# How do you multiply 4 2/3 div 1 5/8?

Mar 12, 2016

The question is given in fractions so the answer has to be in fractions.

$2 \textcolor{w h i t e}{.} \frac{34}{39}$

#### Explanation:

$\textcolor{b r o w n}{\text{Multiply any number by 1 and you do not change its value}}$
color(brown)("This is a 'trick' to convert a whole number into a fraction."

We know that $4 \times 1 = 4$

But $\frac{3}{3}$ is another way of writing 1

So instead of writing $4 \times 1 = 4$ we could write $4 \times \frac{3}{3} = 4$

But $4 \times \frac{3}{3} \text{ is the same as } \frac{4 \times 3}{3} = \frac{12}{3}$

So $\frac{12}{3}$ is 4 converted into thirds!
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$\textcolor{b l u e}{\text{Answering your question}}$

Given:$\textcolor{g r e e n}{\text{ } 4 \frac{2}{3} \div 1 \frac{5}{8}}$

Converting 4 into thirds and 1 into eights

$\textcolor{g r e e n}{\text{ } \left(\frac{12}{3} + \frac{2}{3}\right) \div \left(\frac{8}{8} + \frac{5}{8}\right)}$

$\textcolor{g r e e n}{\text{ } \frac{14}{3} \div \frac{13}{8}}$

Using the shortcut rule of: when dividing turn the divisor (what you are dividing by) upside down and then multiply

$\textcolor{g r e e n}{\text{ } \frac{14}{3} \times \frac{8}{13}}$

$\textcolor{g r e e n}{\text{ } \frac{14 \times 8}{3 \times 13}}$

$\textcolor{g r e e n}{\text{ } \frac{112}{39}}$

$\textcolor{b l u e}{\text{ } 2 \frac{34}{39}}$
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$\textcolor{b r o w n}{\text{Another trick}}$

Suppose you have the whole number of say 6. Although not normally done it is perfectly correct to write 6 as $\frac{6}{1}$

So if you have $3 \div 6$ you are permitted to write it as

$\frac{3}{1} \div \frac{6}{1} = \frac{3}{1} \times \frac{1}{6} = \frac{3 \times 1}{1 \times 6} = \frac{3}{6}$