# What is the quotient of -5.2/3.9?

Jan 5, 2017

$- 1 \frac{1}{3}$

#### Explanation:

$\textcolor{b l u e}{\text{Simplify the fraction}}$

Write as:$\text{ } - \left(\frac{5.2}{3.9}\right)$

Don't like decimals so lets get rid of them.

color(green)(-(5.2/3.9color(red)(xx1)) = -(5.2/3.9color(red)(xx10/10))

$= - \frac{52}{39}$

Note that - 52 is the same as - 39 - 13

$- \frac{39}{39} - \frac{13}{39} \text{ "=" "-1-1/3" " =" } - \frac{4}{3}$

But $\text{ "-4/3" " =" " -3/3-1/3" " =" } - 1 \frac{1}{3}$
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$\textcolor{b l u e}{\text{Now compare this to } - \left(5.2 \div 3.9\right)}$

Using a calculator we get $- 1.3333333 \ldots$

which is the same as $- 1 \frac{1}{3}$
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This is because:

$\frac{5.2}{3.9} \to \frac{5.2 \div 3.9}{3.9 \div 3.9} = \frac{5.2 \div 3.9}{1} = \frac{1.33333 \ldots}{1} = \frac{1 \frac{1}{3}}{1} = 1 \frac{1}{3}$

Jan 5, 2017

$- \frac{4}{3} = - 1 \frac{1}{3} \approx - 1.333$

#### Explanation:

At a time when many students tend to depend on a calculator, many will not realise that working with fractions can be easier than using decimals, and there are often really simple methods to do calculations.

A quotient is the answer to a division

In this case:

$\frac{- 5.2}{3.9} \text{ } \leftarrow$ dividing BY a decimal is not a good idea.

Get rid of the decimals by multiplying by $\frac{10}{10}$

$\frac{- 5.2}{3.9} \times \frac{10}{10} = \frac{- 52}{39}$

This is where knowing the multiplication times tables helps.

$52 \mathmr{and} 39$ are both divisible by 13. Cancel to simplest form:

$\frac{- 52 \div 13}{39 \div 13} = \frac{- 4}{3}$

This can be written as $- \frac{4}{3} = - 1 \frac{1}{3} \approx - 1.333$