Solve the Equation: Finding the Missing Sign in (-5)·(?3)=15

Integer Multiplication with Missing Sign

Fill in the corresponding sign for the following question

(5)(?3)=15 (-5)\cdot(?3)=15

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's complete the correct sign.
00:12 Since the solution is positive, we need a sign that results in a positive outcome.
00:21 Remember, a negative times a negative always equals a positive.
00:26 So, the right sign here is negative.
00:29 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the corresponding sign for the following question

(5)(?3)=15 (-5)\cdot(?3)=15

2

Step-by-step solution

We must first consider what we need to multiply by a negative in order to obtain a positive number.

Let's remember the rule:

(x)×(x)=+x (-x)\times(-x)=+x

Therefore, the answer is as follows:

3 -3

3

Final Answer

() (-)

Key Points to Remember

Essential concepts to master this topic
  • Rule: Negative times negative equals positive, positive times negative equals negative
  • Technique: Work backward: 15 ÷ (-5) = -3, so missing sign is negative
  • Check: Verify: (-5) × (-3) = 15 because negative × negative = positive ✓

Common Mistakes

Avoid these frequent errors
  • Thinking positive × negative can equal positive
    Don't assume the missing sign is positive just because the answer is positive = wrong logic! A positive times a negative always gives a negative result. Always remember that only negative × negative gives a positive product.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( (+6)\cdot(+9)= \)

FAQ

Everything you need to know about this question

Why can't the missing sign be positive if the answer is positive?

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Because positive × negative = negative, not positive! If we had (+3), then (-5) × (+3) = -15, which doesn't match our target of 15.

How do I remember the multiplication sign rules?

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Use this simple pattern: Same signs = positive, Different signs = negative. So (-) × (-) = (+) and (+) × (-) = (-).

Can I work backwards to find the missing number?

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Yes! Divide the result by the known number: 15 ÷ (-5) = -3. This tells you the missing number is -3, so the sign is negative.

What if I get confused about which rule to use?

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Start with what you know: we need (-5) × (something) = 15. Since 15 is positive and (-5) is negative, the 'something' must be negative to make the product positive.

Is there a quick way to check my answer?

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Absolutely! Just multiply it out: (-5) × (-3) = 15. If you get 15, you're correct. If you get -15, you chose the wrong sign.

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