# What Number is halfway between 1/2 and 3/4 on a number line?

May 15, 2015

If $a$ and $b$ are any numbers, then halfway between them is the average $\frac{a + b}{2} = \left(\frac{1}{2}\right) \cdot \left(a + b\right)$.

So halfway between $\frac{1}{2}$ and $\frac{3}{4}$ is

$\left(\frac{1}{2}\right) \cdot \left(\left(\frac{1}{2}\right) + \left(\frac{3}{4}\right)\right)$

$= \left(\frac{1}{2}\right) \cdot \left(\left(\frac{2}{4}\right) + \left(\frac{3}{4}\right)\right)$

$= \left(\frac{1}{2}\right) \cdot \left(\frac{2 + 3}{4}\right)$

$= \left(\frac{1}{2}\right) \cdot \left(\frac{5}{4}\right)$

$= \frac{1 \cdot 5}{2 \cdot 4}$

$= \frac{5}{8}$

Jun 16, 2017

$\frac{5}{8}$

#### Explanation:

Here is another method of finding a fraction halfway between 2 others.

Convert both fractions to a common denominator.

$\frac{1}{2} \mathmr{and} \frac{3}{4}$ can be shown as: $\frac{2}{4} \mathmr{and} \frac{3}{4}$

$2 \frac{1}{2}$ is obviously halfway between $2 \mathmr{and} 3 ,$ but the fraction
$\frac{2 \frac{1}{2}}{4}$ is not comfortable..

Use another denominator: Let's try eighths.

$\frac{1}{2} \mathmr{and} \frac{3}{4}$ are the same as

$\frac{\textcolor{b l u e}{4}}{8} \mathmr{and} \frac{\textcolor{b l u e}{6}}{8}$

$5$ is halfway between color(blue)(4 and 6)" rarr ((color(blue)(4+6))/2 = 5)

So the fraction we want is $\frac{5}{8}$