Subtracting Negative Numbers: Determining the Sign of a-b

Negative Number Subtraction with Sign Uncertainty

a and b are negative numbers.

Therefore, what kind of number is is a-b?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

a and b are negative numbers.

Therefore, what kind of number is is a-b?

2

Step-by-step solution

We test using an example:

We define that

a = -1

b = -2

 

Now we replace in the exercise:

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

In this case, the result is positive!

 

We test the opposite case, where b is greater than a

We define that

a = -2

b = -1

 

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

 

In this case, the result is negative!

 

Therefore, the correct solution to the whole question is: "It's impossible to know".

3

Final Answer

Impossible to know.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Subtracting a negative equals adding its positive value
  • Technique: Test examples: (-1) - (-2) = 1, but (-2) - (-1) = -1
  • Check: Compare magnitudes of both numbers to predict sign ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all negative number operations give negative results
    Don't think a - b is always negative when both are negative = wrong conclusion! This ignores that subtraction changes signs. Always test specific examples to see all possible outcomes.

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 both numbers are negative?

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Great question! When you subtract negative numbers, you're actually adding their opposites. So a - b becomes a + (-b). The sign depends on which number has the larger absolute value.

How do I know which examples to test?

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Test at least two cases: one where the first number is closer to zero (like -1 and -2), and one where the second number is closer to zero (like -2 and -1). This shows both possible outcomes.

What does 'impossible to know' really mean here?

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It means the answer could be positive, negative, or zero depending on the specific values of a and b. Without knowing their exact values, we cannot determine a single answer type.

Is there a pattern I can use to predict the sign?

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Yes! If a>b |a| > |b| , then a - b is negative. If a<b |a| < |b| , then a - b is positive. If a=b |a| = |b| , then a - b equals zero.

Why do we write a - b instead of a + (-b)?

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Both forms are mathematically equivalent! Writing a - b is more common, but thinking of it as a + (-b) can help you understand why subtracting a negative number gives a positive result.

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