Chapter 4, Problem 23MCQ

To determine

To determine which fraction is greater using LCD $\frac{7}{10},\frac{18}{25}$

Answer to Problem 23MCQ

  $\frac{7}{10}<\frac{18}{25}$

Explanation of Solution

Given information:

Expression $\frac{7}{10},\frac{18}{25}$

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-

  $\frac{7}{10}=\frac{7}{2\times 5}$

For the other fraction, it is-

  $\frac{18}{25}=\frac{18}{5\times 5}$

In the above fractions, it is clear that the LCD is 5.

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

  $\frac{7}{10}=\frac{1}{5}\left(\frac{7}{2}\right)$

And the other one as-

  $\frac{18}{25}=\frac{1}{5}\left(\frac{18}{5}\right)$

Now our fractions are reduced to

  $\left(\frac{7}{2}\right)$ and $\left(\frac{18}{5}\right)$

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-

  $\left(\frac{7\times 5}{2\times 5}\right)=\frac{35}{25}$

And for the second fraction

  $\left(\frac{18\times 5}{5\times 5}\right)=\frac{90}{25}$

Now, both the fractions have same denominator 25.

  $\frac{35}{25}$ , $\frac{90}{25}$

Since 35 is less than 90, so the first fraction is less than the second one.

  $\frac{7}{10}<\frac{18}{25}$

Conclusion-

  $\frac{7}{10}<\frac{18}{25}$