Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
Chapter 6 – 1 Percents and Their Fraction and Decimal Forms
N% = N per hundred
Ratio =
ே
ଵ଴଴
70% (this form I use most of the time)
଻଴
ଵ଴଴
ଶଷ.ସ
23.4% ଵ଴଴
ଵ଴଴
100% “1”
ଵ଴଴
CONVERTING PERCENTS TO FRACTIONS
32% 90% ଷଶ
ଵ଴଴
ଽ଴
ଵ଻ହ
75% 50% ଴.଴଺
ଵ଴଴
଻ହ
ହ଴௫ଵ
ହ଴௫ଶ
଺଺య
ଷ
ଵ଴଴
66 % ଶହ௫଻
ଶହ௫ସ
ଶହ
ଶହ௫ସ
ସ
ଵ଴଴௫ଵ଴଴
ଶହ௫ଷ
଻
଴.଴଺௫ଵ଴଴
మ
ଶ
଼
ଵ଴
ଵ଴଴
ଽ
ଵ଴଴
0.06% ଶହ௫ସ
ଵ଴଴
175% ଼௫ସ
଺
ଵ଴଴଴଴
ଷ௫ଶ
ହ଴଴଴௫ଶ
ଷ
ହ଴଴଴
ଷ
ସ
ଵ
ଶ
మబబ
య
భబబ
భ
ଶ௫ଵ଴଴
ଷ
‫ݔ‬
ଵ
ଵ଴଴
ଶ
ଷ
CONVERTING PERCENTS TO DECIMALS
a) replace the % with “x0.01”
b) multiply by 0.01, i.e., move decimal point TWO PLACES TO LEFT
1
Chapter 6
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
34% 0.34
78.9% .789
ହ
6 % 6.625% 0.06625
଼
18% 0.18
0.08% 0.0008
Section 6 – 2
Fractions and Decimals and Their Percent Forms
CONVERTING DECIMALS TO PERCENTS NOTATION
a) MOVE decimal point TWO PLACES TO RIGHT
b) add %
0.24 24%
3.47 347%
1 100%
0.321 32.1%
0.253 25.3%
CONVERTING FRACTIONS TO PERCENT NOTATION
a) divide
b) Move TWO RIGHT
or
a) multiply by 100%
b) divide
2
Chapter 6
Basic College Mathematics (ALEKS)
ଵ
0.25 25%
ସ
Chapter Six PERCENTS
or
100
1
∗ 100% =
% = 25%
4
4
ହ
0.625 62.5%
଼
or
5
500
∗ 100% =
% = 62.5%
8
8
ଶ
0.666ത 66.6ത% 66 %
ଶ
ଷ
ଷ
ହ
ଵ
0.833ത 83.3ത% 83 %
଺
ଷ
ହ଻
ଵ଴଴
ଵଽ
ଶହ
57% (remember anything over 100 is percent)
ଵଽ
ଶହ
ସ
଻଺
ସ
ଵ଴଴
‫= ݔ‬
76%
Improper Fraction and Mixed Numbers Percent
1
଻
ଵ଴
ଵଵ
ସ
ଵ଻
ଵ଴
1.7 170%
2.75 275%
ଷ
Write in percent Round to nearest tenth
଻
ଷ
଻
0.4286 0.429 42.9%
3
Chapter 6
Basic College Mathematics (ALEKS)
Fraction
1
5
C
E
Decimal A 0.833ത
Percent B
A.
ଵ
ହ
Chapter Six PERCENTS
F
ଵ
D
37 %
ଶ
0.2
B.
0.2 20%
D.
ଵ
0.833ത 83.3ത% 83 %
ଷ
భ
ଵ
଼ଷయ
ଷ
ଵ଴଴
మఱబ
య
భబబ
భ
C.
83 % F.
37 % 37.5% 0.375
E.
37.5% ଶହ଴
ଷ
∗
ଵ
ଵ଴଴
=
ଶହ
ଷ଴
=
ହ∗ହ
ହ∗଺
=
ହ
଺
ଵ
ଶ
ଷ଻.ହ
ଵ଴଴
Section 6 – 3
=
ଷ଻ହ
ଵ଴଴଴
=
ଷ௫ଵଶହ
଼௫ଵଶହ
=
ଷ
଼
Percent Proportions and Applications
‫)ݏ݅( ݐ݊ݑ݋݉ܣ‬
ܲ݁‫ݐ݊݁ܿݎ‬
=
‫)݂݋( ݁ݏܽܤ‬
100
What is 82% of 250?
஺
ଶହ଴
=
଼ଶ
A*100 = 82 * 250
ଵ଴଴
A=
଼ଶ∗ଶହ଴
ଵ଴଴
= 205
105% of $60 is how much?
஺
$଺଴
=
ଵ଴ହ
A*100 = $60*105
ଵ଴଴
4
A=
$଺଴∗ଵ଴ହ
ଵ଴଴
Chapter 6
= $63
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
21% of what number is 42?
ସଶ
஻
ଶଵ
=
21*B = 42*100
ଵ଴଴
B=
ସଶ∗ଵ଴଴
ଶଵ
= 200
66 trees is 110% of how much?
