Solve 1 × (-1): Multiplying a Positive and Negative Number

Integer Multiplication with Sign Rules

Complete the following exercise:

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

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Step-by-step video solution

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00:00 Solve
00:07 Positive times negative is always negative
00:15 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Complete the following exercise:

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

2

Step-by-step solution

Let's remember the rule:

(+x)×(x)=x (+x)\times(-x)=-x

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

+1×1=1 +1\times-1=-1

3

Final Answer

1 -1

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Positive times negative always equals negative
  • Technique: Apply (+1) × (-1) = -1 directly using multiplication rules
  • Check: Verify that 1 × (-1) gives -1, not 0 or +1 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing multiplication with addition or subtraction
    Don't think 1 × (-1) equals 0 like 1 + (-1) = 0! Multiplication and addition follow completely different rules with signed numbers. Always remember: positive × negative = negative, regardless of the specific numbers involved.

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 isn't 1 × (-1) equal to 0?

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That would be addition, not multiplication! When you add: 1 + (-1) = 0. But when you multiply: 1 × (-1) = -1. These are completely different operations with different rules.

How do I remember the sign rules for multiplication?

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Use this simple pattern: same signs = positive, different signs = negative. Since 1 is positive and -1 is negative, they have different signs, so the answer is negative.

Does the order matter in 1 × (-1)?

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No! Multiplication is commutative, meaning 1 × (-1) = (-1) × 1 = -1. The order doesn't change the result.

What if I multiply any positive number by -1?

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Multiplying by -1 always gives you the opposite of the original number. So 5 × (-1) = -5, and 1 × (-1) = -1.

Can I use a number line to check this?

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Yes! Think of 1 × (-1) as taking 1 group of (-1). On a number line, you'd move 1 unit to the left from zero, landing on -1.

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