Chapter 4, Problem 14CT

To determine

To determine which fraction is greater using LCD $\frac{11}{12},\frac{11}{20}$

Answer to Problem 14CT

  $\frac{11}{12}>\frac{11}{20}$

Explanation of Solution

Given information:

Expression $\frac{11}{12},\frac{11}{20}$ `

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-

  $\frac{11}{12}=\frac{11}{2\times 3\times 2}$

For the other fraction, it is-

  $\frac{11}{20}=\frac{11}{2\times 2\times 5}$

In the above fractions, it is clear that the LCD is $2\times 2$ which is 4.

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

  $\frac{11}{12}=\frac{1}{4}\left(\frac{11}{3}\right)$

And the other one as-

  $\frac{11}{20}=\frac{11}{4}\left(\frac{11}{5}\right)$

Now our fractions are reduced to

  $\left(\frac{11}{3}\right)$ and $\left(\frac{11}{5}\right)$

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-

  $\left(\frac{11}{3}\right)\times \frac{5}{5}=\frac{55}{15}$

And for the second fraction

  $\left(\frac{11}{5}\right)\times \frac{3}{3}=\frac{33}{15}$

Now, both the fractions have same denominator 15.

  $\frac{55}{15}$ , $\frac{33}{15}$

Since 55 is greater than 33, so the first fraction is greater than the second one.

  $\frac{11}{12}>\frac{11}{20}$

Conclusion-

  $\frac{11}{12}>\frac{11}{20}$