Chapter 4, Problem 13CT

To determine

To determine which fraction is greater using LCD $\frac{3}{5},\frac{8}{15}$

Answer to Problem 13CT

  $\frac{3}{5}>\frac{8}{15}$

Explanation of Solution

Given information:

Expression $\frac{3}{5},\frac{8}{15}$

Formula Used: Least Common Denominator

Calculation:

The first step here is to identify the Least Common Denominator for both fractions. So, break the denominators into its multiples-

  $\frac{3}{5}=\frac{3}{5}$

For the other fraction, it is-

  $\frac{8}{15}=\frac{8}{3\times 5}$

In the above fractions, it is clear that the LCD is 5.

In the second step, extract the LCD, and rewrite the fractions as-

  $\frac{3}{5}=\frac{1}{5}\left(3\right)$

And the other one as-

  $\frac{8}{15}=\frac{1}{5}\left(\frac{8}{3}\right)$

Now our fractions are reduced to

  $\left(\frac{3}{1}\right)$ and $\left(\frac{8}{3}\right)$

now make the denominators of both fractions same by multiplying each fractions denominator, with the numerator & denominator of the other fraction.

So for first fraction-

  $\left(\frac{3}{1}\right)\times \frac{3}{3}=\frac{9}{3}$

And for the second fraction

  $\left(\frac{8}{3}\right)\times \frac{1}{1}=\frac{8}{3}$

Now, both the fractions have same denominator 3.

  $\frac{9}{3}$ , $\frac{8}{3}$

Since 9isgreater than 8, so the first fraction is greater than the second one.

  $\frac{3}{5}>\frac{8}{15}$

Conclusion-

  $\frac{3}{5}>\frac{8}{15}$