Which diagram best shows how fraction bars can be used to evaluate One-half divided by one-fourth?

Question

A fraction bar labeled 1. Under the 1 are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing one-fourth. 2 one-fourths are circled.
A fraction bar labeled one-fourth. Under the one-fourth are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing 1. 2 boxes containing 1 are circled.
A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 8 boxes containing one-half. One box containing one-half is circled.
A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 2 boxes containing one-half. One box containing one-half is circled.

Answer 1

To evaluate $\frac{1}{2}÷\frac{1}{4}$, we can think about it in terms of how many times $\frac{1}{4}$ fits into $\frac{1}{2}$.

1. Understanding the Expression: $\frac{1}{2}÷\frac{1}{4}$ can be rewritten as multiplying by the reciprocal: $\frac{1}{2}\times 4=2$. This means that $\frac{1}{2}$ contains $2$ pieces of $\frac{1}{4}$.

2. Using Fraction Bars: We would use a bar to represent 1 whole unit and show that there are 2 halves under that bar, and then visually show how many quarters (which are $\frac{1}{4}$) fit into those halves.

Given your options:

• Option 1: A fraction bar labeled 1. Under the 1 are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing one-fourth. 2 one-fourths are circled.

  • This shows 2 halves and 4 quarters and indicates how $\frac{1}{2}$ contains 2 pieces of $\frac{1}{4}$.

• Other Options: Other options do not accurately show how many quarters fit into a half.

Correct Answer: The first option is the best representation, as it clearly shows there are 2 halves, and under each half, the corresponding quarters are displayed clearly.