Question
Macy jogs 27 miles a month.
Part A
Explain how to use compensation to find how many miles Macy jogs in 6 months.
(2 points)
Part A
Explain how to use compensation to find how many miles Macy jogs in 6 months.
(2 points)
Answers
GPT-4o mini
To use compensation to find how many miles Macy jogs in 6 months, follow these steps:
1. **Identify the Problem**: Macy jogs 27 miles each month, and we need to find out how far she jogs in 6 months.
2. **Multiply Without Compensating**: The straightforward calculation would be 27 miles/month × 6 months = 162 miles.
3. **Using Compensation**: Instead of multiplying directly, we can round the number of miles to a more convenient figure for easier math. For instance, let’s round 27 miles to 30 miles (which is an easier number to work with), and then multiply:
\[
30 \text{ miles/month} \times 6 \text{ months} = 180 \text{ miles}
\]
4. **Compensate for the Rounding**: Since we rounded 27 miles up to 30 miles, we need to compensate for this increase. Calculate how much we added by rounding:
\[
30 \text{ miles} - 27 \text{ miles} = 3 \text{ miles}
\]
5. **Adjust the Total**: We rounded up by 3 miles for each of the 6 months, which gives us a total of an extra \(3 \text{ miles} \times 6 \text{ months} = 18 \text{ miles}\).
6. **Final Calculation**: To find the actual miles jogged, subtract this extra amount from our previous total:
\[
180 \text{ miles} - 18 \text{ miles} = 162 \text{ miles}
\]
By using compensation, we rounded to a simpler number, calculated, and then adjusted back, arriving at the same result of 162 miles. This method can make mental calculations easier.
1. **Identify the Problem**: Macy jogs 27 miles each month, and we need to find out how far she jogs in 6 months.
2. **Multiply Without Compensating**: The straightforward calculation would be 27 miles/month × 6 months = 162 miles.
3. **Using Compensation**: Instead of multiplying directly, we can round the number of miles to a more convenient figure for easier math. For instance, let’s round 27 miles to 30 miles (which is an easier number to work with), and then multiply:
\[
30 \text{ miles/month} \times 6 \text{ months} = 180 \text{ miles}
\]
4. **Compensate for the Rounding**: Since we rounded 27 miles up to 30 miles, we need to compensate for this increase. Calculate how much we added by rounding:
\[
30 \text{ miles} - 27 \text{ miles} = 3 \text{ miles}
\]
5. **Adjust the Total**: We rounded up by 3 miles for each of the 6 months, which gives us a total of an extra \(3 \text{ miles} \times 6 \text{ months} = 18 \text{ miles}\).
6. **Final Calculation**: To find the actual miles jogged, subtract this extra amount from our previous total:
\[
180 \text{ miles} - 18 \text{ miles} = 162 \text{ miles}
\]
By using compensation, we rounded to a simpler number, calculated, and then adjusted back, arriving at the same result of 162 miles. This method can make mental calculations easier.