9514 1404 393
Answer:
In order of improvement:
Step-by-step explanation:
In my engineering experience, a method of estimating should satisfy two requirements:
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Multiplication and division by 2 are generally easy to perform mentally.
We note that 45% is about 50%.
50% of 76 is 76/2 = 38 . . . a good starting estimate
45% is down 5% from 50%, so the actual value will be 5/50 = 10% lower than this first estimate
A good second estimate is 38 -0.10(40) = 34.
A better estimate is 38 -3.8 = 34.2, which is the actual value of the expression.
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Alternate approach
You could also transform the problem to 76% of 45, which is about 3/4 of 44, or about 33. Figuring the error adjustment on this approach is somewhat more difficult, as it is factors of 1/75 and 1/44 too low. 1 part in 44 is not too difficult to figure, as it is 33/44 = 3/4, so a better estimate is 33.75. It takes a calculator to figure 1 part in 75 of this, which is 0.45. Adding that amount gets you to the actual value of 34.2.
