Gavin and his three friends want to share (1)/(3) of a cake equally. Gavin says that each friend will get (1)/(9) of the cake. Use the drop-down menus to explain whether or not Gavin is correct.
The correct answer and explanation is :
Answer:
Gavin is not correct.
Each friend will actually get $\frac{1}{12}$ of the cake.
Explanation (300+ words):
Let’s break the problem down step-by-step to understand why Gavin’s answer is incorrect and how to find the correct one.
Step 1: Understand the Situation
Gavin and his three friends are sharing $\frac{1}{3}$ of a cake. That means they are not sharing the entire cake—only a third of it. Also, there are four people total (Gavin + 3 friends), and they are dividing that one-third of a cake equally among themselves.
Step 2: Divide the Fraction
We are trying to divide $\frac{1}{3}$ by 4 (since four people are sharing it equally).
In mathematical terms:
$$
\frac{1}{3} \div 4 = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}
$$
So, each person gets $\frac{1}{12}$ of the whole cake.
Step 3: Why Gavin is Incorrect
Gavin claims that each person gets $\frac{1}{9}$ of the cake. That would imply that:
$$
\frac{1}{9} \times 4 = \frac{4}{9}
$$
This means they would be eating almost half the cake ($\frac{4}{9}$), which is more than the $\frac{1}{3}$ they were supposed to share. So Gavin’s estimate is too large.
Step 4: Double-Check the Correct Answer
Let’s multiply the correct portion per person by 4 people:
$$
\frac{1}{12} \times 4 = \frac{4}{12} = \frac{1}{3}
$$
This confirms that dividing $\frac{1}{3}$ into four equal parts gives $\frac{1}{12}$ per person.
Final Conclusion
Gavin is incorrect. Each of the four people should receive $\frac{1}{12}$ of the whole cake when $\frac{1}{3}$ of it is shared equally among them. This result ensures that the total amount shared still adds up to $\frac{1}{3}$ of the cake.