଺଺ ௧௥௘௘௦
஻
ଵଵ଴
=
B=
ଵ଴଴
110*B = 66 trees*100
଺଺ ௧௥௘௘௦∗ଵ଴଴
ଵ଴ହ
= 60 trees
What percent of $48 is $15?
$ଵହ
$ସ଼
=
௉
$48*P = $15*100
ଵ଴଴
P=
$ଵହ∗ଵ଴଴
$ସ଼
= 31.25%
1638 people is what percent of 1260 people?
ଵ଺ଷ଼
ଵଶ଺଴
=
௉
ଵ଴଴
1260*P = 1638*100 P =
It was estimated that 24.7% of
adults smoked. In a group of 2000
adults, how many are smokers?
8 students get “A”. If 19% got
“A’s” how many student in class?
Round to nearest student.
425 donations were made. If 60
donations were in the 100-199
dollar range, what % were in this
range? Round to tenth.
5
஺
ଶ଴଴଴
A=
଼
஻
=
ଵ଺ଷ଼∗ଵ଴଴
ଶସ.଻
ଵ଴଴
ଶସ.଻∗ଶ଴଴଴
ଵ଴଴
=
B=
଺଴
ସଶହ
P=
ଵଽ
ଵଽ
=
ଵ଴଴
ସଶହ
100*A=24.7*2000
= 494 people
= 42.1 42 students
௉
଺଴଴଴
= 130%
19*B =8*100
ଵ଴଴
଼଴଴
ଵଶ଺଴
425*P = 60*100
= 14.12 14.1%
Chapter 6
Basic College Mathematics (ALEKS)
Section 6 – 4
Chapter Six PERCENTS
Percent Equations and Applications
Translating to Equations
“OF” times or multiply
“WHAT” variable (unknown) any letter
“IS” equals or “=”
“%” or “percent” times 0.01 or
ଵ
ଵ଴଴
What is 40% of 90?
ଵ
W = 40*
∗ 90 =
ଵ଴଴
ସ଴∗ଽ଴
ଵ଴଴
= 36
235% of 60 amounts to (is) what number?
235*
ଵ
ଵ଴଴
ଶଷହ∗଺଴
∗ 60 = ܰ =
ଵ଴଴
= 141
94 is 80% of what number?
94 = 80*
ଵ
ଵ଴଴
∗ܰ N=
ଽସ∗ଵ଴଴
଼଴
= 117.5
5.6 is 0.8% of what number?
5.6 = 0.8*0.01*N
0.008*N = 5.6 N =
ହ.଺
଴.଴଴଼
= 700
16.1 is what percent of 46?
16.1 = P *
ଵ
ଵ଴଴
∗ 46
P=
ଵ଺.ଵ∗ଵ଴଴
ସ଺
= 35%
What percent of $150 is $213?
P*
ଵ
ଵ଴଴
∗ $150 = $213
6
P=
$ଶଵଷ∗ଵ଴଴
$ଵହ଴
= 142%
Chapter 6
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
ଵସଷ
She read 143 pages. It is 22% of
the book. How many pages in
book?
஻
B=
He had $60. He spent $28 of
dinner and $19 on the movie and
popcorn, what percent did he
spend? Round to tenth %.
ଶଶ
=
22*B = 143*100
ଵ଴଴
ଵସଷ଴଴
= 650 ‫ݏ݁݃ܽ݌‬
ଶଶ
Spent = $28+$19 = $47
$ସ଻
௉
=
60*P=47*100
$଺଴
P=
஺
85% of students passed. If there
were 40 students, how many
passed?
ସ଴
ଵ଴଴
ସ଻଴଴
=
A=
= 78. 3ത = 78.3ത%
଺଴
଼ହ
100*A = 40*85
ଵ଴଴
ସ଴∗଼ହ
= 34 ‫ݏݐ݊݁݀ݑݐݏ‬
ଵ଴଴
Section 6 – 5 Applications Involving Sales Tax, Commission,
Discount, and Markup
Sales Tax = Sales Tax Rate *
ଵ
* Purchase Price
ଵ଴଴
Total Price = Purchase Price + Sales Tax
A calculator costs $110 and sale
tax rate is 4.5% What is the sales
tax and total price.
ST = 4.5*
DVD sells for $15. Sales Tax is
$0.90. What is the sales tax rate?
$0.90 =
ଵ
ଵ଴଴
∗ $110 = $4.95
TP = $110+4.95 = 114.95
ௌ்
ଵ଴଴
∗ $15 ST =
ST = 6%
7
Chapter 6
$଴.ଽ଴∗ଵ଴଴
$ଵହ
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
Sales tax equals $21.50. Sales tax
rate is 5%, what is the price?
5
∗ܲ
100
$ଶଵ.ହ଴∗ଵ଴଴
P=
= $430
$21.50 =
ହ
Commission = Commission Rate *
ଵ
*Total Sales
ଵ଴଴
1
∗ $160,000
100
$6400 ∗ 100
ܴܽ‫= ݁ݐ‬
= 4%
$160,000
House sold for $160,000 and
earned a commission of $6400.
