Chapter 1, Problem 16MS

To determine

To rewrite: The fraction $\frac{5}{12}$ and $\frac{3}{2}$ using least common denominator.

Answer to Problem 16MS

The given fraction with least common denominator is $\frac{5}{12}\text{and }\frac{18}{12}$ .

Explanation of Solution

Given:

The fractions are $\frac{5}{12}$ and $\frac{3}{2}$ .

Calculation:

The given fractions $\frac{5}{12}$ and $\frac{3}{2}$ have denominators 12 and 2.

Determine the LCM of denominators as follows:

  $\begin{array}{l}12=2^2\times 3^1\\ 2=2^1\\ \text{LCM}=2^2\times 2=12\end{array}$

Hence, multiply with constant to make both the denominators as 12.

Multiply the fraction

  $\frac{5}{12}$ by 1 and $\frac{3}{2}$ by 6 to make the common denominator 12 as follows:

  $\begin{array}{c}\frac{5}{12}\times \frac{1}{1}=\frac{5}{12}\\ \frac{3}{2}\times \frac{6}{6}=\frac{18}{12}\end{array}$

Thus, the given fraction with least common denominator is $\frac{5}{12}\text{and }\frac{18}{12}$ .