Solve (-3)×(-5): Multiplying Two Negative Numbers

Q: Why does negative times negative equal positive?

Think of it as "opposite of opposite" - when you reverse a reverse, you get back to the original direction! Mathematically, $ (-1) \times (-1) = +1 $ is the foundation of this rule.

Q: How do I remember all the sign rules?

Use this simple pattern: Same signs = positive, Different signs = negative. So $ (+) \times (+) = (+) $ and $ (-) \times (-) = (+) $, but $ (+) \times (-) = (-) $.

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

Count the negative signs! An even number of negatives gives a positive result, while an odd number gives a negative result. For example: $ (-2) \times (-3) \times (-4) = -24 $ (3 negatives = odd = negative).

Q: Does this rule work for division too?

Yes! The same sign rules apply to division. $ (-15) ÷ (-3) = +5 $ because you're dividing two negative numbers. Same signs = positive result.

Q: How can I check if my answer is correct?

Use the reverse operation! Since $ (-3) \times (-5) = 15 $, check that $ 15 ÷ (-5) = -3 $ or $ 15 ÷ (-3) = -5 $.

Negative Number Multiplication with Sign Rules

What is the answer to the following exercise?

$(-3)\cdot(-5)=$

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Step-by-step video solution

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00:00 Solve

00:09 Negative times negative is always positive

00:16 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

What is the answer to the following exercise?

$(-3)\cdot(-5)=$

Step-by-step solution

Let's remember the rule:

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

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

$-3\times-5=+15$

Final Answer

$15$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative times negative always equals positive
Technique: Calculate $3 \times 5 = 15$ , then apply positive sign
Check: Verify pattern: $(-3) \times (-5) = +15$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the sign rule for negative multiplication
Don't just multiply the numbers and keep a negative sign = wrong answer of -15! This ignores the fundamental rule that two negatives make a positive. Always remember: negative × negative = positive.

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" - when you reverse a reverse, you get back to the original direction! Mathematically, $(-1) \times (-1) = +1$ is the foundation of this rule.

How do I remember all the sign rules?

Use this simple pattern: Same signs = positive, Different signs = negative. So $(+) \times (+) = (+)$ and $(-) \times (-) = (+)$ , but $(+) \times (-) = (-)$ .

What if I have more than two negative numbers?

Count the negative signs! An even number of negatives gives a positive result, while an odd number gives a negative result. For example: $(-2) \times (-3) \times (-4) = -24$ (3 negatives = odd = negative).

Does this rule work for division too?

Yes! The same sign rules apply to division. $(-15) ÷ (-3) = +5$ because you're dividing two negative numbers. Same signs = positive result.

How can I check if my answer is correct?

Use the reverse operation! Since $(-3) \times (-5) = 15$ , check that $15 ÷ (-5) = -3$ or $15 ÷ (-3) = -5$ .

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