8}$ .

Explanation of Solution

Given:

The fractions are $\frac{5}{8}$ and $\frac{3}{4}$ .

Calculation:

The given fractions $\frac{5}{8}$ and $\frac{3}{4}$ have denominators 4 and 8.

Determine the LCM of denominators as follows:

  $\begin{array}{l}8=2^3\\ 4=2^2\\ \text{LCM}=2^3=8\end{array}$

Hence, multiply with constant to make both the denominators as 8.

Multiply the fraction $\frac{5}{8}$ by 1 and $\frac{3}{4}$ by 2 to make the common denominator as follows:

  $\begin{array}{c}\frac{5}{8}\times \frac{1}{1}=\frac{5}{8}\\ \frac{3}{4}\times \frac{2}{2}=\frac{6}{8}\end{array}$

Thus, the given fraction with least common denominator is $\frac{5}{8}\text{and }\frac{6}{8}$ .