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

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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

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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

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 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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