Calculate (-2)×(-1/2): Determining the Product's Sign

Sign Rules with Negative Multiplication

What will be the sign of the result of the next exercise?

(2)(12)= (-2)\cdot(-\frac{1}{2})=

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Step-by-step video solution

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00:00 What will be the sign of the result?
00:09 Negative times negative always equals positive
00:17 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

What will be the sign of the result of the next exercise?

(2)(12)= (-2)\cdot(-\frac{1}{2})=

2

Step-by-step solution

Let's recall the law:

(x)×(x)=+x (-x)\times(-x)=+x

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

2×12=+1 -2\times-\frac{1}{2}=+1

3

Final Answer

Positive

Key Points to Remember

Essential concepts to master this topic
  • Rule: Negative times negative always equals positive
  • Technique: (2)×(12)=+1 (-2) \times (-\frac{1}{2}) = +1 because signs cancel
  • Check: Count negatives: two negatives make positive result ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the sign rule for negative multiplication
    Don't think (-2) × (-1/2) = -1 just because you see negative numbers! This ignores the fundamental rule. When multiplying two negatives, the negative signs cancel out and create a positive result. Always remember: negative × negative = 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?

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Think of it like opposites canceling out! When you multiply two negative numbers, you're essentially removing two negative signs, leaving you with a positive result. It's a fundamental rule in mathematics.

How can I remember the sign rules for multiplication?

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Use this simple pattern: same signs = positive, different signs = negative. So (+)(+) = +, (-)(-)= +, but (+)(-) = - and (-)(+) = -.

What's the actual value of (-2) × (-1/2)?

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The calculation gives us (2)×(12)=+1 (-2) \times (-\frac{1}{2}) = +1 . First determine the sign (positive), then multiply the numbers: 2 × 1/2 = 1.

Do I need to worry about fractions changing the sign rule?

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No! The sign rules work exactly the same with fractions, decimals, or whole numbers. The type of number doesn't change how positive and negative signs interact.

What if I have more than two negative numbers?

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

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