Solve (-1)×(-1): Step-by-Step Negative Number Multiplication

Q: Why does negative times negative equal positive?

Think of it as reversing a reversal! The first negative reverses direction, and the second negative reverses it back to positive. It's like saying 'not not happy' means happy!

Q: What's the pattern for multiplying signed numbers?

Same signs = positive result and different signs = negative result. So (+)(+) = +, (-)(-)= +, but (+)(-) = - and (-)(+) = -.

Q: How can I remember this rule?

Use the phrase: 'Two negatives make a positive!' You can also think of real situations - if you remove a debt (negative), you gain money (positive).

Q: Does this work for any negative numbers?

Yes! Whether it's $ (-3) \times (-2) = 6 $ or $ (-100) \times (-0.5) = 50 $, the rule always applies: negative × negative = positive.

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 of negatives gives a negative result.

Negative Number Multiplication with Sign Rules

Complete the following exercise:

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

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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 always equals 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:

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

Step-by-step solution

Let's recall the law:

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

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

$-1\times-1=+1$

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative times negative equals positive (like signs = positive)
Technique: Apply (-1) × (-1) = +1 using sign multiplication rules
Check: Verify that two negative factors produce one positive result ✓

Common Mistakes

Avoid these frequent errors

Thinking negative × negative = negative
Don't assume (-1) × (-1) = -1 because both numbers are negative! This ignores the fundamental sign rule and gives the wrong answer. Always remember: when multiplying two numbers with the same sign, the result is positive.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why does negative times negative equal positive?

Think of it as reversing a reversal! The first negative reverses direction, and the second negative reverses it back to positive. It's like saying 'not not happy' means happy!

What's the pattern for multiplying signed numbers?

Same signs = positive result and different signs = negative result. So (+)(+) = +, (-)(-)= +, but (+)(-) = - and (-)(+) = -.

How can I remember this rule?

Use the phrase: 'Two negatives make a positive!' You can also think of real situations - if you remove a debt (negative), you gain money (positive).

Does this work for any negative numbers?

Yes! Whether it's $(-3) \times (-2) = 6$ or $(-100) \times (-0.5) = 50$ , the rule always applies: negative × negative = positive.

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 of negatives gives a negative result.

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