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A percentage is a non negative number that specifies "how much" of some whole
amount.
It is written as a number followed by the percent '%' symbol.
Examples: 1% 24.5%
50% 100% 150% 0%
"Percent" literally means one part per 100. Regardless of what the
"whole amount" is, when we say we have 100% of that amount, we mean we have all
of it. A convenient way to think of percent is, divide the whole amount
into 100 equal parts, then each part represents 1% of the whole amount, that
is, 1 of the 100 equal parts.
Example: Say we're talking about a box of 100 apples.
We can divide this box into 100 equal parts, namely 100 individual
apples. 1% of this box would then be 1 apple. 12% of this box
would be 12 apples. 50% of this box would be 50 apples. And, 100%
of this box would be all 100 apples.
Example: We have a box of 300 thumb tacks. 300/100 = 3 pins
for each 1%.
10% of this box of tacks would be 10 of the 100 equal parts of 3 tacks, that
is 10% represents 10*3 = 30 tacks. Likewise, 50% would represent 50*3=150
tacks, or half the box.
If someone tossed in 150 more tacks then the box would have 150% of the
original, 300 tacks + the extra 150 tacks = 450 tacks.
We're clearly talking about a fractional amount of some total quantity.
Since percent literally means 1 per 100 then 1% is 1/100, 12%
is 12/100, 67% is 67/100, and so forth. And these numbers are
0.01, 0.12, 0.67 respectively. 100% is 100/100 = 1.00,
120% is 120/100 = 1.20 So, we can quickly convert
percentages to fractions and then to decimals. Likewise, given the
decimal we can quickly get the percentage by multiplying the decimal by
100. (for example, 0.12 * 100 = 12%)
Example: Say we have 35% of 500 lbs of gravel.
This means we have (35/100)*500lbs
which is 175 pounds of gravel.
Example: Say I have 200 lbs of that original 500 lbs of
gravel. What percent is this?
Well, 200/500 = 2/5 = 0.40 and 0.40 =
40/100 = 40%
Example: Say I have 15 receipts which is 30% of a
total number of receipts. What is this total number of receipts?
Well, 15 receipts represents
30%. 10% must be 1/3 of 15 or 5 receipts. So, 100% is 30% +
30% + 30% + 10% which is 15 + 15 + 15 + 5 = 50 receipts.
A more direct approach
using algebra is
15 = (30/100) * Total
(100/30) * 15 = (100/30)*(30/100) * Total
(10/3) * 15 =
1 * Total
(150/3) = 50 = Total
Example: 3/8 represents what
percent? Well, write this fraction as an equivalent fraction with a
denominator of 100 or carry out the division and convert the result directly to
a percentage.
carry out
the division: 3/8 = 0.375
= 37.5 % (take 0.375 * 100 )
Example: 2/5 is (20/20)
* (2/5) = 40/100 = 40%
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