Positive Numbers a and b: Determining Their Sum Properties

Addition Properties with Positive Number Operations

a and b are positive numbers and therefore their sum is...?

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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 and therefore their sum is...?

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Step-by-step solution

To solve this problem, we need to understand the properties of positive numbers and their behavior under addition.

  • Step 1: Identify the given information.
    We have two numbers, aa and bb, and both are positive (a>0a > 0 and b>0b > 0).
  • Step 2: Apply the properties of positive numbers.
    According to the properties of real numbers, if both aa and bb are positive, their sum a+ba + b is also positive.
  • Step 3: Conclude based on addition of positive numbers.
    Given a>0a > 0 and b>0b > 0, it follows directly a+b>0a + b > 0.

Therefore, the sum of the two positive numbers aa and bb is Positive.

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Final Answer

Positive

Key Points to Remember

Essential concepts to master this topic
  • Rule: Adding any two positive numbers always gives positive result
  • Technique: If a>0 a > 0 and b>0 b > 0 , then a+b>0 a + b > 0
  • Check: Test with examples: 3 + 5 = 8 (positive) ✓

Common Mistakes

Avoid these frequent errors
  • Confusing positive number properties with other operations
    Don't assume the sum could be negative or zero when both numbers are positive = wrong conclusion! This ignores the fundamental property that positive + positive = positive. Always remember that adding positive numbers can only increase the total value.

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 the sum of two positive numbers be zero?

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Because when you add positive amounts together, you're combining them! Think of it like adding money: 3+3 + 5 = 8.Youcantget8. You can't get 0 by adding positive amounts.

What if the positive numbers are very small, like 0.01?

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Size doesn't matter! Even tiny positive numbers like 0.01+0.001=0.011 0.01 + 0.001 = 0.011 give a positive result. As long as both numbers are greater than zero, their sum is positive.

Could there be an exception to this rule?

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No exceptions! This is a fundamental property of positive real numbers. It's as reliable as saying 2 + 2 = 4. The sum of positive numbers is always positive.

How is this different from multiplying positive numbers?

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Great question! Both addition and multiplication of positive numbers give positive results. The key difference is that multiplication can make numbers larger or smaller, but addition always increases the total.

What happens if one number is positive and one is negative?

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That's a different situation! This problem specifically states both numbers are positive. When mixing positive and negative numbers, the result depends on which has the larger absolute value.

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