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By McGraw-Hill Professional
Updated on Sep 21, 2011

There are two basic rules for adding integers:

Rule 1: To add two integers with like signs (i.e., both integers are positive or both integers are negative), add the absolute values of the numbers and give the sum the common sign .

#### Solution 1

Since both integers are positive, add the absolute values of each, 2 + 4 = 6; then give the answer a + sign. Hence, (+2) + (+4) = +6.

#### Solution 2

Since both integers are negative, add the absolute values 3 + 2 = 5; then give the answer a-sign. Hence, (–3) + (–2)= –5. The rule can be demonstrated by looking at the number lines shown in Fig. 2-3 .

Fig. 2-3.

In the first example, you start at 0 and move two units to the right, ending at +2. Then from +2, move 4 units to the right, ending at +6. Therefore, (+2) + (+4) = +6.

In the second example, start at 0 and move 3 units to the left, ending on –3. Then from –3, move 2 units to the left, ending at –5. Therefore, (–3) + (–2)= –5.

Rule 2: To add two numbers with unlike signs (i.e., one is positive and one is negative), subtract the absolute values of the numbers and give the answer the sign of the number with the larger absolute value .

#### Solution 3

Since the numbers have different signs, subtract the absolute values of the numbers, 5 – 2 = 3. Then give the 3 a positive sign since 5 is larger than 3 and the sign of the 5 is positive. Therefore, (+5) + (–2)= +3.

#### Solution 4

Since the numbers have different signs, subtract the absolute values of the numbers, 4 – 3 = 1. Then give the 1 a negative sign since 4 is larger than 3. Therefore, (+3) +(–4)= –1. This rule can be demonstrated by looking at the number lines shown in Fig. 2-4 .

Fig. 2-4.

In the first case, start at 0 and move five units to the right, ending on +5. From there, move 2 units to the left. You will end up at +3. Therefore, (+5) +(–2)= +3.

In the second case, start at 0 and move 3 units to the right, ending at +3. From there, move 4 units to the left. You will end on –1. Therefore, (+3) + (–4) = –1.

To add three or more integers, you can add two at a time from left to right .

#### Example 5

Add (–3) + (–4) + (+2) + (+8) +(–5)

#### Solution 5

Math Note: When 0 is added to any number, the answer is the number. For example, 0 + 6 = 6, (–3) + 0 = –3.

### Addition of Integers Practice Problems

#### Practice

1. (+8) + (+2)

2. (–5) + (–12)

3. (+6) +(–10)

4. (–9) + (+4)

5. (+6) +(–3)

6. (–12) + 0

7. (+10) +(–11) + (+1)

8. (+3) + (–4) + (+2)

9. (–5) + (+12) +(–3) + (+6)

10. (–6) + (–8) + (+3) + (+4) +(–2)

1. +10

2. –17

3. –4

4. –5

5. +3

6. –12

7. 0

8. +1

9. +10

10. –9

More practice problems for this concept can be found at: Integers Practice Test.

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