Question

What is the quotient of -5.2/3.9?

Answer 1

`-1 1/3`

Explanation:

`color(blue)("Simplify the fraction")`

Write as:`" " -(5.2/3.9)`

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))`

`=- 52/39`

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

`-39/39 - 13/39" "=" "-1-1/3" " =" " -4/3`

But `" "-4/3" " =" " -3/3-1/3" " =" " -1 1/3`
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`color(blue)("Now compare this to "-(5.2-:3.9))`

Using a calculator we get `-1.3333333...`

which is the same as `-1 1/3`
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This is because:

`5.2/3.9 -> (5.2-:3.9)/(3.9-:3.9) = (5.2-:3.9)/1=(1.33333...)/1 = ( 1 1/3)/1=1 1/3`

Answer 2

`-4/3 = -1 1/3 ~~ -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:

`(-5.2)/3.9" "larr` dividing BY a decimal is not a good idea.

Get rid of the decimals by multiplying by `10/10`

`(-5.2)/3.9 xx 10/10 = (-52)/39`

This is where knowing the multiplication times tables helps.

`52 and 39` are both divisible by 13. Cancel to simplest form:

`(-52div13)/(39div 13) = (-4)/3`

This can be written as `-4/3 = -1 1/3 ~~ -1.333`