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Subtracting Positive and Negative Numbers

Subtracting positive and negative numbers can also be tricky because there are several rules to remember and follow.

Rule 1: Subtracting a positive number from a positive number—this is normal subtraction.

Example 1: Don’t let all this talk of positive and negative numbers throw you off track—if you see a positive number minus a positive number, subtract it like normal! For example, if you see 5 – 3, subtract normally! 5 – 3 = 2.

Rule 2: Subtracting a positive number from a negative number—start at the negative number, and count backwards the additional amount you’re subtracting.

Example 2: Let’s say we had the problem -5 – 3. This would be read as “negative five minus three.” This can be thought of on a number line, which means we’re going to start at the negative number (-5) and keep counting back the -3, arriving at -8, like this:

The large red dot above the -5 shows that that’s where we’re starting our problem. The red arrow shows that we counted backwards (subtracted) 3. The red circle around the –8 shows that that’s our answer.

Thus, -5 – 3 = -8.

You can also think about these problems as addition problems—you add the numbers together (5 + 3 = 8) and then, since both numbers have a minus sign in front of them, you would add a negative sign in front of your answer, like this: -8. If this makes more sense, you can do these problems like this—but only problems that are written like this: -5 – 3. If there are any other signs (addition, subtraction, etc) you need to follow the rule for that type of problem.

Rule 3: Subtracting a negative number from a negative number—when you see the subtraction (minus) sign followed by a negative sign, turn the two signs into a plus sign. Thus, instead of subtracting a negative, you are adding a positive. So, – -5 becomes +5, and continue normally with the addition.

Example 3: Let’s say we had the problem -6 – -3. This would be read as “negative six minus negative three.” This can be thought of on a number line, which means we’re going to start at by changing the – -3 into +3, like this:

Now our problem reads -6 + 3, which we can solve as a normal addition problem on the number line, like this:

The large red dot above the -6 shows that that’s where we’re starting our problem. The blue arrow shows that we counted forward (added) 3. The blue circle around the –3 shows that that’s our answer.

Rule 4: Subtracting a negative number from a positive number—when you see the subtraction (minus) sign followed by a negative sign, turn the two signs into a plus sign. Thus, instead of subtracting a negative, you’re adding a positive, so you have a simple addition problem.

Example 4: Let’s say we had the problem 5 – (-3). This would be read as “five minus negative three.” This would work the same way as the previous example, so the – (-3) would change to a +3; therefore, your new problem would read 5 + 3, which is a simple addition problem, resulting in 8.

Subtracting Positive and Negative Numbers Quiz

Problems

1. 4 – 2 2. -8 – 5 3. -4 – (-7) 4. 6 – (-3) 5. -9 – 1
6. -10 – (-8) 7. 9 – 4 8. 2 – (-7) 9. -7 – 8 10. -5 – (-6)

Solutions

1. 2 2. -13 3. 3 4. 9 5. -10
6. -2 7. 5 8. 9 9. -15 10. 1