Calculate (-3)×(-1): Multiplying Two Negative Numbers

Q: Why does negative times negative equal positive?

Think of it as reversing a reversal! A negative number is like going backwards, so multiplying by another negative (going backwards again) brings you forward to positive territory.

Q: How can I remember the sign rules for multiplication?

Use this simple pattern: Same signs = Positive, Different signs = Negative. So (+)(+) = +, (-)(-) = +, but (+)(-) = - and (-)(+) = -.

Q: What's the difference between -3 × -1 and (-3) × (-1)?

There's no difference! The parentheses just make it clearer that we're multiplying the number negative three by the number negative one.

Q: Is the answer +3 or just 3?

Both $ +3 $ and $ 3 $ are correct! When a number is positive, we usually don't write the + sign, but writing it helps show you applied the sign rules correctly.

Q: What if I had (-3) × (+1) instead?

Then you'd have different signs (negative × positive), so the answer would be $ -3 $. Different signs always give a negative result!

Integer Multiplication with Negative Sign Rules

Complete the following exercise:

$(-3)\cdot(-1)=$

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Step-by-step video solution

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00:00 Solve

00:07 Negative times negative is always positive

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$(-3)\cdot(-1)=$

Step-by-step solution

Let's recall the rule:

$(-x)\times(-x)=+x$

Therefore, the sign of the exercise result will be positive:

$-3\times-1=+3$

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying two negative numbers, the result is positive
Technique: (-3) × (-1) = +3 because negative times negative equals positive
Check: Apply sign rule: two negatives make positive, so answer is +3 ✓

Common Mistakes

Avoid these frequent errors

Treating all negative multiplications as negative results
Don't assume (-3) × (-1) = -3 because you see negative signs! This ignores the multiplication sign rules and gives wrong answers. Always remember: negative × negative = positive, while negative × positive = negative.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why does negative times negative equal positive?

Think of it as reversing a reversal! A negative number is like going backwards, so multiplying by another negative (going backwards again) brings you forward to positive territory.

How can I remember the sign rules for multiplication?

Use this simple pattern: Same signs = Positive, Different signs = Negative. So (+)(+) = +, (-)(-) = +, but (+)(-) = - and (-)(+) = -.

What's the difference between -3 × -1 and (-3) × (-1)?

There's no difference! The parentheses just make it clearer that we're multiplying the number negative three by the number negative one.

Is the answer +3 or just 3?

Both $+3$ and $3$ are correct! When a number is positive, we usually don't write the + sign, but writing it helps show you applied the sign rules correctly.

What if I had (-3) × (+1) instead?

Then you'd have different signs (negative × positive), so the answer would be $-3$ . Different signs always give a negative result!

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