Chapter 4, Problem 27CR

To determine

To determine which fraction is greater using LCD $\frac{7}{30},\frac{11}{36}$

Answer to Problem 27CR

  $\frac{7}{30}<\frac{11}{36}$

Explanation of Solution

Given information:

Expression $\frac{7}{30},\frac{11}{36}$

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-

  $\frac{7}{30}=\frac{7}{5\times 2\times 3}$

For the other fraction, it is-

  $\frac{11}{36}=\frac{11}{2\times 3\times 2\times 3}$

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

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

  $\frac{7}{30}=\frac{1}{6}\left(\frac{7}{5}\right)$

And the other one as-

  $\frac{11}{36}=\frac{1}{6}\left(\frac{11}{6}\right)$

Now our fractions are reduced to

  $\left(\frac{7}{5}\right)$ and $\left(\frac{11}{6}\right)$

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-

  $\left(\frac{7}{5}\right)\times \frac{6}{6}=\frac{42}{30}$

And for the second fraction

  $\left(\frac{11}{6}\right)\times \frac{5}{5}=\frac{55}{30}$

Now, both the fractions have same denominator 30.

  $\frac{42}{30},\frac{55}{30}$

Since 42 is less than 55, so the first fraction is less than the second one.

  $\frac{7}{30}<\frac{11}{36}$

Conclusion-

  $\frac{7}{30}<\frac{11}{36}$