Determine the Sign: Solving 2 × (-2) Multiplication Problem

Integer Multiplication with Sign Rules

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

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's figure out the sign of the result.
00:13 Remember, when you multiply a positive number by a negative number, the result is always negative.
00:26 And that's how we solve this problem. Well done!

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?

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

2

Step-by-step solution

To solve the exercise you need to remember an important rule: Multiplying a positive number by a negative number results in a negative number.

()×(+)=() (−)×(+)=(−)
Therefore, if we multiply negative 2 by 2 the result will be negative 4.

That is, the result is negative.

+2×2=4 +2\times-2=-4

3

Final Answer

Negative

Key Points to Remember

Essential concepts to master this topic
  • Rule: Positive times negative equals negative result
  • Technique: 2×(2)=4 2 \times (-2) = -4 shows positive × negative pattern
  • Check: Verify sign rule: (+) × (-) = (-), so result must be negative ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the negative sign in the result
    Don't just multiply the numbers 2 × 2 = 4 and ignore the signs! This gives +4 instead of -4. The signs determine whether your answer is positive or negative. Always apply the sign rule: positive × negative = negative.

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 positive times negative always negative?

+

Think of it as repeated subtraction! 2×(2) 2 \times (-2) means "take away 2 two times" which gives -4. The positive number tells you how many times to repeat the negative.

What if the numbers were switched to (-2) × 2?

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The result is still negative! Order doesn't matter in multiplication. (2)×2=4 (-2) \times 2 = -4 and 2×(2)=4 2 \times (-2) = -4 both equal -4.

How do I remember the sign rules for multiplication?

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

Is there a difference between -2 × 2 and 2 × (-2)?

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No difference! Both equal -4. The parentheses around (-2) just make it clear that the negative sign belongs to the 2. Both expressions follow the same rule: different signs = negative result.

What happens when I multiply two negative numbers?

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Two negatives make a positive! For example, (2)×(2)=+4 (-2) \times (-2) = +4 . Remember: same signs always give positive results.

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