How to Subtract with Negative Numbers

Subtracting a negative number is the same as adding a positive number — that is, go up on the number line. This rule works regardless of whether you start with a positive number or a negative number.

When subtracting a negative number, remember that the two back-to-back minus signs cancel each other out, leaving you with a plus sign. (Kind of like when you insist you can’t not laugh at your friends, because they’re really pretty ridiculous; the two negatives mean you have to laugh, which is a positive statement.)

Math books often put parentheses around the negative number you’re subtracting so the signs don’t run together, so 3 – –5 is the same as 3 – (–5).

When taking a negative number minus a positive number, drop both minus signs and add the two numbers as if they were both positive; then attach a minus sign to the result.

Sample question

1. Use the number line to subtract –1 – 4.

   –5. On the number line, –1 – 4 means start at –1, down 4, which brings you to –5.

Practice questions

1. Use the number line to solve the following subtraction problems:

   a. –3 – 4

   b. 5 – (–3)

   c. –1 – (–8)

   d. –2 – 4

   e. –4 – 2

   f. –6 – (–10)

2. Solve the following subtraction problems without using the number line:

   a. 17 – (–26)

   b. –21 – 45

   c. –42 – (–88)

   d. –67 – 91

   e. 75 – (–49)

   f. –150 – (–79)

Following are the answers to the practice questions:

1. Subtraction problems

   a. –3 – 4 = –7. Start at –3, down 4.

   b. 5 – (–3) = 8. Start at 5, up 3.

   c. –1 – (–8) = 7. Start at –1, up 8.

   d. –2 – 4 = –6. Start at –2, down 4.

   e. –4 – 2 = –6. Start at –4, down 2.

   f. –6 – (–10) = 4. Start at –6, up 10.

2. Subtraction problems without the number line

   a. 17 – (–26) = 43. Cancel the adjacent minus signs to turn the problem into addition:

   17 – (–26) = 17 + 26 = 43

   b. –21 – 45 = –66. Drop the signs, add the numbers, and negate the result:

   21 + 45 = 66, so –21 – 45 = –66

   c. –42 – (–88) = 46. Cancel the adjacent minus signs to turn the problem into addition:

   –42 – (–88) = –42 + 88

   Now switch around the numbers (with their signs) to turn the problem back into subtraction:

   88 – 42 = 46

   d. –67 – 91 = –158. Drop the signs, add the numbers, and negate the result:

   67 + 91 = 158, so –67 – 91 = –158

   e. 75 – (–49) = 124. Cancel the adjacent minus signs to turn the problem into addition:

   75 – (–49) = 75 + 49 = 124

   f. –150 – (–79) = –71. Cancel the adjacent minus signs to turn the problem into addition:

   –150 – (–79) = –150 + 79

   Now switch around the numbers (with their signs) to turn the problem back into subtraction:

   79 – 150 = –71