Gavin and his three friends want to share \frac{1}{3} of a cake equally. Gavin says that each friend will get \frac{1}{9} of the cake. Use the drop-down menus to explain whether or not Gavin is correct. Click the arrows to choose an answer from each menu. Gavin is correct . To find how much cake each person gets, divide \frac{1}{3} by , or multiply \frac{1}{3} by . Therefore, each of the friends gets of the cake.
The Correct Answer and Explanation is:
Drop-down Menu Answers:
- Gavin is not correct.
- To find how much cake each person gets, divide 13\frac{1}{3}31 by 4,
- or multiply 13\frac{1}{3}31 by 14\frac{1}{4}41.
- Therefore, each of the friends gets 112\frac{1}{12}121 of the cake.
Explanation
Gavin and his three friends want to share 13\frac{1}{3}31 of a cake equally. This means the total amount to be shared is only a third of the cake, not the whole cake. There are four people in total (Gavin plus three friends), so we need to divide 13\frac{1}{3}31 by 4.
Mathematically, dividing by a number is the same as multiplying by its reciprocal. So, we calculate:13÷4=13×14=112\frac{1}{3} \div 4 = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}31÷4=31×41=121
Each person, therefore, gets 112\frac{1}{12}121 of the whole cake.
Gavin incorrectly says that each friend will get 19\frac{1}{9}91 of the cake. That would be correct only if 13\frac{1}{3}31 were divided among three people. In that case:13÷3=13×13=19\frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}31÷3=31×31=91
But since there are four people sharing the cake, not three, his answer is incorrect. He likely forgot to include himself in the count.
This is a common mistake when dividing shared portions — it’s important to count all participants, including yourself if you’re part of the group. Always check whether the division accounts for everyone.
In summary, to divide 13\frac{1}{3}31 of a cake equally among 4 people, we divide by 4 (or multiply by 14\frac{1}{4}41). That gives each person 112\frac{1}{12}121 of the cake. So Gavin is not correct; the correct share for each person is 112\frac{1}{12}121.
