How do I calculate the following:
13 - (-14) =
How do I calculate the following:
13 - (-14) =
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
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.) :-)