Sales Tax Example

In the state of Michigan, sales tax is 6%. That means for every buck you spend, you have to fork over an extra six cents so that the State of Michigan can plant a new crop of potholes on the roads to ensure that there will never be a shortage of work for auto mechanics. (It's like a farm subsidy for industrialists.)

So you walk into Best Buy, pick out a new version of Doom ($45.00, but worth every penny for the new exploding head effect) and head for the line, visions of mayhem to come dancing in your head. Half an hour later, you get to a cashier, who appears to be a derelict abducted from a dark alley on another planet. You aren't sure how it took 8 minutes to present you with a total for a single object that scanned on the first try, but you are quite sure that you're going to double check the amount before handing over your Visa card.

So before we can treat a number with a % on it like any other number, we need to undo what that goofball who multiplied it by 100 did, which would be to divide it by 100. 6 divided by 100 is 0.06.

So to get 6% of $45.00, we

(6 / 100 )    turn 6% into a number again
* $45.00     multiplied by 45.00 (which is what we want 6% of)
=$2.70       which gives us 2.70 in tax
If we add the tax to what we spent, we get $45.00 + $2.70 = $47.70. If that doesn't agree with what's on the receipt, then it's time to call the manager.

Another way to go about calculating the same amount gets rid of the step where we add the sales tax in. We know we're going to have to hand over 100% of the purchase price ($45.00) and we also know we're going to have to hand over 6% in sales tax, for a total of 106%. We could calculate 106% of the purchase price and get the same bottom line on the receipt.

(106 / 100 )    turn 106% into a number again
* $45.00     multiplied by 45.00 (which is what we want 6% of)
=$47.70       which gives us 2.70 in tax

Gratuitous Math Fact

Both of these calculations are doing exactly the same thing, just doing it in a different order. There are some basic properties associated with multiplication and addition and the one we're using here is:
x(a + b) = xa + xb


This is called the distributive property, and if we were to fill in the blanks, a would be 6%, b would be 100%, and x would be $45.00.