One can teach fourth-grade students how to estimate quotients by providing instruction on substituting the original problem with compatible numbers. These are numbers that are close in value to the originals, but are easier to compute mentally. Another approach is to use related multiplication facts that are more familiar to the students.
Continue ReadingFor example, if asked to estimate the quotient of 181 divided by five, students can round off 181 to 200. Given that 100 divided by five equals 20, the quotient of 200 divided by five would be twice as much, or 40. Hence, 181 divided by five is approximately 40.
Since multiplication is the inverse of division, learners might also think of related multiplication problems. Students assigned the task of estimating the quotient of 45 divided by six might ask what number multiplied by six has a product close to 45. Since six times eight equals 48, it follows that 45 divided by six is approximately eight.
Another approach is to adjust the quotient, which means to shorten both the dividend and divisor by the same number of digits, and then divide the resulting numbers. For instance, to estimate the quotient of 312 divided by 55, a student can delete the digit in the ones place from each number to obtain 31 divided by five, which is approximately six.
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