To explain the cases that arise in problems involvingpercents, the is important to specify the termsthat will be used. Price (r) is the number ofhundredths parts taken. This is the number followedby the percent sign. The basic (b) is thewhole on which the price operates. Percentage (p) is the component of the basedetermined through the rate. In the example

5% the 40 = 2

5% is the rate, 40 is the base, and also 2 is the percentage.

You are watching: The portion is equal to the base divided by the rate.

There are three situations that usually arise in dealingwith percentage, together follows:

Case I-To find the percentage once the baseand price are known.

EXAMPLE: What number is 6% the 50?

Case II-To discover the rate when the base and percentageare known.

EXAMPLE: 20 is what percent the 60?

Case III-To find the base once the percentage and also rate room known.

EXAMPLE: The number 5 is 25% that what number?

Case i In the example

6% of 50 = ?

the \"of\" has actually the same definition as it does in fountain examples,such as


In other words, \"of\" method to multiply. Thus, tofind the percentage, main point the basic by the rate.Of food the rate must be readjusted from apercent to a decimal prior to multiplying deserve to be done. Price times base equates to percentage.


6% that 50 = 3

0.06 x 50 = 3

The number that is 6% of 50 is 3.

FRACTIONAL PERCENTS.-A spring percent to represent a part of 1 percent. In a instance such as this, that is sometimes much easier to uncover 1 percent of the number and also then discover the fractional part. Because that example, we would discover 1/4 percent that 840 together follows:



To explain situation II and also case III, we notification in the foregoing instance that the base synchronizes to the multiplicand, the rate coincides to the multiplier, and the percentage synchronizes to the product.


Recalling that the product separated by among its determinants gives the various other factor, we deserve to solve the adhering to problem:

?% of 60 = 20

We are given the base (60) and also percentage (20).


We then division the product (percentage) by the multiplicand (base) to get the other variable (rate). Percentage separated by base equates to rate. The price is uncovered as follows:


The dominion for situation II, as shown in the foregoingproblem, is together follows: To discover the rate when thepercentage and also base are known, divide the percentageby the base. Compose the quotient in the decimal formfirst, and finally as a percent.

Case III

The unknown aspect in instance III is the base, and also therate and also percentage space known.



We divide the product by its known variable to findthe other factor.Percentage separated by rate amounts to base. Thus,


The dominance for case III may be proclaimed as follows: Tofind the boss when the rate and percentage space known,divide the percentage by the rate.

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Practice problems. In each of the adhering to problems,fact identify which instance is involved; then find the answer.

1. What is 3/4% of 740?2. 7.5% that 2.75 = ?3. 8 is 2% of what number ?4. ?% of 18 = 15.5. 12% that ? = 12.6. 8 is what percent the 32?


1. Case I; 5.552. Case I; 0.206253. Case III; 4004. Instance II; 83 1/3%5. Case III; 1006. Situation II; 25%