Chapter 4, Problem 28CR

To determine

To determine which fraction is greater using LCD $\frac{4}{45},\frac{13}{60}$

Answer to Problem 28CR

  $\frac{4}{45}<\frac{13}{60}$

Explanation of Solution

Given information:

Expression $\frac{4}{45},\frac{13}{60}$

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-

  $\frac{4}{45}=\frac{4}{3\times 3\times 5}$

For the other fraction, it is-

  $\frac{13}{60}=\frac{13}{3\times 4\times 5}$

In the above fractions, it is clear that the LCD is 15.

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

  $\frac{4}{45}=\frac{1}{15}\left(\frac{4}{3}\right)$

And the other one as-

  $\frac{13}{60}=\frac{1}{15}\left(\frac{13}{4}\right)$

Now our fractions are reduced to

  $\left(\frac{4}{3}\right)$ and $\left(\frac{13}{4}\right)$

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-

  $\left(\frac{4}{3}\right)\times \frac{4}{4}=\frac{16}{12}$

And for the second fraction

  $\left(\frac{13}{4}\right)\times \frac{3}{3}=\frac{39}{12}$

Now, both the fractions have same denominator 12.

  $\frac{16}{12},\frac{39}{12}$

Since 16 is less than 39, so the first fraction is less than the second one.

  $\frac{4}{45}<\frac{13}{60}$

Conclusion-

  $\frac{4}{45}<\frac{13}{60}$