Question

Which of the following rational number is smaller than $\frac{3}{4}$ ?

• A. 5/6
• B. 2/3
• C. 4/5
• D. 9/10

Answer 1

The correct option is B 2/3

Given fraction is $\frac{3}{4}=0.75$ and the option are
(i) $\frac{5}{6}\approx 0.83$
(ii) $\frac{2}{3}\approx 0.67$
(iii) $\frac{4}{5}=0.8$
(iv) $\frac{9}{10}=0.9$
Thus, clearly $\frac{2}{3}\approx 0.67$ is smaller than $0.75=\frac{3}{4}$.
So, $\frac{2}{3}$ is smaller than $\frac{3}{4}$.

(OR)

We have to compare the given fraction with each of the following. For comparison between two fractions, we can use the cross multiplication method.

(i) consider $\frac{3}{4}$ and $\frac{5}{6}$

On cross, multiplying, we get

L.H.S: $3\times 6=18$ and

R.H.S: $5\times 4=20$

Since, $20>18$, So $\frac{5}{6}>\frac{3}{4}$