# How do you evaluate 1/2 + 5/8?

Jun 2, 2016

You need to make both fractions have the same denominator first.

#### Explanation:

In this case, the common denominator would be 8.

$\frac{1}{2} \cdot \frac{4}{4} = \frac{4}{8}$

$\frac{4}{8} + \frac{5}{8} = \frac{9}{8}$

You can then choose to present it as a mixed fraction, which would be $1 \frac{1}{8}$

Jun 2, 2016

In support of solution by Denise Granger

#### Explanation:

This is a generic tutorial about part of the concept/processing of fractions and numbers in general. Some which you have heard before. Some of which likely not!

$\textcolor{red}{\text{Forms a very important basis for number handling}}$

A fraction has 2 parts. The top number and the bottom number.

$\textcolor{b l u e}{\underline{\text{The top number is the count}}}$ of what you are looking at (numerator). The name comes from enumerate - give number to - count!

$\textcolor{g r e e n}{\underline{\overline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{red}{\underline{\text{The bottom number is the 'indicator of size'}}}} \textcolor{w h i t e}{.} |}}$ denominator

I think this as $\left(\text{count")/("size}\right)$ or $\left(\text{count")/("unit size indicator}\right)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## You can not directly add, subtract or divide unless the unit size of what you are dealing with is the same.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Think of 1+2 = 3. You are directly adding the count. This is because their unit size is the same. It takes 1 of what you are counting to make a whole of something. So technically you could write $\frac{1}{1} + \frac{2}{1} = \frac{3}{1}$ and be perfectly correct. Not normally done though!

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Think of $\frac{1}{2} + \frac{5}{2}$. The unit size is 2 in that it take 2 of them to make a whole. By adding the count you do not change the unit size of 2. So $\frac{1}{2} + \frac{5}{2} = \frac{1 + 5}{2} = \frac{6}{2}$ You end up with a count of 6 where each of the 6 is of unit size 2. As you know you are able to compare it an equivalent unit size of 1 by doing this:

$\frac{6}{2} \equiv \frac{6 \div 2}{2 \div 2} = \frac{3}{1} = 3$

The $\equiv$ means equivalent to.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Think of $\frac{6}{2} \div \frac{3}{2}$ this gives you the same answer as $6 \div 3$ because they are of the same unit size. The shortcut method of invert and multiply has built into its method converting to same unit size then dividing the count. The only thing is that it does it all in one go.