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4-2 Percentages, Ratios and Relationships CH 4]

selling price when sold. As percent means hundredth, 8% means 8 hundredths, which is 0.08
in decimal form.
% : In mathematics, A percentage (%) symbol is a dimensionless number (pure number) though the value it is
a percentage is a attached to indicates that the value is in hundredths.
number or ratio The percent (%) affects decimal placement for a number and expresses a relationship of
expressed as a the number to another number as a value of the whole, indicated in the opening paragraphs.
fraction of 100. It is Once the relationship is established the % symbol is concatenated to the calculated value.
often denoted using
the percent sign, THE VALUE and POWER OF ONE and PERCENT (%)
"%", or the
abbreviations "pct.", To appreciate the relationship of one number to another as a percentage with the symbol
"pct"; sometimes the % attached requires an understanding of the value of 1; And we are looking at the number as
abbreviation "pc" is if it were a fraction.
also used. A Recall the lesson on reciprocals in Chapter 2 that all numbers have a denominator and
percentage is a that denominator when not stated is 1; The value of one. Given the value of 300, it contains
dimensionless an implied denominator of 1. Given Hallie, the implied denominator is 1. Given the value of W
number (pure the implied denominator is 1.
number). Concurrent with that idea is that when any number is divided by itself it has a value of 1.
Such that 425 divided by 425 equals 1 (425 ÷ 425 = 1 or as a fraction 425/425 = 1).
Similarly 12 divided by 12 equals 1 (12 ÷ 12 = 1 or 12/12 = 1). Again, this value 1 occurs
again when Kellen divided by Kellen equals one (Kellen ÷ Kellen= 1 or Kellen / Kellen = 1).
Let’s summarize this concept; any value divided by itself equals 1.

425 Kellen 12
= 1 = 1 = 1
425 Kellen 12

In your thinking try this relationship: percent divided by percent? It too equals 1. The
arithmetic just explained validates this concept in that percent divided by percent equals 1
( percent ÷ percent = 1, or percent / percent =1) and expressed as the symbol % we note the
same; % divided by % equals 1 or % ÷ % = 1 and % / % = 1:

%
= 1
%

again, any value divided by itself equals 1.

In arithmetic the antonym of division is multiplication, thus we can say that when any
number is multiplied by the value of one the resulting answer is equal to that number. The
number 435 when multiplied by 1 equals 435. Similarly, when 1 is multiplied by 212 the
result is 212. And when Declan is multiplied by 1 the result is Declan, or when one is
multiplied by Hallie the result is Hallie.

435 x 1 = 435
1 x 212 = 212
Declan x 1 = Declan
1 x Hallie = Hallie
To restate the observation, when any number is multiplied by the value of 1 the resulting
answer is equal to that number.

As stated earlier, when a % is divided by a % the value of that division is 1 (%/% = 1).
However, a unique thing happens when a percent value (%) is divided or multiplied to any
number it merely adds (concatenates) the percent (%) to the value. Such that 10 times 50%
becomes 500% (10 x 50% = 500%); and 500% ÷ 100% = 5.

50 % 5
x 10 and 100% ) 500%
500 %

Similarly when a percent (%) number is divided by a whole number the resulting answer
is a percent (%), such as 100% / 80 = 1.25%; or when 30 is multiplied by 30 % the answer is
900%; and 900% ÷ 100% = 9.

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