Multiply (-4) × 12: Determining the Sign of the Product

Integer Multiplication with Mixed Signs

What will be the sign of the result of the next exercise?

(4)12= (-4)\cdot12=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 What will be the sign of the result?
00:09 Negative times positive is always negative
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

What will be the sign of the result of the next exercise?

(4)12= (-4)\cdot12=

2

Step-by-step solution

Let's remember the rule:

(+x)×(x)=x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

4×+12=48 -4\times+12=-48

3

Final Answer

Negative

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Negative times positive always equals negative
  • Technique: (4)×12=48 (-4) \times 12 = -48 follows the mixed sign pattern
  • Check: Count signs: one negative, one positive = negative result ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any multiplication gives a positive result
    Don't think all multiplication results are positive = getting +48 instead of -48! This ignores the crucial sign rules. Always remember: different signs multiply to give negative, same signs give 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

Why does negative times positive equal negative?

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Think of multiplication as repeated addition. (4)×12 (-4) \times 12 means adding -4 twelve times: -4 + (-4) + (-4)... = -48. You're adding negative numbers, so the result stays negative!

What if I multiply positive times negative instead?

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The order doesn't matter! 12×(4) 12 \times (-4) gives the same result as (4)×12 (-4) \times 12 . Different signs always produce negative results, regardless of which number comes first.

How do I remember the sign rules?

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Use this simple pattern: Same signs = Positive (+ × + or - × -), Different signs = Negative (+ × - or - × +). Think 'opposites attract trouble' for different signs!

Do I need to worry about the actual numbers or just the signs?

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For determining the sign of the result, focus on the signs first! Once you know it's negative, then calculate 4×12=48 4 \times 12 = 48 and add the negative sign to get -48.

What happens if I have more than two numbers to multiply?

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Count the negative signs! An even number of negatives gives positive, an odd number gives negative. For example: (-2) × (-3) × (-1) has 3 negatives (odd) = negative result.

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