# Prove the following

Question:

$\frac{5}{6}$ lies between $\frac{2}{3}$ and $1 .$

Solution:

True.

Express each of the given rational numbers with 6 as the common denominator. Now,

$(2 / 3)=[(2 \times 3) /(2 \times 2)]=(4 / 6)$

$(1)=[(1 \times 6) /(1 \times 6)]=(6 / 6)$

Then,

$=4 / 6<5 / 6<6 / 6$

$=2 / 3<5 / 6<1$

So, $5 / 6$ lies between $2 / 3$ and 1 .