Question

1. the model is shaded to represent the remaining \\(\frac{1}{2}\\) of a cake. four friends will each receive an equal amount of the remaining cake until it is all gone.

which equation can be used to determine the fraction of the whole cake each friend will receive?

a \\(\frac{1}{2} \div 8 = \frac{1}{16}\\)

b \\(\frac{1}{2} \div 4 = \frac{1}{8}\\)

c \\(\frac{1}{2} \times 4 = \frac{4}{2}\\)

Explanation:

Step1: Analyze the problem

We have $\frac{1}{2}$ of a cake left, and we need to divide it equally among 4 friends. So we need to find the amount each friend gets, which is dividing the remaining cake ($\frac{1}{2}$) by the number of friends (4).

Step2: Evaluate the options

• Option A: $\frac{1}{2}\div8$ divides by 8, but there are only 4 friends, so A is incorrect.
• Option B: $\frac{1}{2}\div4$ correctly represents dividing $\frac{1}{2}$ of the cake by 4 friends. Calculating $\frac{1}{2}\div4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$, which is correct.
• Option C: $\frac{1}{2}\times4$ is multiplying, which would increase the amount, not divide it, so C is incorrect.

Answer:

B. $\frac{1}{2} \div 4 = \frac{1}{8}$