To analyze Miguel's division of 754 by 0.52, let's first clarify how division with a decimal works. When dividing by a decimal, it is typically easier to eliminate the decimal from the divisor.
In this case, Miguel should have multiplied 0.52 by 100 to convert it into 52 and also multiplied 754 by 100, turning the problem into 75400 divided by 52. This is a standard approach to ensure that both numbers are working with whole numbers.
Now, let's evaluate each of the options:
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He included a 5 in the quotient, which does not belong.
This may or may not be true depending on the calculations. We need to verify if he was incorrect overall. -
He multiplied the divisor by 10 and the dividend by 100.
This is not accurate because he needed to multiply the divisor by 100, not 10. So this statement suggests an error. -
He subtracted 208 from 234 incorrectly.
We need to check this as well. If his calculations get messed up because of incorrect previous steps, this might be true too, but the previous errors need evaluation first. -
He multiplied the divisor by 100 and the dividend by 10.
This is incorrect because Miguel should have multiplied the divisor by 100 and the dividend by 100, not just 10.
Given the analysis reflects that Miguel's method of dealing with the decimal point was flawed, we can conclude that he multiplied the divisor incorrectly. Therefore, the correct assessment of Miguel's error is:
He multiplied the divisor by 100 and the dividend by 10.
This highlights a fundamental error in how he set up the division problem with regard to the decimal.
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