Comparing Fractions: Who Ate More of the Apple?

Here is a classic problem that explores the concept of fractions and comparing them: John ate 3/5th of an apple, and the remaining part was eaten by his sister Sally. The question is, how much of the apple did Sally eat? Which sibling had the larger share, and by how much?

Understanding the Problem

Let's break down the problem step-by-step. Initially, we know that the entire apple is represented as one whole, which can be written as 5/5. John ate 3/5 of the apple, leaving the remaining part for Sally to eat.

Calculating Sally's Share

To find out how much Sally ate, we subtract the amount John ate from the whole apple:

[text{Sally's share} frac{5}{5} - frac{3}{5}]

Performing the subtraction:

[text{Sally's share} frac{2}{5}]

Therefore, Sally ate (frac{2}{5}) of the apple.

Determining the Larger Share

Now, let's compare the shares of John and Sally. John ate (frac{3}{5}) of the apple, while Sally ate (frac{2}{5}) of the apple.

To determine which sibling had the larger share, we look at the absolute difference between the two fractions:

[text{Difference} frac{3}{5} - frac{2}{5} frac{1}{5}]

John had the larger share by (frac{1}{5}) of the apple.

Additional Insight

It's important to understand that the fraction (frac{1}{5}) directly tells us the amount by which John's share exceeds Sally's. This can be converted to a decimal for a more intuitive understanding:

[frac{1}{5} 0.2 text{ (or 20%) of the apple}]

So, John ate 20% more of the apple than Sally.

Visual Representation

A visual representation can also help in understanding the fractions more clearly:

Divide the apple into 5 equal parts. John's share: 3 parts (out of 5). Sally's share: 2 parts (out of 5).

By looking at the divided parts, it becomes easier to see that John had 1 more part than Sally, hence the larger share.

Conclusion

Through this problem, not only do we learn about comparing fractions, but we also understand the practical application of fractions in daily life scenarios like sharing food. Next time you're faced with a similar problem, or even a real-life situation, you can employ these steps to understand and solve the problem effectively.

Tips for Mastering Fractions

1. **Practice with Visual Aids**: Use shapes like circles or rectangles to represent fractions visually. This can be particularly helpful when comparing fractions or understanding their relative sizes. 2. **Real-Life Examples**: Apply fractions to practical situations, such as sharing fruits or dividing a pizza among friends. Real-life scenarios can make learning fractions more relatable and memorable. 3. **Fraction Games and Apps**: Engage with educational games and apps that focus on fractions. These can be a fun and interactive way to improve your fraction skills.

By following these tips and practicing regularly, you can become proficient in understanding and comparing fractions, making this mathematical concept second nature.