Question

How do you evaluate `(-9)+14`?

Answer 1

There are various way of approaching this. I am going to show you one you may not have seen before.

`color(brown)("Explained in detail. With practice you will do a lot")` `color(brown)("of this in your head and be much more efficient.")`

Split the 14 into `9+5`. This is called partitioning.

There is no sign to the left of the brackets so it is automatically:

`+(-9)`

Think of this as `+1(-9)" which is the same as "(+1)xx(-9)`

In multiply, if the signs are different then the answer is negative

`(-9)" "=" "(+1)xx(-9)" " =" " -9`
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`color(blue)("Having dealt with the above we now answer the question")`

Write: `color(green)((-9))color(red)(+14)" as "color(green)(-9color(red)(+9+5)`

But `-9+9" " ->" "+9-9=0` giving

`0+5`

so `(-9)+14=+5`

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~~~~~~~~~~~~ More efficient approach ~~~~~~~~~~~~~~~~~~~~~~
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`(-9)+14 = 14-9 = 5`