 How to Subtract with Negative Numbers - dummies

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