# How do you simplify 45-13 4/11?

Nov 12, 2016

$\setminus \frac{348}{11}$

## Conversions:

Convert $45$ to eleventh fractional form:
$\setminus \textcolor{red}{45 = \setminus \frac{45 \setminus \times 11}{11} = \setminus \frac{495}{11}}$
Convert $13 \setminus \frac{4}{11}$ to improper fraction form:
$\setminus \textcolor{b l u e}{13 \setminus \frac{4}{11} = \setminus \frac{\left(13 \setminus \times 11\right) + 4}{11} = \setminus \frac{143 + 4}{11} = \setminus \frac{147}{11}}$

## Input in original equation:

$\setminus \textcolor{red}{\setminus \frac{495}{11}} - \setminus \textcolor{b l u e}{\setminus \frac{147}{11}} = \setminus \frac{495 - 147}{11}$
$= \setminus \frac{348}{11}$

Nov 12, 2016

$31 \frac{7}{11}$

#### Explanation:

Subtracting a fraction from a whole number is generally quite quick and easy if you remember that a whole number can be written as a fraction with an equal numerator and denominator.

$1 = \frac{8}{8} = \frac{15}{15} = \frac{23}{23} \ldots .$

In $45 - 13 \frac{4}{11} \text{ }$ subtract the 13 as a whole number first:

$\textcolor{red}{45 - 13} \frac{4}{11}$

$= \textcolor{red}{32} - \frac{4}{11}$

$= 31 + \frac{11}{11} - \frac{4}{11}$

$= 31 \frac{7}{11}$

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Background examples

Consider: $\textcolor{b l u e}{7} - \frac{1}{2} \rightarrow \textcolor{b l u e}{6 + \frac{2}{2}} - \frac{1}{2} = 6 \frac{1}{2}$

$\textcolor{b l u e}{11} - \frac{3}{4} \rightarrow \textcolor{b l u e}{10 + \frac{4}{4}} - \frac{3}{4} = 10 \frac{1}{4}$

$\textcolor{red}{5 - 1} \frac{2}{3} = \textcolor{red}{4} - \frac{2}{3} = 3 \frac{2}{3}$