# How do you find a "REAL NUMBER" between pairs of numbers 3 1/3 and 3 2/3?

Apr 18, 2015

Method 1
One way to do this is to notice that the average of two numbers $n$ and $m$ is always between the numbers.

The average is: $\frac{m + n}{2}$ which can also be written $\frac{1}{2} \left(m + n\right)$.

So, using this way to do it, add the numbers: $3 \frac{1}{3} + 3 \frac{2}{3} = 7$, and now divide by $2$:
$7 \div 2 = 3 \frac{1}{2}$

$3 \frac{1}{2}$ is (the middle number) between $3 \frac{1}{3}$ and $3 \frac{2}{3}$

Method 2

If you like working with decimal numbers, use

$3 \frac{1}{3} = 3.333 \left(3\right)$ and $3 \frac{2}{3} = 3.666 \left(6\right)$ (Parentheses indicate repeated digits)

So any decimal between these will work: for example:

$3.4$, or $3.42597$ or #3.33444(4)