Chapter 4, Problem 25CR

To determine

To determine which fraction is greater using LCD $\left(\frac{1}{12}\right),\left(\frac{3}{40}\right)$

Answer to Problem 25CR

  $\left(\frac{1}{12}\right)>\left(\frac{3}{40}\right)$

Explanation of Solution

Given information:

Expression $\left(\frac{1}{12}\right),\left(\frac{3}{40}\right)$

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-

  $\left(\frac{1}{12}\right)=\left(\frac{1}{2\times 2\times 3}\right)$

For the other fraction, it is-

  $\left(\frac{3}{40}\right)=\left(\frac{3}{2\times 2\times 2\times 5}\right)$

In the above fractions, it is clear that the LCD is 4.

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

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

And the other one as-

  $\begin{array}{l}\left(\frac{3}{40}\right)=\frac{1}{4}\left(\frac{3}{10}\right)\\ \end{array}$

Now our fractions are reduced to

  $\left(\frac{1}{3}\right)$ and $\left(\frac{3}{10}\right)$

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-

  $\frac{1}{3}\times \frac{10}{10}=\frac{10}{30}$

And for the second fraction

  $\left(\frac{3}{10}\right)\times \frac{3}{3}=\frac{9}{30}$

Now, both the fractions have same denominator 30.

  $\frac{10}{30},\frac{9}{30}$

Since 10 is greater than 9, so the first fraction is greater than the second one.

  $\left(\frac{1}{12}\right)>\left(\frac{3}{40}\right)$

Conclusion-

  $\left(\frac{1}{12}\right)>\left(\frac{3}{40}\right)$