Calculate (-2) × (-5): Step-by-Step Negative Number Multiplication

Q: Why does negative times negative equal positive?

Think of it like this: a negative means opposite direction. When you reverse direction twice, you end up going forward! So $ (-2) \times (-5) $ means 'the opposite of 2, taken 5 times in the opposite direction' = positive 10.

Q: How can I remember the sign rules?

Use this simple pattern:Same signs: positive × positive = positive, negative × negative = positiveDifferent signs: positive × negative = negative, negative × positive = negative

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

Count the negatives! An even number of negatives gives a positive result. An odd number of negatives gives a negative result.

Negative Number Multiplication with Sign Rules

Complete the following exercise:

$(-2)\cdot(-5)=$

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Step-by-step video solution

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00:00 Solve

00:07 Negative times negative is always positive

00:16 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

Complete the following exercise:

$(-2)\cdot(-5)=$

Step-by-step solution

Let's remember the rule:

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

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

$-2\times-5=+10$

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative times negative always equals positive
Technique: (-2) × (-5) = +(2 × 5) = +10
Check: Count negatives: two negatives make one positive ✓

Common Mistakes

Avoid these frequent errors

Forgetting the sign rule for negative multiplication
Don't just multiply the numbers and guess the sign = wrong answer like -10! 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 like this: a negative means opposite direction. When you reverse direction twice, you end up going forward! So $(-2) \times (-5)$ means 'the opposite of 2, taken 5 times in the opposite direction' = positive 10.

How can I remember the sign rules?

Use this simple pattern:

Same signs: positive × positive = positive, negative × negative = positive
Different signs: positive × negative = negative, negative × positive = negative

What if I have more than two negative numbers?

Count the negatives! An even number of negatives gives a positive result. An odd number of negatives gives a negative result.

Is (-2) × (-5) the same as -2 × -5?

Yes! Both expressions mean exactly the same thing. The parentheses just make it clearer that we're multiplying negative two by negative five.

How do I check my answer?

Use the sign rule: two negatives make a positive, so your answer must be positive. Then multiply the absolute values: $2 \times 5 = 10$ , so $(-2) \times (-5) = +10$ ✓

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