Multiplying Integers
Same signs give positive; different signs give negative.
Key idea
Same signs give positive; different signs give negative.
In depth
Same signs give a positive product, different signs give a negative. Why: (−1) × (−1) must be 1 to keep the distributive law consistent. Count the negative factors: an even count gives positive.
Worked example
(−3) × (−4) = 12; (−3) × 4 = −12; (−2)×(−3)×(−1) = −6.
Formula
Real-world uses
- Calculating total change in value over several periods
- Sign rules in spreadsheets and programming
Common mistake
Applying the rule for addition (keep the sign) to multiplication.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Multiplying Integers?
Same signs give positive; different signs give negative. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Multiplying Integers?
The key formula is (−)(−) = +, (−)(+) = −.
Where is Multiplying Integers used in real life?
Real-world examples: Calculating total change in value over several periods; Sign rules in spreadsheets and programming.
What should I learn before Multiplying Integers?
Make sure you are comfortable with Adding Integers, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Multiplying Integers?
Applying the rule for addition (keep the sign) to multiplication.
How can I practise Multiplying Integers?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Multiplying Integers?
Move on to Absolute Value next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.