Chapter 4, Problem 26CR

To determine

To determine which fraction is greater using LCD $\frac{4}{15},\frac{7}{27}$

Answer to Problem 26CR

  $\frac{4}{15}>\frac{7}{27}$

Explanation of Solution

Given information:

Expression $\frac{4}{15},\frac{7}{27}$

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-

  $\frac{4}{15}=\frac{4}{3\times 5}$

For the other fraction, it is-

  $\frac{7}{27}=\frac{7}{3\times 3\times 3}$

In the above fractions, it is clear that the LCD is 3.

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

  $\frac{4}{15}=\frac{1}{3}\left(\frac{4}{5}\right)$

And the other one as-

  $\frac{7}{27}=\frac{1}{3}\left(\frac{7}{9}\right)$

Now our fractions are reduced to

  $\left(\frac{4}{5}\right)$ and $\left(\frac{7}{9}\right)$

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-

  $\left(\frac{4}{5}\right)\times \left(\frac{9}{9}\right)=\frac{36}{45}$

And for the second fraction

  $\left(\frac{7}{9}\right)\times \left(\frac{5}{5}\right)=\frac{35}{45}$

Now, both the fractions have same denominator 45.

  $\frac{36}{45},\frac{35}{45}$

Since 36 is greater than 35, so the first fraction is greater than the second one.

  $\frac{4}{15}>\frac{7}{27}$

Conclusion-

  $\frac{4}{15}>\frac{7}{27}$