Question

Which of the following options is correct regarding the fractions $\frac{1}{3}$ and $\frac{1}{4}$?

• A. $\frac{1}{3}<\frac{1}{4}$
• B. $\frac{1}{3}>\frac{1}{4}$
• C. $\frac{1}{3}=\frac{1}{4}$
• D. None of the above

Answer 1

The correct option is B $\frac{1}{3}>\frac{1}{4}$

For $\frac{1}{3}$ and $\frac{1}{4}$, the denominators are different. Therefore, they are unlike fractions.

First, we have to convert unlike fractions to like fractions to compare.

To convert to like fractions, we have to make the denominators same.

Thus, LCM of 3 and 4 is 12.

Multiplying the numerator and denominator of $\frac{1}{3}$ with 4, we have
$\frac{1\times 4}{3\times 4}=\frac{4}{12}$

Multiplying the numerator and denominator of $\frac{1}{4}$ with 3, we have
$\frac{1\times 3}{4\times 3}=\frac{3}{12}$

Now, we are comparing the like fractions $\frac{4}{12}$ and $\frac{3}{12}$.

Therefore, for like fractions, we compare the numerators.
Hence, $\frac{4}{12}>\frac{3}{12}$
Thus, $\frac{1}{3}>\frac{1}{4}$