Solve: Finding the Missing Sign in (4)·(?)=-12

Integer Multiplication with Negative Products

Fill in the corresponding sign for the following question

(4)(?3)=12 (4)\cdot(?3)=-12

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Complete the appropriate sign
00:04 The solution is negative, so we want a sign that results in a negative outcome
00:11 Positive times negative always equals negative
00:15 Therefore the appropriate sign is negative
00:18 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 corresponding sign for the following question

(4)(?3)=12 (4)\cdot(?3)=-12

2

Step-by-step solution

Let's consider what we would need to multiply by a positive in order to obtain a negative number.

Let's remember the rule:

(+x)×(x)=x (+x)\times(-x)=-x

Therefore, the answer will be:

3 -3

3

Final Answer

() (-)

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Positive times negative always equals negative result
  • Technique: Since 4 × (-3) = -12, the missing sign is negative
  • Check: Verify 4 × (-3) = -12 matches the given equation ✓

Common Mistakes

Avoid these frequent errors
  • Thinking positive × positive can equal negative
    Don't assume (+3) works because 4 × 3 = 12, not -12! Positive times positive always gives positive results. Always remember: to get a negative product, one factor must be negative while the other is positive.

Practice Quiz

Test your knowledge with interactive questions

Determine the correct answer for the following exercise:

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

How do I remember the sign rules for multiplication?

+

Use this simple pattern: Same signs = Positive, Different signs = Negative. So (+) × (+) = (+) and (-) × (-) = (+), but (+) × (-) = (-) and (-) × (+) = (-).

Why can't the answer be positive 3?

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Because 4 × (+3) = +12, not -12! Since we need a negative result (-12), and 4 is positive, the unknown number must be negative to get a negative product.

What if I get confused about which number should be negative?

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Look at what you're given! We know 4 is positive and the result is negative. Since different signs give negative results, the missing number must be negative.

How can I check my answer quickly?

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Simply multiply: 4 × (-3) = -12. If this matches the right side of the equation, you're correct! Always substitute your answer back to verify.

Do these sign rules work for division too?

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Yes! Division follows the same pattern: same signs give positive results, different signs give negative results. So (-12) ÷ 4 = -3 and (-12) ÷ (-4) = +3.

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