Solve (-3) × (-10): Step-by-Step Negative Number Multiplication

Q: Why does negative times negative equal positive?

Think of it as "opposite of opposite" - if negative means going backward, then negative times negative means going backward in the backward direction, which brings you forward (positive)!

Q: How do I remember the sign rules?

Use this simple pattern: Same signs = Positive (+ × + or - × -), Different signs = Negative (+ × - or - × +). Like × Like = Positive!

Q: What if I have more than two negative numbers?

Count the negative signs! An even number of negatives gives positive, an odd number gives negative. (-2) × (-3) × (-4) has 3 negatives (odd) = negative result.

Q: Is (-3) × (-10) the same as -3 × -10?

Yes! The parentheses just make it clearer that the entire number is negative. Both expressions mean the same thing: negative three times negative ten.

Q: Can I just ignore the negative signs and add them back later?

No! This leads to wrong answers. You must apply the sign rules correctly: multiply the numbers (3 × 10 = 30) then determine the sign (negative × negative = positive).

Negative Number Multiplication with Sign Rules

Complete the following exercise:

$(-3)\cdot(-10)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:07 Negative times negative is always positive

00:15 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:

$(-3)\cdot(-10)=$

Step-by-step solution

Let's remember the rule:

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

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

$-3\times-10=+30$

Final Answer

$30$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative times negative always equals positive
Technique: (-3) × (-10) = +(3 × 10) = +30
Check: Two negative signs cancel to make positive result ✓

Common Mistakes

Avoid these frequent errors

Keeping negative sign in final answer
Don't calculate (-3) × (-10) = -30! This ignores the fundamental rule that two negatives make a positive. Always remember: negative × negative = positive, so the answer must be +30.

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 "opposite of opposite" - if negative means going backward, then negative times negative means going backward in the backward direction, which brings you forward (positive)!

How do I remember the sign rules?

Use this simple pattern: Same signs = Positive (+ × + or - × -), Different signs = Negative (+ × - or - × +). Like × Like = Positive!

What if I have more than two negative numbers?

Count the negative signs! An even number of negatives gives positive, an odd number gives negative. (-2) × (-3) × (-4) has 3 negatives (odd) = negative result.

Is (-3) × (-10) the same as -3 × -10?

Yes! The parentheses just make it clearer that the entire number is negative. Both expressions mean the same thing: negative three times negative ten.

Can I just ignore the negative signs and add them back later?

No! This leads to wrong answers. You must apply the sign rules correctly: multiply the numbers (3 × 10 = 30) then determine the sign (negative × negative = positive).

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