Question

During his initial days of stay in Earth 2, Bill had got his accommodation with “1/5” and “1/2” in “House of Rational Numbers, Q”. Having located these occupants, he wanted to locate other occupants satisfying the following conditions:

1. They lie between 1/5 and 1/2.

2. They have a denominator 10.

Which of the following occupants satisfy these properties?

• A. $\frac{2}{10}$
• B. $\frac{3}{10}$
• C. $\frac{4}{10}$
• D. $\frac{5}{10}$

Answer 1

Answer: (B), (C)

The correct options are
B

$\frac{3}{10}$

C

$\frac{4}{10}$

$\frac{1}{5}$ and $\frac{1}{2}$ are rational numbers.
To find the rational numbers between these two, we need to first make the denominators of both the numbers equal.

Since another condition is that the denominators should be 10, let’s see if we can make 10 as the common denominator.

If we multiply both the numerator and denominator of $\frac{1}{5}$ with 2, we get $\frac{1\times 2}{5\times 2}=\frac{2}{10}$ and similarly, multiplying the numerator and denominator of $\frac{1}{2}$ by 5, we get $\frac{1\times 5}{2\times 5}=\frac{5}{10}$.

So, we need to find numbers which are in between $\frac{2}{10}$ and $\frac{5}{10}$.

This now becomes a simple intuition that $\frac{3}{10}$ and $\frac{4}{10}$ lie in between these numbers.