Percent refers to "how much of
some whole."
The word percent has two parts to it:
'per' and 'cent'.
'cent is a root which literally means
100. 'Per' mean 'a group'.
So we assign the number '100' to the
whole group taken as one. And as we take from that group we can talk
about how many we take in terms of a number form 1 to 100.
So, if we have 100 books and we take
15 from that group we say we've take 15 percent of that group of
books. We write it this way : 15% of all the books we now have.
We don't have to start with 100
objects. Say we started with 60 pens. We take 9 pens, then we've
taken 15% of the pens.
Say we have 450 flags. If we take 45
of these flags then we'd have 10% of the flags.
`100% of anything is 'all of it,' any
other percent is some of it.
Since 10% means 10 out of a 100, we
can write it as 0.10 (10 one hundredths). So if we want to find 10%
of 34 we only need to multiply 34 by 0.10 to get 3.4. Ten groups of
3.4 gives us the total in this case of 34.
Notice that writing these decimals,
0.05 (5%), 0.26 (26%), .... 0.99 (99%),
the next would be 1.00 (100%). Usually
we do not talk about having more than 100% of anything (but occasions
do arise where it makes sense,) which means the largest decimal would
be 1.000... and the smallest, well 0. 0% would mean none of the
whole (not usually used.)
Working with percents requires
multiplication and division. But you do need to know how to convert
back and forth between percents and decimals.
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15% = 0.15
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0.11 = 11%
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1% = 0.01
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0.045 = 4.5%
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2.64% = 0.0264
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0.1005 = 10.05%
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100% = 1.00
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0.06 = 6%
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The first column requires a division by
100, and the 2nd a multiplication by 100.
Now we're ready for some examples.
1) What is 14% of 50?
(notice the keyword 'of'. 'of'
always means multiplication, so)
first change 14% to 0.14, then
multiply (0.14)(50) = 7
7 is 14% of 50
2) What is 0.3% of 90?
divide 0.3 by 100 to get 0.003
multiply by 90 to get (0.003)(90) = 0.27
0.27 is 0.3% of 90
Now, let's ask the question a
different way
3) 13 is what percent of 120?
( this is an equation in disguise;
'is' always means = and 'of always means multiplication, so)
13 '=' P x 120
solving for P we get
13/120 = P
0.108 = P
To answer the question we need to
convert 0.108 to a percent
0.108 x 100 = 10.8 %
4) 12.5 is what percent of 25?
12.5 = P x 25
P = 12.5/25 = 0.50 (multiply by
100 to get...)
P = 50%
One last way to ask the question:
5) 35 is 12% of what number?
35 '=' 0.12 x N
35/0.12 = N
292 = N
6) 6.5 is 13% of what number?
6.5 = 0.13 x N
6.5/0.13 = N
50 = N
Percents are used in interest
calculations, markups and markdowns.
With interest we have simple and
compound interest.
If a bank yields 2.5% simple monthly
interest on the amount you have deposited in that bank, then you will
receive 2.5% of your original opening balance each month.
For example, if you deposited $2600,
then at the end of the first month you'd receive (0.025)(2600) = $65.
So your account would have $2600 + $65 = $2665. Now the next month
you'd receive the same interest of $65, so at the end of that month
you'd have $2665 + $65 = $2730.
Now if the same bank used compound
interest, then given the same circumstances after the first month
you'd have $2665. Now this amount is used to calculate the interest
for the next month like this: (2665)(0.025) = $66.63, so your
account contain $2665 + $66.63 = $2731.63. The next month would
yield (2731.63)(0.025) = $68.29, so the account would contain
$2731.63+$68.29 = $2799.92.
Compound interest is better, slightly,
but better.
One last place to visit with percents
deal with markup and markdown.
If a store keeper marks up his clothing
by 10%, then each piece of clothing would cost 10% more than
previously.
For example if a jacket originally had
a sticker equal to $54, then its new price would be 10% of this $54
more. 10% = 0.10, 0.10x54 = 5.4. So we add $5.40 to $54 to get
$59.40.
If this storekeeper, instead, decides
to markdown everything by 5% then this jacket would have a price
equal to: 5% = 0.05, 0.05x54 = $2.70. So, we subtract $2.70 from
$54 to get 54 - 2.7 = $51.30.
Suppose one day we walk into that store
and see this jacket with a price equal to $125. We figure that we'd
pass until he had a sale. Well after a few weeks we hear about a
sale and return to this store. We see this jacket selling for $95.
What was the markdown on this jacket?
Well we need to find the difference
between the two prices and compare that to the original price.
125 - 95 = 30. We're
asking 30 is what percent of 125.
30 = P x 125
P = 30/125
P = 24%
The markdown was 24%.
So which is the better deal? Well,
by waiting we spent less money. Did we save money? No, we still
spent money. Saying that we 'saved' money has to be the best
gimmick ever created by business. Suppose initially you had no money
to buy this jacket, but did later on at this sale, then you had no
money to put into a 'savings' account (the difference) to actually
save the money. But the wheel goes around to get you to buy under the
pretext of 'saving'.
Giving tips:
Suppose you are at a restaurant and
tour friend is handed the bill. the bill was $23.54 (a light lunch).
Before the server leaves your friend hands him the money and bill
quicker than anyone you've ever seen. Let's say the tip was 15%, how
could he calculate that so quickly?
Well 15% is 10% + 5%; 5 is half of
10,and multiplying by 10 moves the decimal left by 1.
Let's see: 10% of 23.54 is 2.35,
half of 2.35 is 1.17, so 2.35 + 1.17
is 3.52 which makes the amount $27.06
That's exact, why not round off?
the amount is $24.00,
10% is 2.4,
half again is
1.2 call it 1,
1 + 2 = 3 +
24 = $27
Another example,
say the tip is 20%
then 20% of 23.54 is (multiple by 2,
forget about the cents) = 46,
move decimal by 1 to get 4.6, add the 4
to 23 to get 27, bump up one to
get $28.
This is another FREE ALGEBRA PRINTABLE presented to you from the
Algebra section of
K12math.com