# How do you simplify 3 2/3 + 1 1/4 - 2 5/12?

Sep 1, 2017

Method broken down into a lot of detail. Once you get used to these you can do a lot of it in your head and rattle the answer off in a couple of lines.

$2 \frac{1}{2}$

#### Explanation:

$\textcolor{b l u e}{\text{The teaching bit!}}$

Stating the obvious: When adding and subtracting you are dealing with counts.

A fractions structure is such that we have:

$\left(\text{count")/("size indicator of what you are counting")->("numerator")/("denominator}\right)$

You can not DIRECTLY add or subtract counts unless the size indicators are the same. This is why 2+3 works as really it is $\frac{2}{1} + \frac{3}{1}$ The size indicator of their $\underline{\text{unit size}}$ are the same.

Consider $\frac{3}{16}$ the count is 3 and the unit size is $\frac{1}{16}$

So you have 3 of unit size $\frac{1}{16} = 3 \times \frac{1}{16} = \frac{3}{16}$
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In the end I make them all have the same 'unit size' (denominator)

Consider $3 \frac{2}{3} \leftarrow \text{ Detailed explanation}$

Write as $3 + \frac{2}{3}$ this is the same as

color(green)([3color(red)(xx1)]+2/3

color(green)([3/1color(red)(xx3/3)]+2/3

color(green)([(3color(red)(xx3))/(1color(red)(xx3))]+2/3

$\left[\frac{9}{3}\right] + \frac{2}{3} = \frac{11}{3}$
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Consider $1 \frac{1}{4}$

Using the same method as above this is $\frac{5}{4}$
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Consider $2 \frac{5}{12}$

Using the same method this is $\frac{29}{12}$
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Putting it all together

$\frac{11}{3} + \frac{5}{4} - \frac{29}{12}$

Again using the above approach we have

$\frac{44}{12} + \frac{15}{12} - \frac{29}{12} \text{ "=" } \frac{44 + 15 - 29}{12}$

$= \frac{30}{12}$

$= \frac{30 \div 6}{12 \div 6}$

$= \frac{5}{2} \textcolor{w h i t e}{\text{ddd") rarr color(white)("ddd}} \frac{2 + 2 + 1}{2}$

$= \frac{2}{2} + \frac{2}{2} + \frac{1}{2} \text{ " =" } 2 \frac{1}{2}$