Number Properties: Analyzing Two Numbers with Positive Sum

Sum Analysis with Multiple Number Types

The sum of two numbers is positive.

Therefore, the two numbers are...?

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Step-by-step written solution

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1

Understand the problem

The sum of two numbers is positive.

Therefore, the two numbers are...?

2

Step-by-step solution

Testing through trial and error:

Let's assume both numbers are positive: 1 and 2.

1+2 = 3

Positive result.

Let's assume both numbers are negative -1 and -2

-1+(-2) = -3

Negative result.

Let's assume one number is positive and the other negative: 1 and -2.

1+(-2) = -1

Negative result.

Let's test a situation where the value of the first number is greater than the second: -1 and 2.

2+(-1) = 1

Positive result.

That is, we can see that when both numbers are positive, or in certain types of cases when one number is positive and the other negative, the sum is positive.

3

Final Answer

Answers a+c are correct.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Positive sums occur when positive numbers dominate the total
  • Technique: Test cases: 3 + 2 = 5 (both positive) and 5 + (-2) = 3
  • Check: Try all combinations: positive + positive, negative + negative, mixed cases ✓

Common Mistakes

Avoid these frequent errors
  • Assuming only positive numbers can create positive sums
    Don't think positive + positive is the only way to get positive sums = missing valid cases! Mixed numbers can also produce positive results when the positive number has greater absolute value. Always consider all possible number combinations: both positive, both negative, and mixed cases.

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

Can two negative numbers ever give a positive sum?

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No, never! When you add two negative numbers, you're combining negative values: (-3) + (-5) = -8. The result is always more negative than either individual number.

How can one positive and one negative number give a positive sum?

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This happens when the positive number has a larger absolute value than the negative number. For example: 7 + (-3) = 4 because 7 is greater than 3.

What does 'absolute value' mean in this context?

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Absolute value is the distance from zero, ignoring the sign. So |-5| = 5 and |5| = 5. When comparing mixed numbers, the one with larger absolute value 'wins' and determines the sign of the sum.

Are there any patterns I should remember?

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Yes! Remember these patterns:

  • Positive + Positive = Always Positive
  • Negative + Negative = Always Negative
  • Positive + Negative = Depends on which has larger absolute value

Why does the explanation show 'answers a+c are correct'?

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Because a positive sum can result from two different scenarios: either both numbers are positive (answer a), OR one number is positive and one is negative with the positive having larger absolute value (answer c).

How do I approach these types of problems?

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Test concrete examples! Don't just think abstractly. Pick specific numbers like 2 and 3, or -4 and 7, then calculate their sums. This helps you see which combinations actually work.

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