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)

1 answer

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.

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