Question

What is the best estimate of 45 percent of 76

Answer 1

9514 1404 393

Answer:

In order of improvement:

• 38
• 34
• 34.2 (actual value)

Step-by-step explanation:

In my engineering experience, a method of estimating should satisfy two requirements:

1. it should be relatively easy to accomplish mentally
2. it should provide a means of estimating the error in the estimate

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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.

Answer 2

Answer:

1/2(80)

Step-by-step explanation:

Well, 45% of 76 is 34.2

Which can be solved by converting 45% to .45 and then multiplied by 76

1/4(80) can be converted into .25*80 which is 20

1/5(80) can be converted into .20*80 which is 16

1/2(80) can be converted into .50*80 which is 40

1/9(80) can be converted into .11*80 which is 8.88

The closest one is 1/5(80) which solves the estimate,