Multiplication & Division of Integers explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
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Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Multiplying and dividing integers uses simple sign rules.
These rules are needed for algebra, equations, fractions, coordinates, and later topics.
First calculate the number part. Then decide the sign.
For multiplication and division, the sign rule is the same.
Same signs give a positive answer. Different signs give a negative answer.
This rule is different from addition and subtraction. Do not use addition sign rules for multiplication.
Division by zero is not allowed.
Meaning: Integer multiplication finds products of signed whole numbers.
Definition: A product is the answer to multiplication.
Multiply the absolute values first. Then decide the sign.
Meaning: Integer division finds quotients of signed whole numbers.
Definition: A quotient is the answer to division.
Divide the absolute values first. Then use the same sign rule as multiplication.
Meaning: A product or quotient can contain several signed numbers.
Definition: The final sign depends on how many negative signs are present in multiplication.
An even number of negative factors gives a positive product. An odd number gives a negative product.
Easy
Question: Fin x 8.
Medium
Question: Fin / -7.
Exam-level
Question: Simplify (-3) x 4 x (-5).
Using addition sign rules
Why it happens: Students learn integer addition first.
Correct approach: For multiplication and division, use same signs positive and different signs negative.
Thinking two negatives always make a positive
Why it happens: The phrase is remembered without context.
Correct approach: Two negatives make a positive in multiplication and division, not always in addition.
Dividing by zero
Why it happens: Zero is treated like any other number.
Correct approach: Division by zero is undefined and must not be done.
Why i positive?
Multiplication patterns show that a negative times a negative must be positive for arithmetic to stay consistent.
I negative?
Yes. Different signs give a negative quotient.
What if there are three negative factors?
An odd number of negative factors gives a negative product.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.