1.6 Integer Arithmetic Review
Learning Objectives
- Add, subtract, multiply, and divide integers without a calculator.
- Apply integer rules mentally and quickly.
Launch
To help simplify algebraic expressions accurately and confidently, this section reviews the rules for integer arithmetic.
Addition of Integers
Rules
- Same signs → add the numbers and keep the sign.
- Example:
- Example:
- Example:
- Different signs → subtract the smaller absolute value from the larger and keep the sign of the larger absolute value.
- Example:
(since 9 has the larger absolute value, the answer is positive) - Example:
(since 10 has the larger absolute value, the answer is negative)
- Example:
Example 1.6.1a
Simplify: 
Solution
The signs are different, so subtract:
Keep the sign of the number with the larger absolute value (–12):
Example 1.6.1b
Simplify: 
Solution
The signs are the same. Add the numbers and keep the sign:
Subtraction of Integers
Rule
Subtraction can be rewritten as adding the opposite:
Example 1.6.2
Simplify: 
Solution
Rewrite as addition:
Example 1.6.3
Simplify: 
Solution
Rewrite as addition:
The signs are different, so subtract:
Keep the sign of the larger absolute value (–5):
Multiplication of Integers
Rules
Example 1.6.4
Simplify: 
Solution
The signs are different, so the result is negative.
Final answer: 
Example 1.6.5
Simplify: 
Solution
Multiplying two negatives makes a positive.
Final answer: 
Division of Integers
Rules
Example 1.6.6
Simplify: 
Solution
The signs are different, so the result is negative.
Final answer: 
Example 1.6.7
Simplify: 
Solution
Dividing two negatives makes a positive.
Final answer: 
Try It
Key Takeaways
- Addition: Same signs → add and keep the sign; different signs → subtract and keep the sign of the larger absolute value.
- Subtraction: Rewrite as adding the opposite.
- Multiplication and Division: Two negatives make a positive; one negative makes a negative.
- With practice, integer arithmetic should be manageable mentally and quickly.
