Question

math - 5th grade

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 $\frac{1}{2} \times 4 = \frac{4}{2}$
d $\frac{1}{2} \times 8 = \frac{8}{2}$

Explanation:

Step1: Analyze the problem

We have $\frac{1}{2}$ of a cake left, and we need to divide this remaining cake equally among 4 friends. So we need to perform a division operation: divide the remaining fraction ($\frac{1}{2}$) by the number of friends (4).

Step2: Evaluate each option

• Option A: $\frac{1}{2} \div 8$ uses 8 instead of 4 (the number of friends), so it's incorrect.
• Option B: $\frac{1}{2} \div 4$ correctly represents dividing the remaining $\frac{1}{2}$ cake among 4 friends. Calculating $\frac{1}{2} \div 4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$, which is the fraction each friend gets from the whole cake.
• Option C: $\frac{1}{2} \times 4$ is a multiplication, which doesn't represent dividing the remaining cake among friends, so it's incorrect.
• Option D: $\frac{1}{2} \times 8$ is also a multiplication and uses 8 instead of 4, so it's incorrect.

Answer:

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