# How do you simplify 4 1/4 div 2?

Sep 22, 2016

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

#### Explanation:

While using fractions, we convert division into multiplication by taking the multiplicative inverse or reciprocal of the divisor.

As reciprocal of a fraction is nothing but numerator and denominator reversed, if we have to divide $\frac{a}{b}$ by $\frac{c}{d}$, we just multiply $\frac{a}{b}$ and $\frac{d}{c}$.

If one of the numbers is not a fraction, we write it as fraction. For example $p$ as $\frac{p}{1}$.

Hence $4 \frac{1}{4} \div 2$

= (4xx4+1)/4-:2/

= $\frac{17}{4} \times \frac{1}{2} = \frac{17 \times 1}{4 \times 2} = \frac{17}{8}$

= $\frac{2 \times 8 + 1}{8} = \frac{2 \times 8}{8} + \frac{1}{8} = 2 \frac{1}{8}$

Oct 3, 2016

$\frac{17}{8}$

Full explanation given as to how it all works.

#### Explanation:

Given:$\text{ } 4 \frac{1}{4} \div 2$

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the $4 \frac{1}{4}$

Write as:$\text{ } 4 + \frac{1}{4}$

Multiply by 1 and you do not change the value, but 1 comes in many forms. So we can change the way it looks without changing the intrinsic value.

Multiply the 4 by 1 but in the form of $\textcolor{m a \ge n t a}{1 = \frac{4}{4}}$

$\left[4 \textcolor{m a \ge n t a}{\times \frac{4}{4}}\right] + \frac{1}{4}$

$\left[\frac{16}{4}\right] + \frac{1}{4} \text{ "=" } \frac{16 + 1}{4}$

$\text{So "4 1/4" is the same as } \frac{17}{4}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all together: $\to \frac{17}{4} \div 2$

$\textcolor{m a \ge n t a}{\text{Shortcut method "->" Invert the 2 and multiply}}$

$\textcolor{b l u e}{\frac{17}{4} \times \frac{1}{2} = \frac{17}{8}} \leftarrow \text{ shortcuts make calculation faster}$

'.............................................................................................
$\textcolor{m a \ge n t a}{\text{First principle method "->" turn the 2 into quarters}}$

Multiply the 2 by 1 but in the form of $\textcolor{g r e e n}{1 = \frac{4}{4}}$

$\frac{17}{4} \div \left[2 \textcolor{g r e e n}{\times \frac{4}{4}}\right]$

$\frac{17}{4} \div \frac{8}{4}$

Fraction structure is $\left(\text{count")/("size indicator")" "->" "("numerator")/("denominator}\right)$

$\textcolor{b r o w n}{\text{As both the size indicators are the same we can just divide counts}}$

$\implies \frac{17}{4} \div \frac{8}{4} \text{ "=" "17-:8" "=" } \textcolor{b l u e}{\frac{17}{8}}$