If a positive fraction is added to​ itself, is the result larger or smaller than the​ fraction?

When a positive fraction is added to itself, the result is always larger than the original fraction.

Let's break this down:

1. Let the positive fraction be \(\frac{a}{b}\), where \(a\) and \(b\) are positive integers.
2. Adding the fraction to itself means you are calculating:
   \[
   \frac{a}{b} + \frac{a}{b} = \frac{2a}{b}
   \]
3. The result \(\frac{2a}{b}\) is exactly twice the original fraction \(\frac{a}{b}\).

Since \(2a > a\) for any positive integer \(a\), it follows that \(\frac{2a}{b} > \frac{a}{b}\). Therefore, the result of adding the fraction to itself is larger than the original fraction.

Would you like more details or have any questions?

Here are some questions to consider:
1. How does the result change if you multiply the fraction by a constant other than 2?
2. What happens when a fraction is subtracted from itself?
3. Can adding a fraction to a different fraction result in a smaller number?
4. How does the size of the fraction change if you add a smaller fraction to it?
5. What is the effect of adding fractions with different denominators?

**Tip:** Adding a fraction to itself can also be thought of as multiplying the fraction by 2, which always results in a larger number if the fraction is positive.

Explore how adding a positive fraction to itself affects its size. This detailed explanation covers the arithmetic operation involving fractions, specifically adding fractions to themselves. Suitable for students in Grades 4-6.

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