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Q.

Which rational number lies exactly halfway between $\frac{2}{3}$ and $\frac{3}{4}$ ?

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a

\frac{16}{24}

b

\frac{17}{24}

c

\frac{18}{24}

d

none of these

answer is B.

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Detailed Solution

The given rational numbers are

\frac{2}{3}

and

\frac{3}{4} .

To find rational number lies exactly halfway between

\frac{2}{3}

and

\frac{3}{4} .

We know that a rational number

n_{1}

can be find in between

a and b

such that

a < n_{1} < b

using the formula

n_{1} = \frac{a + b}{2}

.
Substitute

a = \frac{2}{3}, b = \frac{3}{4}

in the formula.

\Rightarrow n_{1} = \frac{\frac{2}{3} + \frac{3}{4}}{2}

By cross multiplying and solving, we get

\Rightarrow n_{1} = \frac{\frac{8 + 9}{12}}{2}

{\Rightarrow n}_{1} = \frac{17}{2 \times 12}

{\Rightarrow n}_{1} = \frac{17}{24}

Thus, the midpoint of

\frac{2}{3}

and

\frac{3}{4}

is

\frac{17}{24}

.
Hence option

2

is correct.

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