Chapter 4, Problem 25MCQ

To determine

To determine which fraction is greater using LCD $\frac{11}{18},\frac{13}{24}$

Answer to Problem 25MCQ

  $\frac{11}{18}>\frac{13}{24}$

Explanation of Solution

Given information:

Expression $\frac{11}{18},\frac{13}{24}$

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-

  $\frac{11}{18}=\frac{11}{3\times 3\times 2}$

For the other fraction, it is-

  $\frac{13}{24}=\frac{13}{2\times 3\times 2\times 2}$

In the above fractions, it is clear that the LCD is 6.

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

  $\frac{11}{18}=\frac{1}{6}\left(\frac{11}{3}\right)$

And the other one as-

  $\frac{13}{24}=\frac{1}{6}\left(\frac{13}{4}\right)$

Now our fractions are reduced to

  $\left(\frac{11}{3}\right)$ 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-

  $\frac{11\times 4}{3\times 4}=\frac{44}{12}$

And for the second fraction

  $\frac{13\times 3}{4\times 3}=\frac{39}{12}$

Now, both the fractions have same denominator 12.

  $\frac{44}{12}$ , $\frac{39}{12}$

Since 44 is greater than 39, so the first fraction is g than the second one.

  $\frac{11}{18}>\frac{13}{24}$

Conclusion-

  $\frac{11}{18}>\frac{13}{24}$