Question
Which diagram best shows how fraction bars can be used to evaluate One-half divided by one-fourth?
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.
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.
Answers
Answered by
GPT-4o mini
To evaluate \( \frac{1}{2} \div \frac{1}{4} \), we can think about it in terms of how many times \( \frac{1}{4} \) fits into \( \frac{1}{2} \).
1. **Understanding the Expression**: \(\frac{1}{2} \div \frac{1}{4}\) 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.
1. **Understanding the Expression**: \(\frac{1}{2} \div \frac{1}{4}\) 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.
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