How do you simplify $6 \frac{1}{2} \div 2 \frac{1}{3}$ $6 1/2 div 2 1/3$ ?

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How do you simplify $6 \frac{1}{2} \div 2 \frac{1}{3}$ $6 1/2 div 2 1/3$ ?

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Answer 1 · 2016-12-24T16:11:33

$\frac{39}{14}$ $39/14$

Explanation:

The first step to simplifying this expression is to convert the mixed fractions into improper fractions. This is done by multiplying the integer or whole number part of the fraction by the correct form of $1$ $1$ and then adding it to the fraction:

$6 \frac{1}{2} \div 2 \frac{1}{3} \to ((\frac{2}{2} \times 6) + \frac{1}{2}) \div ((\frac{3}{3} \times 2) + \frac{1}{3}) \to$ $6 1/2 -: 2 1/3 -> ((color(red)(2/2) xx 6) + 1/2) -: ((color(blue)(3/3) xx 2) + 1/3) ->$

$(\frac{12}{2} + \frac{1}{2}) \div (\frac{6}{3} + \frac{1}{3}) \to \frac{13}{2} \div \frac{7}{3}$ $(color(red)(12/2) + 1/2) -: (color(blue)(6/3) + 1/3) -> 13/2 -: 7/3$

This can now be rewritten as:

$\frac{\frac{13}{2}}{\frac{7}{3}}$ $(13/2)/(7/3)$

The rule for dividing fractions is:

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \times d}{b \times c}$ $color(red)((a/b)/(c/d) = (a xx d)/(b xx c))$

Using this rule on our expression gives:

$\frac{\frac{13}{2}}{\frac{7}{3}} = \frac{13 \times 3}{2 \times 7} = \frac{39}{14}$ $(13/2)/(7/3) = (13 xx 3)/(2 xx 7) = 39/14$

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