Concept used:

Number which can be written on number line called real number.

Calculation:

\(\displaystyle\text{Let}\ {a}={2}\ \text{and}\ {b}={3}\)

\(\displaystyle{a}\ {<}\ {b}\)

\(\displaystyle{2}\ {<}\ {3}\)

Then

\(\displaystyle{\frac{{{a}\ +\ {b}}}{{{2}}}}={\frac{{{2}\ +\ {3}}}{{{2}}}}\)

\(\displaystyle={\frac{{{5}}}{{{2}}}}\)

\(\displaystyle={2.5}\)

Hence, \(\displaystyle{\frac{{{a}\ +\ {b}}}{{{2}}}}\) is in between a and b.

\(\displaystyle{a}\ {<}\ {\frac{{{a}\ +\ {b}}}{{{2}}}}\ {<}\ {b}\)

Conclusion:

For real number a and b, if \(\displaystyle{a}\ {<}\ {b}\ \text{then}{<}\ {\frac{{{a}\ +\ {b}}}{{{2}}}}\ {<}\ {b}\)