How to Add with Negative Numbers

When you understand what negative numbers mean, you can add them just like the positive numbers you’re used to. The number line can help make sense of this. You can turn every problem into a sequence of ups and downs. When you’re adding on the number line, starting with a negative number isn’t much different from starting with a positive number.

Adding a negative number is the same as subtracting a positive number — that is, go down (to the left) on the number line. This rule works regardless of whether you start with a positive or negative number.

After you understand how to add negative numbers on the number line, you’re ready to work without the number line. This becomes important when numbers get too large to fit on the number line. Here are some tricks:

• Adding a negative number plus a positive number: Switch around the two numbers (and their signs), turning the problem into subtraction.

• Adding a positive number plus a negative number: Drop the plus sign, turning the problem into subtraction.

• Adding two negative numbers: Drop both minus signs and add the numbers as if they were both positive; then attach a minus sign to the result.

Sample questions

1. Use the number line to add –3 + 5.

   2. On the number line, –3 + 5 means start at –3, up 5, which brings you to 2:

2. Use the number line to add 6 + –2.

   4. On the number line, 6 + –2 means start at 6, down 2, which brings you to 4:

3. Use the number line to add –3 + –4.

   –7. On the number line, –3 + –4 means start at –3, down 4, which brings you to –7:

4. Add –23 + 39.

   16. Switch around the two numbers with the signs attached:

   –23 + 39 = + 39 – 23

   Now you can drop the plus sign and use the minus sign for subtraction:

   39 – 23 = 16

Practice questions

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

   a. –5 + 6

   b. –1 + –7

   c. 4 + –6

   d. –3 + 9

   e. 2 + –1

   f. –4 + –4

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

   a. –17 + 35

   b. 29 + –38

   c. –61 + –18

   d. 70 + –63

   e. –112 + 84

   f. –215 + –322

Following are answers to the practice questions:

1. Addition problems

   a. –5 + 6 = 1. Start at –5, go up 6.

   b. –1 + –7 = –8. Start at –1, go down 7.

   c. 4 + –6 = –2. Start at 4, go down 6.

   d. –3 + 9 = 6. Start at –3, go up 9.

   e. 2 + –1 = 1. Start at 2, go down 1.

   f. –4 + –4 = –8. Start at –4, go down 4.

2. Addition problems without the number line

   a. –17 + 35 = 18. Switch around the numbers (with their signs) to turn the problem into subtraction:

   –17 + 35 = 35 – 17 = 18

   b. 29 + –38 = –9. Drop the plus sign to turn the problem into subtraction:

   29 + –38 = 29 – 38 = –9

   c. –61 + –18 = –79. Drop the signs, add the numbers, and negate the result:

   61 + 18 = 79, so –61 + –18 = –79.

   d. 70 + –63 = 7. Turn the problem into subtraction:

   70 + –63 = 70 – 63 = 7

   e. –112 + 84 = –28. Turn the problem into subtraction:

   –112 + 84 = 84 – 112 = –28

   f. –215 + –322 = –537. Drop the signs, add the numbers, and negate the result:

   215 + 322 = 537, so –215 + –322 = –537