Determine the Sign: Finding the Sum of Positive 'a' and Negative 'b'

Integer Addition with Unknown Magnitudes

a is a positive number.

b is a negative number.

What kind of number is the sum of b and a?

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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.

What kind of number is the sum of b and a?

2

Step-by-step solution

We will illustrate with an example:

Let's assume that a is 1 and b is -2

1+ (-2) =
1-2 = -1

Answer: Negative

Now let's assume that a is 2

and b is -1

2+(-1) =
2-1 = 1

Even though the operation is negative, the number remains positive.

That is, if the absolute value of the positive number (a) is greater than that of the negative (b), the result will still be positive.

As we do not have data regarding this information, it is impossible to know what the sum of a+b will be.

3

Final Answer

.Impossible to know.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum depends on which absolute value is larger
  • Technique: Compare |a| and |b|; if |2| > |-1| then result is positive
  • Check: Test multiple examples like 3+(-1)=2 and 1+(-3)=-2 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the result is always negative because one number is negative
    Don't think negative + positive = negative automatically! This ignores magnitude comparison and gives wrong predictions. Always compare the absolute values first - the larger magnitude determines the sign of the result.

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 negative since b is negative?

+

Because the magnitude matters! If the positive number a is larger than the absolute value of negative b, the sum will be positive. For example: 5 + (-2) = 3 (positive).

What happens if the absolute values are equal?

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If |a| = |b|, then a + b = 0. For example, if a = 3 and b = -3, then 3 + (-3) = 0. The positive and negative cancel each other out.

How do I know which absolute value is bigger without knowing the actual numbers?

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That's exactly the point! Since we don't know the specific values of a and b, we cannot determine which absolute value is larger, so the sign is impossible to know.

Can you give me more examples to understand this better?

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  • Case 1: a = 7, b = -3 → 7 + (-3) = 4 (positive)
  • Case 2: a = 2, b = -8 → 2 + (-8) = -6 (negative)
  • Case 3: a = 5, b = -5 → 5 + (-5) = 0 (zero)

All three outcomes are possible!

Is there a quick rule I can remember?

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Yes! When adding a positive and negative number: The result takes the sign of whichever number has the larger absolute value. If we don't know the magnitudes, we can't predict the sign.

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