Multiply (-16) × (-5): Determining the Sign of the Product

Integer Multiplication with Negative Signs

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

(16)(5)= (-16)\cdot(-5)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's figure out the sign of the answer!
00:18 Remember, a negative times a negative makes a positive.
00:30 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

(16)(5)= (-16)\cdot(-5)=

2

Step-by-step solution

To determine the sign of the expression (16)(5)(-16)\cdot(-5), we follow these logical steps:

  • Step 1: Identify the signs of the numbers involved. Both numbers (16)(-16) and (5)(-5) are negative.
  • Step 2: Apply the rule for multiplication of signed numbers: The product of two numbers with the same sign (both negative) is always positive.

Therefore, the sign of the result for the expression (16)(5)(-16)\cdot(-5) is Positive.

3

Final Answer

Positive

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Two negative numbers multiplied together always give positive result
  • Technique: Negative × Negative = Positive, like (16)×(5)=+80 (-16) \times (-5) = +80
  • Check: Count negative signs: even number of negatives = positive answer ✓

Common Mistakes

Avoid these frequent errors
  • Thinking negative times negative equals negative
    Don't assume that multiplying two negative numbers gives a negative result = wrong sign! This ignores the fundamental rule that same signs multiply to positive. Always remember: negative × negative = positive, just like positive × positive = 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?

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Think of it as reversing a reversal. A negative number reverses direction, so multiplying by another negative reverses it back to positive! It's like saying "not not happy" means "happy".

What if I have more than two negative numbers?

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Count the negative signs! If there's an even number of negatives, the answer is positive. If there's an odd number of negatives, the answer is negative.

Do I need to calculate the actual number?

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For this type of question asking about the sign only, you just need to determine positive or negative. But calculating (16)×(5)=80 (-16) \times (-5) = 80 can help confirm your sign rule!

How is this different from addition?

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Addition and multiplication have different sign rules! For addition: negative + negative = negative. For multiplication: negative × negative = positive. Don't mix them up!

What about positive times negative?

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When signs are different (positive × negative or negative × positive), the result is always negative. Same signs = positive, different signs = negative.

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