Pre-Algebra
Numbers and operations
Multiplying and dividing integers
20 practice questions
0 video lessons
Theory + worked examples
Multiplying and Dividing Integers
Texas Pre-Algebra (TEKS) • Standard 7.3(A) • Numbers & Operations
Multiplying and Dividing Integers is a topic in Numbers & Operations in the Texas Essential Knowledge and Skills. It is aligned to Standard 7.3(A), which requires students to multiply and divide integers and determine the sign of the result.
When multiplying or dividing integers, same signs give a positive result and different signs give a negative result.
Theory
For multiplying and dividing integers, first multiply or divide the digits, then decide the sign:
- Same signs give a positive result.
- Different signs give a negative result.
Count the negatives: an even count is positive, an odd count negative.
The sign rules.
Counting negative factors.
Sign rules:
\[(-)(-) = +,\qquad (+)(-) = -\]
The same rules apply to division.
How to multiply or divide integers
- Multiply or divide the absolute values.
- Count the negative signs.
- Even count: positive. Odd count: negative.
- Attach the sign to the answer.
Example 1 — Two negatives
Find \((-6)(-4)\).
Solution
Same signs give a positive.
| \((-6)(-4)\) | \(=\) | \(24\) |
Example 2 — Different signs
Find \(-7\cdot 3\).
Solution
Different signs give a negative.
| \(-7\cdot 3\) | \(=\) | \(-21\) |
Example 3 — Division
Find \(-20\div(-5)\).
Solution
Same signs give a positive.
| \(-20\div(-5)\) | \(=\) | \(4\) |
Example 4 — Count the signs
Find \((-1)(-2)(-3)\).
Solution
Three negatives — odd — so the product is negative.
| \((-1)(-2)(-3)\) | \(=\) | \(-6\) |
Common pitfalls
\((-)(-)=+\): two negatives multiply to a positive.
These are multiplication rules, not the addition rules.
Division follows the same sign rules.
Frequently asked questions
What is a negative times a negative?
A positive.
What is a positive times a negative?
A negative.
Do the rules apply to division?
Yes, exactly the same.
What is \((-1)(-2)(-3)\)?
\(-6\) — three (odd) negatives.
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