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Estimating Sales Tax without a calculator

by Ty
(Maysville, Mo)











































Estimating Sales Tax

You are buying a jacket that cost $69.95.

If the sales tax rate is 7.75%, would it be more reasonable to expect the sales tax to be about $4.90 or $5.60?

Comments for Estimating Sales Tax without a calculator

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Jan 25, 2013
Sales Tax
by: Staff


Answer

Part I

This problem is an example of how to use the Guess and Check Strategy

1. Determine what information the problem provides, along with what you need to find.

2. Select a strategy

3. Solve the problem using your strategy

4. Review your results. Are they reasonable?


The sales tax is a multiplication problem.

Sales tax = (Cost of Purchase) * (tax rate in decimal form)

The decimal form of 7.75% is 0.0775

Sales tax = ($69.95) * (0.0775)

If you had a calculator you would multiply ($69.95) * (0.0775).

However, you can estimate the sales tax without a calculator using several different strategies.

This is one of those strategies:

To estimate the answer without using a calculator and without completing the multiplication long hand, split the two numbers into parts:

69.95 = 70.00 - .05

0.0775 = .08 - .0025

Sales tax = ($69.95) * (0.0775)

= (70.00 - .05) * (.08 - .0025)

At this point, ask youself: is the .05 particularly significant to this problem?

Probably not. Drop it from the calculation.

= (70.00) * (.08 - .0025)

Now, ask youself: is the .0025 significant?

Again . . . Probably not. Drop it from the calculation.

= (70.00) * (.08)

= $5.60, your rough estimate of the sales tax

The real answer is:

Sales tax = ($69.95) * (0.0775) = $5.42

The rough estimate of $5.60 is reasonably close.



Jan 25, 2013
Sales Tax
by: Staff

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Part II

Why does this technique work?

The answer is the Distributive Property applies to all real numbers.

For example, 4 multiplied by 13 is equivalent to 4 multiplied by (7 + 6).

Simply put, the Distributive Property states that it makes no difference whether you: multiply 4 times each number individually, and then add the results . . . or . . . add the two numbers together, then multiply the result by 4.

The result is the same either way.



Math – Distributive Law - 4 multiplied by 13 is equivalent to 4 multiplied by (7 + 6)









Thanks for writing.

Staff
www.solving-math-problems.com


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