Chapter 4, Problem 22MCQ

To determine

To determine which fraction is greater using LCD $\frac{3}{8},\frac{4}{9}$

Answer to Problem 22MCQ

  $\frac{3}{8}<\frac{4}{9}$

Explanation of Solution

Given information:

Expression $\frac{3}{8},\frac{4}{9}$

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-

  $\frac{3}{8}=\frac{3}{2\times 2\times 2}$

For the other fraction, it is-

  $\frac{4}{9}=\frac{4}{3\times 3}$

In the above fractions, it is clear that the LCD is 1. So our fractions cannot be reduced further.

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-

  $\frac{3\times 9}{8\times 9}=\frac{27}{72}$

And for the second fraction

  $\frac{4\times 8}{9\times 8}=\frac{32}{72}$

Now, both the fractions have same denominator 72.

  $\frac{27}{72}$ , $\frac{32}{72}$

Since 27 is less than 32, so the first fraction is less than the second one.

  $\frac{3}{8}<\frac{4}{9}$

Conclusion-

  $\frac{3}{8}<\frac{4}{9}$