Question

Which of the following fraction is the greatest?

• A. $\frac{2}{3}$
• B. $\frac{1}{6}$
• C. $\frac{4}{18}$
• D. None of the above

Answer 1

The correct option is A $\frac{2}{3}$

Let's compare $\frac{2}{3},\frac{1}{6}\text{and}\frac{4}{18}:$

Step 1: Find the LCM of denominators of the given fractions.
i.e. LCM of 3, 6 and 18:
3 can be written as $3:3\times 1$
6 can be written as $6:3\times 2$
18 can be written as $18:3\times 3\times 2$


Taking the factors with highest powers common, we get
$3^2$ from 18, $2^1$ from 6 and $1$ from 3.

Multiplying them, we get $3^2\times 2^1\times 1=18$ as the required LCM.

Step 2: Now, we multiply $\frac{2}{3}$ and $\frac{1}{6}$ with $6$ and $3$ respectively to make their denominators as $18.$

$\therefore \frac{2}{3}=\frac{2\times 6}{3\times 6}=\frac{12}{18}$

$\frac{1}{6}=\frac{1\times 3}{6\times 3}=\frac{3}{18}$

and denominator of $\frac{4}{18}$ is already 18.

Step 3: When fractions have the same denominator, then the largest fraction is the one with the largest numerator.

So, just compare the numerators 12, 3 and 4.

Since $12>4>3$
$\therefore \frac{12}{18}>\frac{4}{18}>\frac{3}{18}$
$\Rightarrow \frac{2}{3}>\frac{4}{18}>\frac{1}{6}$