Debbie ate 1/8 of a large brownie julian ate 1/2 of a small brownie julian says I ate more than you because 1/2 > 1/8
The Correct Answer and Explanation is:
Julian’s claim that he ate more than Debbie because 1/2 > 1/8 is not necessarily correct. While it’s true that one-half is a larger fraction than one-eighth, the actual amount eaten depends not just on the fraction but also on the size of the whole item—in this case, the brownie.
Debbie ate 1/8 of a large brownie, and Julian ate 1/2 of a small brownie. If the large brownie is significantly bigger than the small brownie, then 1/8 of the large one could actually be more than 1/2 of the small one.
To illustrate this, imagine the large brownie weighs 240 grams, and the small brownie weighs 80 grams:
- Debbie’s portion:
18×240=30\frac{1}{8} \times 240 = 3081×240=30 grams - Julian’s portion:
12×80=40\frac{1}{2} \times 80 = 4021×80=40 grams
In this case, Julian did eat more (40 grams vs. 30 grams), so his claim would be correct.
However, suppose the large brownie weighed 400 grams and the small brownie still weighed 80 grams:
- Debbie’s portion:
18×400=50\frac{1}{8} \times 400 = 5081×400=50 grams - Julian’s portion:
12×80=40\frac{1}{2} \times 80 = 4021×80=40 grams
Now, Debbie actually ate more than Julian (50 grams vs. 40 grams), even though her fraction (1/8) is smaller than Julian’s (1/2).
This shows that comparing fractions without knowing the size of the whole can be misleading. Julian’s statement assumes the brownies are the same size, which isn’t stated in the problem. Since Debbie had part of a large brownie and Julian had part of a small one, we cannot say for sure who ate more without knowing the actual sizes.
Conclusion: Julian’s reasoning is flawed. Even though 1/2 is mathematically greater than 1/8, this does not automatically mean he ate more. The size of each brownie must be considered.
