Understanding Fractions: How Much Pizza Did Stephen Eat?

Stephen ate 3/4 of half a pizza, but how much of the whole pizza did he actually consume? This problem provides us with a clear example of working with fractions and understanding their relationships. Let's break down the process step by step to find the answer.

Breaking Down the Problem

The problem asks us to find out how much of a whole pizza Stephen ate. To solve this, we need to understand and work with the fractions provided.

Half of a pizza: We start by acknowledging that half of a pizza is represented by the fraction (frac{1}{2}). This is the basic division of the whole pizza into two equal parts.

Stephen's consumption: Stephen then ate (frac{3}{4}) of this half. This means that he consumed a portion of the already divided half.

Multiplying the Fractions

To find out how much of the whole pizza he ate, we need to multiply these fractions:

Multiplication of fractions: We multiply the numerators (top numbers) and the denominators (bottom numbers) separately. The equation is:

(frac{3}{4} times frac{1}{2} frac{3 times 1}{4 times 2} frac{3}{8})

Result: Therefore, Stephen ate (frac{3}{8}) of the whole pizza.

This fraction indicates that out of the total 8 slices (if we divide the whole pizza into 8 slices), Stephen ate 3 slices. This is the final answer to the problem, reflecting the correct portion of the whole pizza that Stephen consumed.

Additional Insights

Understanding the difference between (frac{3}{4}) of half a pizza and (frac{3}{4}) of a whole pizza is crucial. Let's explore this further:

How much is 3/8 of a whole pizza?: Since a whole pizza is represented by (frac{8}{8}), we can calculate the equivalent in terms of a whole pizza:

(frac{3}{4} times frac{1}{2} frac{3}{8})

By converting (frac{3}{8}) to a percentage of a whole pizza, we find that it is indeed 37.5% of the whole pizza.

Comparison with 3/4 of a whole pizza:: If Stephen had eaten (frac{3}{4}) of a whole pizza, that would be 6 slices out of 8, or 75% of the whole pizza. This is significantly more than the 37.5% that he actually consumed by eating (frac{3}{4}) of half a pizza.

Thus, the critical takeaway is that fractions must be applied to the correct base (in this case, half a pizza), and not to the whole pizza directly.

Practice and Application

Working through problems like these helps in mastering the concept of fractions and their application in real-world scenarios. Whether it’s in cooking, sharing, or any situation where portions need to be divided and calculated, understanding fractions can be incredibly useful.

Conclusion

In conclusion, Stephen ate (frac{3}{8}) of a whole pizza. This example demonstrates the importance of accurately applying fractions and understanding their relationships to the correct base. Whether you're a student, a professional, or someone who enjoys cooking, grasping these concepts can make a big difference in your daily calculations and problem-solving skills.

Key Takeaways:
- (frac{3}{4}) of half a pizza equals (frac{3}{8}) of a whole pizza.
- Understanding the correct base is crucial when working with fractions.