Find the Sum: Adding Positive Number 'a' and Negative Number 'b'

Integer Addition with Unknown Magnitudes

a is a positive number.

b is a negative number.

The sum of a+b is...?

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Step-by-step written solution

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1

Understand the problem

a is a positive number.

b is a negative number.

The sum of a+b is...?

2

Step-by-step solution

We will use trial and error in order to test this:

Let's assume that the value of the positive number is greater than the value of the negative number 1 and 2.

1+(-2) = -1

The result is negative.

We will try to make the value of the second number greater than the first 2 and 1.

2+(-1)= 1

The result is positive.

That is, we can see that the result depends on the values of the two numbers, so we cannot know from the beginning what the result will be.

3

Final Answer

It is not possible to know.

Key Points to Remember

Essential concepts to master this topic
  • Rule: When adding positive and negative numbers, the result depends on their magnitudes
  • Technique: Test with examples: 3 + (-5) = -2, but 5 + (-3) = 2
  • Check: Try multiple number pairs to confirm the sign can vary ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the result always has a predictable sign
    Don't assume a + b is always positive or always negative when a > 0 and b < 0! The sign depends on which number has the larger absolute value. Always consider that either outcome is possible without knowing the specific values.

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 can't I just say the answer is positive since a is positive?

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Because the magnitude (absolute value) of the negative number might be larger! For example: 2 + (-7) = -5. The negative number 'wins' when it's larger in absolute value.

What determines whether the sum is positive or negative?

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It's all about which number is farther from zero. If |a| > |b|, the sum is positive. If |b| > |a|, the sum is negative. If they're equal, the sum is zero!

How can I remember this rule?

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Think of it like a tug-of-war! The positive number pulls one way, the negative pulls the other. Whichever side has more 'strength' (larger absolute value) wins and determines the sign.

Are there any shortcuts to solving this type of problem?

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Yes! When you see 'a is positive, b is negative' without specific values, always test with different examples. Try cases where the positive is larger, then where the negative is larger.

What if the question gave us actual numbers?

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Then we could determine the exact answer! For instance, if a = 4 and b = -6, then a + b = -2. But without knowing the values, any result is possible.

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