Question

How do you evaluate `55- ( + 22)`?

Answer 1

`33`

Explanation:

When we combine signs (`+` or `-`), the rules are:

The product of a positive and a positive is a positive:
`+xx+=+`

The result of a positive and a negative (or a negative and a positive) is a negative:
`+xx- =-` or `-xx+=-`

The result of a negative and a negative is a positive:
`-xx- =+`

In the above, we have a negative and a positive. Hence, applying the rules:

`55-(+22)=55-22=33`

Answer 2

When multiplying or dividing consider the signs in pairs. If there are more than two consider them one pair at a time. If the sings are different then the answer to that pair is negative. If they are the same then the answer to that pair is positive.

Example: `(-3)xx(+4)xx(-2)`

`color(blue)("First deal with just the signs "->) (-)(+)(-)`

`color(white)(.)`

Grouping on pairs `-> color(red)( [color(white)(.)(-)(+)color(white)(.)] )color(green)((-))`

`color(red)(" First pair "-rarrul("| |"))`

First pair are different to each other so for this bit it is negative. Group this outcome with the next sign and consider that as the next pair.

Grouping in pairs `-> color(red)( [-])color(green)((-))`

`color(magenta)("Second pair "--> ul(|" "|`

Second pair are both the same sign so the final answer is positive.

`color(blue)("Now deal with the numbers")`

`(-3)xx(+4)xx(-2)" " =" " +(3xx4xx2)" "=" "+24`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

`55-(+22)`

Think of this as:

`55-1(+22)`

Multiply everything inside the brackets by `-1`. The signs are different so the outcome is negative.

`55-22=33`