How do you simplify $\frac{2}{\frac{3}{11}}$ $2/(3/11)$ ?

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How do you simplify $\frac{2}{\frac{3}{11}}$ $2/(3/11)$ ?

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Answer 1 · 2016-10-30T10:41:40

$\frac{22}{3} = 7 \frac{1}{3}$ $22/3 = 7 1/3$

Explanation:

In order to know how to calculate this, first decide what it means...

This is another way of writing $2 \div \frac{3}{11}$ $2 div 3/11$

We could also write $\frac{2}{1} \div \frac{3}{11}$ $2/1 div 3/11$ to have both as fractions.

Dividing by a fraction is the same as "X by the reciprocal"

$\frac{2}{1} \times \frac{11}{3} = \frac{22}{3} \leftarrow$ $2/1 xx11/3 = 22/3" "larr$ multiply straight across.

But compare the two ways of writing this:

$\frac{\frac{2}{1}}{\frac{3}{11}} = \frac{2 \times 11}{1 \times 3} \leftarrow$ $(2/1)/(3/11) = (2xx11)/(1xx3)" "larr$ can you see a short cut?

$\frac{\frac{2}{1}}{\frac{3}{11}} = \frac{(2 \times 11)}{(1 \times 3)} = \frac{22}{3}$ $(color(red)(2)/color(blue)1)/(color(blue)3/color(red)(11)) = color(red)((2xx11))/color(blue)((1xx3)) = 22/3$

As a general rule note that: $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \times d}{b \times c}$ $(a/b)/(c/d) = (axxd)/(bxxc)$

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How do you simplify $\frac{2}{\frac{3}{11}}$ $2/(3/11)$ ?

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