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

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 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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