Solve (-2)⋅(?)3=-12: Finding the Missing Multiplication Sign

Integer Multiplication with Sign Rules

Fill in the corresponding sign for the following question

(−2)⋅(?3)=−12 (-2)\cdot(?3)=-12

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's choose the right sign.
00:13 We need a positive result, so select a sign that gives a positive outcome.
00:18 Remember, negative times positive is always negative.
00:23 Therefore, the correct sign we need here is positive.
00:28 And that's how we find our solution!

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

(−2)⋅(?3)=−12 (-2)\cdot(?3)=-12

2

Step-by-step solution

We must first consider which value when multiplied by a negative results in a negative 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
  • Sign Rule: Negative times positive equals negative product
  • Technique: (-2) × (+3) = -6, but we need -12
  • Check: Verify (-2) × (+3) = -6, not -12, so recalculate ✓

Common Mistakes

Avoid these frequent errors
  • Confusing multiplication sign rules
    Don't assume any positive number works just because negative × positive = negative! This ignores the actual value needed. Always check that your number gives the exact result: (-2) × (+4) = -8, not -12.

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

How do I know if the missing number should be positive or negative?

+

Look at the final result! Since (−2)×(?)=−12 (-2) \times (?) = -12 and the result is negative, you need a positive number because negative × positive = negative.

What number should go in the blank?

+

Divide the result by the known number: −12÷(−2)=+6 -12 ÷ (-2) = +6 . So the missing number is +6, not +3 as shown in some examples.

Why can't the answer be negative?

+

If you used a negative number, you'd get: (−2)×(−6)=+12 (-2) \times (-6) = +12 . But we need -12, not +12! Remember: negative × negative = positive.

How can I check my answer quickly?

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Simply multiply your answer by -2. If you get -12, you're correct! For example: (−2)×(+6)=−12 (-2) \times (+6) = -12 ✓

What if I forget the sign rules?

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Use this memory trick:

  • Same signs (both + or both -) = positive result
  • Different signs (one + and one -) = negative result

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