# How do you evaluate 5\frac { 3} { 4} + 4\frac { 1} { 2} ?

Apr 14, 2017

Explained in a lot of detail

$10 \frac{1}{4}$

#### Explanation:

Once well practised you will be able to solve this problem type in just a few lines.

Consider this as $5 + \frac{3}{4} + 4 + \frac{1}{2}$

$\textcolor{b r o w n}{\text{The whole number part is } 5 + 4 = 9}$

Consider the fraction part.

We have $\frac{3}{4} + \frac{1}{2}$
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A fractions structure is such that you have:

$\left(\text{count")/("indicator the size of what is being counted")->("numerator")/("denominator}\right)$

You can not $\underline{\text{directly add}}$ the counts unless the 'size indicators' are the same.

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its actual value.
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$\textcolor{g r e e n}{\frac{3}{4} \text{ "+" } \left[\frac{1}{2} \textcolor{red}{\times 1}\right]}$

$\textcolor{g r e e n}{\frac{3}{4} \text{ "+" } \left[\frac{1}{2} \textcolor{red}{\times \frac{2}{2}}\right]}$

$\frac{3}{4} \text{ "+" "2/4" "=" } \frac{3 + 2}{4} = \frac{5}{4}$

but $\frac{5}{4}$ is the same as $\frac{4}{4} + \frac{1}{4} = 1 + \frac{1}{4}$

color(brown)("So the fraction part is "3/4+1/2=1 1/4
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$\textcolor{b l u e}{\text{Putting it all together}}$

$\textcolor{b l u e}{9 + 1 \frac{1}{4} = 10 \frac{1}{4}}$