Solve the Equation: Finding the Missing Factor in (-6)×?=-12

Integer Division with Negative Numbers

Fill in the missing number:

(6)?=12 (-6)\cdot?=-12

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:05 Negative times positive always equals negative
00:08 Therefore the unknown is positive
00:14 Now let's find the unknown
00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing number:

(6)?=12 (-6)\cdot?=-12

2

Step-by-step solution

Let's remember the law:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about which number we need to multiply by 6 to get 12:

6×2=12 6\times2=12

Now let's put the numbers together with the appropriate sign as written in the law above, as follows:

6×(+2)=12 -6\times(+2)=-12

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Negative times positive equals negative in multiplication
  • Technique: Divide both sides: -12 ÷ (-6) = 2
  • Check: Substitute back: (-6) × 2 = -12 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting sign rules with negative numbers
    Don't assume the answer is negative just because -6 is negative = wrong sign! The missing factor could be positive or negative depending on the product. Always use division: -12 ÷ (-6) to find the correct sign.

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 is the answer positive when we're multiplying by a negative number?

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Remember the sign rules: negative × positive = negative. Since (-6) is negative and the result (-12) is negative, the missing factor must be positive to make this work!

How do I remember the multiplication sign rules?

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Use this pattern: same signs = positive, different signs = negative. Since (-6) and (-12) are both negative, they have the same sign, so the missing factor is positive.

Can I just ignore the negative signs and add them later?

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No! The signs are part of the numbers and affect the final answer. Always work with the complete numbers, including their signs, from the beginning.

What if I got -2 as my answer?

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Check your work: (-6) × (-2) = +12, not -12! Remember that negative times negative equals positive. The correct answer is +2.

How can I double-check my multiplication with negative numbers?

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Always substitute your answer back into the original equation. If (-6) times your answer equals -12, then you're correct. This is the best way to catch sign errors!

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