Find a rational number lying between 1/3 and 1/2.

5/12. 1/3 = 4/12 and 1/2 = 6/12, so 5/12 lies between them. The mean 1/2(1/3 + 1/2) = 5/12 also confirms this.

Find a rational number lying between $\frac{1}{3}$ and $\frac{1}{2}$ .

Class 9Number SystemsNumber Systems

\frac{1}{3} = \frac{4}{12}

and

\frac{1}{2} = \frac{6}{12}

, so

\frac{5}{12}

lies between them. The mean

\frac{1}{2} (\frac{1}{3} + \frac{1}{2}) = \frac{5}{12}

also confirms this.

Answer: A)

\frac{5}{12}

**Sum/difference of two irrationals can be rational.** Example:

(1 + 2) + (1 - 2) = 2

.
**Product of two irrationals can be rational.** Example:

2 \times 2 = 2

.
**Sum of a rational and an irrational is always irrational.**

3 + 2

is irrational.
**Product of a non-zero rational and an irrational is always irrational.**

5 \times 2

is irrational.

These facts let you build new irrationals and prove things irrational by contradiction.

Don't just memorise the answer — build a daily practice habit.