How do I calculate the following:

13 - (-14) =

How do I calculate the following:

13 - (-14) =

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You can change it to an addition problem by noticing that the negative sign is basically -1 and multiplying the -1 by all terms inside the parentheses. That is,

13 - (-14) ==> 13 + -(-14) ==> 13 + -1(-14)

==> 13 + (-1*(-14)) = 13 + (14) = 27

In this problem, the parentheses do not denote an order of operation--they are merely there to distinguish the minus sign from the negative sign. Anytime you are subtracting, think of "adding the opposite." The opposite of a positive number is a negative number, and the opposite of a negative number is a positive number.

So basic subtraction can be thought of like this:

Problem: 4 - 3 =

Now, change the subtraction symbol to addition ("adding") and change the positive 3 to a negative 3 (the opposite of positive 3 is negative 3)

So we have: 4 + (-3) =

= 1

Another example:

10 - (-2) =

Remember, whenever you see subtraction think, "add the opposite". What is the opposite of -2? That should be +2. So...

10 + (+2) =

= 12

Notice in this problem there are two negative numbers:

-10 - (-7) =

Let's "add the opposite" for this problem...

-10 + (+7) =

= -3

For your problem, the work looks like this:

13 - (-14) =

13 + (+14) =

= 27

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## Comments

Hi, Daniel. Your explanation is on target and easy to understand. I would also encourage students to simplify to one sign in the last step. I have worked with college algebra students who still do the double sign and then get confused in more complicated problems. It also avoids the "is this a negative sign or a subtraction sign" confusion. (If asked, I tell them that a subtraction sign makes the number negative.) :-)