Page 44 - Calculating Agriculture Cover 20191124 STUDENT - A

4-6 Percentages, Ratios and Relationships CH 4]

language we identify different words as expressing a mathematical function such as percent
of which we are instructed in the division of a number or the multiplication of a number. An
example is the sales tax you pay on taxable goods purchased in retail stores is expressed as a
percent to calculate the sales tax, and the amount of your purchase increases, and that sales
tax portion is sent to the state governments Tax Board.
You take a trip to a local Bass Pro Shop or Cabela’s to purchase a fishing rod, reel,
hooks, weights, bait, lures and other fishing equipment. The total store cost of your purchase
is $158.29. The tax in your store for your state and city amounts to 8% of your purchase
cost. What will be the tax added to your purchase price and forwarded to the State tax
coffers. The of in this problem references multiplication and the added indicates that there is
also addition.
The tax calculation is:

Purchase value x Tax Rate as a percent = Sales tax to be collected.

 $158.29 x 8% =
 $158.29 x ( 8% ÷ 100% ) = Convert the % value to a decimal value.
$158.29 x 0.08 = $12.66

With the tax of $12.66 added to your purchase price, your Total Cost is calculated for the
goods you are purchasing, such that:

Purchase value + Sales Tax = Total Cost
$158.29 + $12.66 = $170.95

This calculation of Total Cost can also be resolved by remembering that the Store Cost for
this purchase represents 100% of your purchase (the whole), and that 100% equals 1. Then
adding the Tax Rate percent (8%), expressed as a decimal (0.08) will yield a value (1 + 0.08 =)
1.08 which when multiplied to the Purchase value allows you to calculate your Total Cost
(Purchase value + Sales Tax) via multiplication. Review the simplicity of this calculation:

Purchase value x ( 1 + Sales Tax rate as a decimal ) = Total Cost
$158.29 x (1 + 0.08) =

$158.29 x 1.08 = $170.95

Identifying Amounts, Percents, and Bases

When students first study mathematics they come to understand percents as an amount
of the base sum to an item. The un-concatenated term "per cent" simply means "per
hundred"; as such it is easily understood as a portion out of 100, including fractions and
sometimes numbers higher than 100.
With percent problems, students are often asked to identify the three core parts of the
problem—the amount, the percent rate, and the base—wherein the amount is the number
taken out of the base by being reduced by a certain percentage or calculated by the percent
rate.
The percent symbol when read "twenty-five percent" simply means 25 out of 100. It is
useful to be able to understand that a percent can be expressed as a fraction and as a
decimal, meaning that 25 percent can also mean 25 /100 which can be reduced to 1/4 or
0.25, when written as a decimal.
When you are asked to determine 7 percent of 170, this means to calculate 7 hundredths
(0.07) of 170 the fractional part of the number, which is found through multiplication. The
solution is then calculated by multiplying 170 by 0.07.

Example: Calculate 7% of 170. (Stated for calculation as 0.07 x 170)

Solution: % Rate x Base = Amount
0.07 x 170 = 11.9

INSTRUCTOR Copyrighted Material