Question
Find the Error Carli made 9 greeting cards in 3/4 hour. She determined her unit rate to be 1/12 card per hour. Find her error and correct it
She set up her rate as 3/4 hour/9 greeting cards. Her unit rate of 1/12 is (greeting cards, hours) per (greeting card, hour), not (hours, greeting cards) per (greeting card, hour)
She set up her rate as 3/4 hour/9 greeting cards. Her unit rate of 1/12 is (greeting cards, hours) per (greeting card, hour), not (hours, greeting cards) per (greeting card, hour)
Answers
GPT-4o mini
Carli made 9 greeting cards in \( \frac{3}{4} \) hour. To find her unit rate, we need to determine how many cards she makes in one hour.
1. Start with the formula for unit rate:
\[
\text{Unit Rate} = \frac{\text{Total Cards}}{\text{Total Time in hours}}
\]
2. Substitute in her numbers:
\[
\text{Unit Rate} = \frac{9 \text{ cards}}{\frac{3}{4} \text{ hour}}
\]
3. To divide by a fraction, we multiply by its reciprocal:
\[
\text{Unit Rate} = 9 \text{ cards} \times \frac{4}{3} \text{ hours}^{-1} = \frac{36}{3} \text{ cards per hour} = 12 \text{ cards per hour}
\]
Carli's error was in how she calculated her unit rate. She incorrectly calculated it as \( \frac{1}{12} \) cards per hour instead of \( 12 \) cards per hour.
To correct:
- The correct unit rate is \( 12 \) greeting cards per hour, not \( \frac{1}{12} \) cards per hour.
1. Start with the formula for unit rate:
\[
\text{Unit Rate} = \frac{\text{Total Cards}}{\text{Total Time in hours}}
\]
2. Substitute in her numbers:
\[
\text{Unit Rate} = \frac{9 \text{ cards}}{\frac{3}{4} \text{ hour}}
\]
3. To divide by a fraction, we multiply by its reciprocal:
\[
\text{Unit Rate} = 9 \text{ cards} \times \frac{4}{3} \text{ hours}^{-1} = \frac{36}{3} \text{ cards per hour} = 12 \text{ cards per hour}
\]
Carli's error was in how she calculated her unit rate. She incorrectly calculated it as \( \frac{1}{12} \) cards per hour instead of \( 12 \) cards per hour.
To correct:
- The correct unit rate is \( 12 \) greeting cards per hour, not \( \frac{1}{12} \) cards per hour.
can u pick the the stuff in the parentheses?
GPT-4o mini
Certainly! Here's the explanation with the terms in parentheses specified as "units" (cards and hours), which then can be clarified without symbols:
Carli made 9 greeting cards in \( \frac{3}{4} \) hour. To find her unit rate (the number of greeting cards made in one hour), follow these steps:
1. **Unit Rate Formula**:
\[
\text{Unit Rate} = \frac{\text{Total Cards (greeting cards)}}{\text{Total Time (hours)}}
\]
2. **Plug in the Numbers**:
\[
\text{Unit Rate} = \frac{9 \text{ (greeting cards)}}{\frac{3}{4} \text{ (hours)}}
\]
3. **Dividing by a Fraction**:
When dividing by a fraction, multiply by its reciprocal:
\[
\text{Unit Rate} = 9 \text{ (greeting cards)} \times \frac{4}{3} \text{ (hours)}^{-1} = \frac{36}{3} \text{ (greeting cards per hour)} = 12 \text{ (greeting cards per hour)}
\]
**Error Summary**:
Carli made an error by stating her unit rate as \( \frac{1}{12} \) greeting cards per hour instead of recognizing that she makes **12 greeting cards per hour**.
So the correct unit rate is **12 greeting cards per hour**.
Carli made 9 greeting cards in \( \frac{3}{4} \) hour. To find her unit rate (the number of greeting cards made in one hour), follow these steps:
1. **Unit Rate Formula**:
\[
\text{Unit Rate} = \frac{\text{Total Cards (greeting cards)}}{\text{Total Time (hours)}}
\]
2. **Plug in the Numbers**:
\[
\text{Unit Rate} = \frac{9 \text{ (greeting cards)}}{\frac{3}{4} \text{ (hours)}}
\]
3. **Dividing by a Fraction**:
When dividing by a fraction, multiply by its reciprocal:
\[
\text{Unit Rate} = 9 \text{ (greeting cards)} \times \frac{4}{3} \text{ (hours)}^{-1} = \frac{36}{3} \text{ (greeting cards per hour)} = 12 \text{ (greeting cards per hour)}
\]
**Error Summary**:
Carli made an error by stating her unit rate as \( \frac{1}{12} \) greeting cards per hour instead of recognizing that she makes **12 greeting cards per hour**.
So the correct unit rate is **12 greeting cards per hour**.