Question

How do you evaluate `-42+ ( - 62) + 15`?

Answer 1

The problem you are looking at is based on INTEGERS.

Explanation:

INTEGERS are basically all the numbers, that is, positive and negative. They include zero and are basically natural and whole numbers. They are every number you can think of except the fact that they don't contain IRRATIONAL NUMBERS or RATIONAL NUMBERS (we won't deal with this here).

INTEGERS have very simple rules:-
1. Negative and Positive make a Negative, for example -

`1 + (-2) = -1`
So, you see the negative with 2 turned the whole equation into subtraction rather than addition. And hence, we subtract. The thing you should observe here is that the subtraction is the same. What you do normally, but as we are subtracting a smaller number from a bigger one we add a minus.

1. Two negatives result in a positive, for example -

`-2 + (-3) = -2 - 3 = -5`
So, you see the negative sign with 3 turned operation into subtraction but, as we had two negatives occurring together the resultant operation was positive. The result is same when you add 2 and 3 normally but, here just a negative sign would be added because we are going on the negative side of the number line.

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Solving your problem above:-
`-42 + (-62) + 15`

`= -42 -62 + 15` ( The bracket has been removed and then see rule 2 written above)

`=-104 + 15` (By Rule 2, the negatives have bee added)

`= -89` (The answer. This step has been obtained by Rule 1)

Answer 2

`-89`

Explanation:

`color(blue)("Dealing with the part "+(-62))`

For multiply and divide, when you have two signs the same that part is positive. When you have two signs not the same the answer is negative.

Consider the part that is `+(-62)`. This is the same as `+1(-62)`

So you multiply everything inside the brackets by +1 ending up with:

`(+1)xx(-62) -> -62` as the signs are different.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`-42-62+15`

`-104+15 = -89`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("If you find subtracting a bigger number difficult do this")`

Write as `-(+104-15)`

This temporarily reverses the sign making the subtraction be of the format you are perhaps more used to.

so 104-15 is 89

but what we really have is `-(104-15) = -(89) =-89`