Question

How do you evaluate `\frac { - 1} { 10} \div \frac { 1} { 4}`?

Answer 1

`-2/5`

Explanation:

Divide a negative by a positive is the same as multiply a negative by a positive. In that the answer is negative.

If the signs are the same then the answer is positive. If they are different then the answer is negative.

`" "(-1)/10` is the same as `-1/10` so we have

Dealing with just the signs:

`" "-1/10-:1/4->" negative answer"`

Dealing with the numbers:

`" "1/10-:1/4" "=" "1/10xx4/1`

`" "= 4/10-=(4-:2)/(10-:2) = 2/5`

This gives a final answer of `-2/5`

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`color(blue)("Foot note")`

SUPPOSE that instead of `(-1)/10` we had `(-1)/(-10)` In this case the two signs are the same giving`->+1/10`

However. in this question the signs are different in that we have:
`(-1)/10` which is the same as `(-1)/(+10) = -1/10`