David W. answered • 01/10/17
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While various teachers/tutors, even on this WuzAnt Answers Forum, consider exact evaluation so easy, especially with the convenience of calculators and computers, there is still a crying need for the ability to perform estimation techniques -- many students, teachers, and tutors blindly crank out answers without any feel for whether the answer they have produced is even "in the ball park."
Here, we have a subtraction problem. To calculate the exact value, we would first find a common denominator, then we could simply subtract the new numerators. This takes two (perhaps complicated) multiplications and a subtraction. Many of us would make errors if doing it only in our heads or doing it in an extremely short timeframe (both happen).
So, with estimating, we find close, convenient numbers to speed up the process and to maintain accuracy while doing so.
Looks like 21 is close to 20, which is important because we also have 10. And, when we change a fraction, lowering the numerator when we lower the denominator will keep the new fraction as close as possible, so we now have:
16/20 - 2/10
O.K., now a common denominator of either 10 or 20 is good; let's go with 10 --
8/10 - 2/10 = 6/10
And, reducing that --
6/10 = 3/5
Now, our quick estimate, 3/5 = 0.60, is quite close to the exact answer, 64/105=0.6095. If we calculated 0.6095, we could verify it by calculating 0.60 without paper or calculator; we could also do it much, much faster than creating an exact calculation.
Estimating is a very important skill -- learn it well !!
I first learned that the yearly wage I was offered was "roughly" 2000 times the hourly wage (exactly, the computation uses 2080 hours in 52 weeks of 40 hours each). So, a $20/hr offer is "a little more" than $40,000/yr. With some practice, you can get really quick doing estimating (useful for work, for tests, etc.).
