To use compensation to find how many miles Macy jogs in 6 months, follow these steps:
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Identify the Problem: Macy jogs 27 miles each month, and we need to find out how far she jogs in 6 months.
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Multiply Without Compensating: The straightforward calculation would be 27 miles/month × 6 months = 162 miles.
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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:
\[ 30 \text{ miles/month} \times 6 \text{ months} = 180 \text{ miles} \]
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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:
\[ 30 \text{ miles} - 27 \text{ miles} = 3 \text{ miles} \]
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Adjust the Total: We rounded up by 3 miles for each of the 6 months, which gives us a total of an extra \(3 \text{ miles} \times 6 \text{ months} = 18 \text{ miles}\).
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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.
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