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Negatives: dividing negative numbers

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Question 1

Complete the following without the use of a calculator:

a)

Which of the following are equal to $(\var{n[0]})\div(\var{d[0]})$ ?

Dividing negative numbers can be done by pretending the numbers are positive, doing the division, and then determining whether the actual answer should be positive or negative.

It is also crucial to realise division can be written as a fraction.

Consider $(\var{n[0]})\div(\var{d[0]})$ . Let's move the negatives out the front to get $--\var{-n[0]}\div\var{-d[0]}$ , we can just do the division and get $--\frac{\var{-n[0]}}{\var{-d[0]}}$ , but this is the same as $\frac{\var{-n[0]}}{\var{-d[0]}}$ .

In general, two negatives divided results in a positive.

$\dfrac{-}{+}=-$

$\dfrac{+}{-}=-$

$\dfrac{-}{-}=+$

$\dfrac{+}{+}=+$

This should not be surprising given that division is just multiplying by the reciprocal.

Not marked

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(You will lose 3 marks.)

Answer for part a)

$\displaystyle-\frac{\var{-n[0]}}{\var{-d[0]}}$
$\displaystyle\frac{\var{n[0]}}{\var{-d[0]}}$
$\var{-n[0]}\div\var{-d[0]}\phantom{\dfrac{1}{1}}$
$\displaystyle\frac{\var{-n[0]}}{\var{-d[0]}}$
$\displaystyle\frac{\var{-n[0]}}{\var{d[0]}}$
$\displaystyle\frac{\var{n[0]}}{\var{d[0]}}$

Expected answer:

$\displaystyle-\frac{\var{-n[0]}}{\var{-d[0]}}$
$\displaystyle\frac{\var{n[0]}}{\var{-d[0]}}$
$\var{-n[0]}\div\var{-d[0]}\phantom{\dfrac{1}{1}}$
$\displaystyle\frac{\var{-n[0]}}{\var{-d[0]}}$
$\displaystyle\frac{\var{-n[0]}}{\var{d[0]}}$
$\displaystyle\frac{\var{n[0]}}{\var{d[0]}}$

Score: 0/3

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Or, you could:

There's nothing more to do from here.

b)

Which of the following are equal to $\var{n[1]}\div\var{-d[1]}$ ?

Dividing negative numbers can be done by pretending the numbers are positive, doing the division, and then determining whether the actual answer should be positive or negative.

It is also crucial to realise division can be written as a fraction.

Consider $\var{n[1]}\div\var{-d[1]}$ . This will be the same as $-\frac{\var{-n[1]}}{\var{-d[1]}}$ , and $\frac{\var{n[1]}}{\var{-d[1]}}$ , and even the strange looking $\frac{\var{-n[1]}}{\var{d[1]}}$ .

In general, two negatives divided results in a positive.

$\dfrac{-}{+}=-$

$\dfrac{+}{-}=-$

$\dfrac{-}{-}=+$

$\dfrac{+}{+}=+$

This should not be surprising given that division is just multiplying by the reciprocal.

Not marked

Feedback for .

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This feedback is based on your last submitted answer. Save your changed answer to get updated feedback.

What do you want to do next?

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(You will lose 3 marks.)

Answer for part b)

$\displaystyle-\frac{\var{-n[1]}}{\var{-d[1]}}$
$\var{-n[1]}\div\var{-d[1]}\phantom{\dfrac{1}{1}}$
$\displaystyle\frac{\var{n[1]}}{\var{d[1]}}$
$\displaystyle\frac{\var{n[1]}}{\var{-d[1]}}$
$\displaystyle\frac{\var{-n[1]}}{\var{-d[1]}}$
$\displaystyle\frac{\var{-n[1]}}{\var{d[1]}}$

Expected answer:

$\displaystyle-\frac{\var{-n[1]}}{\var{-d[1]}}$
$\var{-n[1]}\div\var{-d[1]}\phantom{\dfrac{1}{1}}$
$\displaystyle\frac{\var{n[1]}}{\var{d[1]}}$
$\displaystyle\frac{\var{n[1]}}{\var{-d[1]}}$
$\displaystyle\frac{\var{-n[1]}}{\var{-d[1]}}$
$\displaystyle\frac{\var{-n[1]}}{\var{d[1]}}$

Score: 0/3

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Advice

$\endgroup$

Score: 0/6

Total	0/6

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