Compensation is a mental math strategy that involves adjusting numbers to make calculations easier, and then adjusting back to find the final result. To find the difference between 30,000 and 6,985 using compensation, follow these steps:
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Round the Subtrahend: First, round 6,985 to a more manageable number. In this case, we can round it to 7,000.
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Subtract the Rounded Number: Now, perform the subtraction with the rounded number: \[ 30,000 - 7,000 = 23,000 \]
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Compensate for the Adjustment: Since we rounded 6,985 up to 7,000, we need to account for the difference we created by rounding. The difference between 7,000 and 6,985 is: \[ 7,000 - 6,985 = 15 \]
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Adjust the Result: Now, subtract that compensation (15) from the result of the subtraction: \[ 23,000 + 15 = 23,015 \]
Therefore, the difference between 30,000 and 6,985 is 23,015.
To summarize:
- Round 6,985 up to 7,000.
- Subtract: 30,000 - 7,000 = 23,000.
- Adjust back by adding the difference (15) to get the final answer: 23,015.