Determining the Sign: A - B When A and B Are Positive Numbers

Subtraction Results with Unknown Magnitudes

A and B are positive numbers.

Therefore, A - B results in...?

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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 positive numbers.

Therefore, A - B results in...?

2

Step-by-step solution

Let's define the two numbers as 1 and 2.

 

Now let's place them in an exercise:

 

2-1=1

The result is positive!

 

Now let's define the numbers in reverse as 2 and 1.

Let's place an equal exercise and see:

1-2=-1

The result is negative!

 

We can see that the solution of the exercise depends on the absolute value of the numbers, and which one is greater than the other,

Even if both numbers are positive, the subtraction operation between them can lead to a negative result.

3

Final Answer

Impossible to know

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sign depends on which positive number is larger
  • Technique: Compare values first: 5 - 3 = +2, but 3 - 5 = -2
  • Check: Test with specific numbers to verify all possible outcomes ✓

Common Mistakes

Avoid these frequent errors
  • Assuming subtraction of positives is always positive
    Don't think A - B is always positive just because A and B are positive = wrong answer! The result depends on which number is larger. Always remember that 3 - 7 = -4 even though both 3 and 7 are positive.

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

If both numbers are positive, why isn't the answer always positive?

+

Great question! The sign of the result depends on which number is bigger. Think of it like this: if you have 3 dollars and spend 5 dollars, you owe 2 dollars (negative result)!

How can I predict the sign without knowing the exact values?

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You cannot predict the sign without knowing which number is larger. That's exactly why the answer is "Impossible to know" - we need more information!

What if A equals B?

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If A = B, then A - B = 0. But since we don't know if they're equal or which is larger, we still cannot determine the result without more information.

Can you give me more examples?

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Absolutely! Try these:

  • 8 - 3 = +5 (positive result)
  • 3 - 8 = -5 (negative result)
  • 6 - 6 = 0 (zero result)

All three outcomes are possible with positive numbers!

Is this the same rule for multiplication?

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No! Multiplication of two positive numbers is always positive. Subtraction is different because you're finding the difference between numbers, not combining them.

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