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

\( -5-(-2)= \)

-7-7-7-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

FAQ

Everything you need to know about this question

Why can't I just say the answer is negative since both numbers are negative?

+

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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