How do you simplify 414÷2?

Question

lapinar7g1 · Accepted Answer

Step 1
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}

.
Step 2

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

= \frac{4 \times 4 + 1}{4} \div 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}

Emilie Mcpherson · Accepted Answer

Full explanation given as to how it all works.
Explanation:
Given:

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

Consider

4 \frac{1}{4}

Write as:

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

1 = \frac{4}{4}

.

[4 \times \frac{4}{4}] + \frac{1}{4}

[\frac{16}{4}] + \frac{1}{4} = \frac{16 + 1}{4}

So

4 \frac{1}{4}

is the same as

\frac{17}{4}

Putting it all together:

\to \frac{17}{4} \div 2

Shortcut method

\to

Invert the 2 and multiply

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

shortcuts make calculation faster
First principle method

\to

turn the 2 into quarters
Multiply the 2 by 1 but in the form of

1 = \frac{4}{4}

\frac{17}{4} \div [2 \times \frac{4}{4}]

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

Fraction structure is

\frac{count}{size indicator} \to \frac{numerator}{denominator}

As both the size indicators are the same we can just divide counts

\Rightarrow \frac{17}{4} \div \frac{8}{4} = 17 \div 8 = \frac{17}{8}

How do you simplify 4\frac{1}{4} \div 2?

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