Solve Integer Multiplication: 1 × (-1) Step by Step

Q: Why isn't the answer just 1 since I'm multiplying by 1?

Great question! You're multiplying by negative one, not positive one. The negative sign is crucial - it changes the sign of whatever you multiply. Think of it as $ (+1) \times (-1) = -1 $.

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

Use this simple pattern: Same signs = positive, Different signs = negative. Since you have positive 1 and negative 1 (different signs), the answer is negative!

Q: Is there a difference between 1 × (-1) and (-1) × 1?

No difference at all! Multiplication is commutative, meaning the order doesn't matter. Both equal -1 because you still have one positive and one negative factor.

Q: Can I think of this as adding instead?

Not exactly, but you can think of $ 1 \times (-1) $ as taking one group of negative one, which gives you -1. This helps visualize why the answer is negative.

Integer Multiplication with Sign Rules

What is the answer to the following exercise?

$1\cdot(-1)=$

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Step-by-step video solution

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00:00 Solve

00:05 Positive times negative is always negative

00:13 And this is the solution to the question

Step-by-step written solution

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Understand the problem

What is the answer to the following exercise?

$1\cdot(-1)=$

Step-by-step solution

Let's remember the rule:

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

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

$+1\times-1=-1$

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive times negative always equals negative
Technique: Apply (+1) × (-1) = -1 using multiplication signs
Check: One positive factor and one negative factor gives negative result ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the answer
Don't think 1 × (-1) = 1 because you're multiplying by 1! This ignores the crucial negative sign. The rule states positive × negative = negative. Always remember that multiplying by negative one changes the sign.

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 isn't the answer just 1 since I'm multiplying by 1?

Great question! You're multiplying by negative one, not positive one. The negative sign is crucial - it changes the sign of whatever you multiply. Think of it as $(+1) \times (-1) = -1$ .

How do I remember the sign rules for multiplication?

Use this simple pattern: Same signs = positive, Different signs = negative. Since you have positive 1 and negative 1 (different signs), the answer is negative!

What if I had (-1) × (-1) instead?

That would equal +1! When you multiply two negatives, you get a positive result. Remember: same signs give positive answers.

Is there a difference between 1 × (-1) and (-1) × 1?

No difference at all! Multiplication is commutative, meaning the order doesn't matter. Both equal -1 because you still have one positive and one negative factor.

Can I think of this as adding instead?

Not exactly, but you can think of $1 \times (-1)$ as taking one group of negative one, which gives you -1. This helps visualize why the answer is negative.

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