What is the commission rate?
$6400 = ܴܽ‫∗ ݁ݐ‬
Base salary is $50,000.
Commission rate is 6%.
Total salary is $98,000.
What is the total sales?
Commission = 98K - 50K = 48K
6
48,000 =
∗ ݈ܵܽ݁‫ݏ‬
100
Sales =
‫∗ ݁ݐܴܽ ݐ݊ݑ݋ܿݏ݅ܦ = ݐ݊ݑ݋ܿݏ݅ܦ‬
ସ଼଴଴଴∗ଵ଴଴
଺
= $800,000
1
∗ ܱ‫݁ܿ݅ݎܲ ݈ܽ݊݅݃݅ݎ‬
100
Sale Price = Original Price - Discount
Original price = $600. Sales price Discount = $600-$480 = $120
ܴ
= $480. What is the discount rate?
$120 =
∗ 600
100
$ଵଶ଴∗ଵ଴଴
R=
= 20%
଺଴଴
Mark Up = Markup Rate*
ଵ
*Original Price
ଵ଴଴
Retail Price = Original Price + Mark Up
8
Chapter 6
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
ଷହ
Mark Up = 35%.
a) MU =
∗ $100 = $35
ଵ଴଴
A) what is the mark up on $100?
b) RP = $100+$35 = $135
B) what is the retail price?
ହ
∗ 135 = $6.75
c)
ST
=
C) 5% sales tax, what is total cost?
ଵ଴଴
TC = $135 + $6.75 = $141.75
Section 6 – 6
Percent Increase and Decrease
Formula:
Percent Increase =
஺௠௢௨௡௧ ௢௙ ூ௡௖௥௘௔௦௘
Percent Decrease =
Note:
ை௥௜௚௜௡௔௟ ஺௠௢௨௡௧
஺௠௢௨௡௧ ௢௙ ஽௘௖௥௘௔௦௘
ை௥௜௚௜௡௔௟ ஺௠௢௨௡௧
% ூ௡௖ ௢௥ ஽௘௖
ଵ଴଴
‫ ݔ‬100%
=
‫ ݔ‬100%
஺௠௢௨௡௧ ௢௙ ூ௡௖ ௢௥ ஽௘௖
ை௥௜௚௜௡௔௟ ஺௠௢௨௡௧
Demisha’s salary increased from
$42,500 to $44,200. What is the
percent increase.
Inc = $44,200-$42,500 = $1700
$ଵ଻଴଴
% Inc =
‫ݔ‬100 = 4%
From a graph on Page 380, Day 2
= $21.00 and Day 3 = $20.58
What is the % decrease?
Dec = 21.00-20.58 = $0.42
$଴.ସଶ
% Dec =
‫ݔ‬100 = 2%
9
$ସଶହ଴଴
$ଶଵ.଴଴
Chapter 6
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
Chapter Six Section Seven
INTEREST
SIMPLE AND COMPOUND
Simple.Interest = (Pr inciple) x( Rate) x
1
x(Time)
100
Total = Principle + Interest
Time = Years
1
12
Monthly =
30
365
or
1.
I = $4300 x 7 x
1
x1 = $301
100
2.
I = $4300 x7 x
1 3
x = $225.75
100 4
3.
I = $4800 x8.5 x
1
30
x
= $33.53
100 365
Daily =
1
365
T = $4800 + 33.53 = $4833.53
(Not on test – important to know and understand)
Amount = Pr inciple + Interest
A = P • (1 +
4.
R n •t
)
n • 100
P = 2000 R = 9% n = 1 T = 2
A = $2000 • (1 +
5.
9 1• 2
) = $2000 • (1.09) 2 = $2000 • 1.1881 = $2376.20
1x100
ଷ
ଵ
଼
ଶ
P= 7000 R = 6 = 6.375% n = 2 T = 1
3
6.375 2• 2
A = $7000 • (1 +
) = $7000 • (1.031875)3 = $7690.938 = $7690.94
2 • 100
10
Chapter 6
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
Chapter Six Section Eight
Min.Payment = (Pr inciple) x( Rate) x
INTEREST RATES ON CREDIT
CARDS AND LOANS
1
100
1.
1
= $97.3518
100
a)
MP = $4867.59 x 2 x
b)
I = $4867.59 x 21.3x
MP = $97
1
1
x = $86.3997225
100 12
I = $86.40
Applied to Principle = $97 - $86.40 = $10.60
c)
I = $4867.59 x13.6 x
1
1
x = $55.17
100 12
Applied = $97 - $55.17 = $41.83
d)
Difference = $41.83 - $10.60 = $31.23
2.
a)
I = $32,680 x3.37 x
1
1
x = $91.78
100 12
Applied = $321 - $91.78 = $229.22
1
1
x = $149.78
100 12
b)
I = $32,680 x5.5 x
c)
120 x $ 58 = $6960
Increase = $149.78 - $91.78 = $58
Don’t DO 3 – 5 (Not on test)
Read Page 405
$153,000 @ 6.625%
30 yrs Interest $199,684.80
11
Chapter 6
Basic College Mathematics (ALEKS)
Chapter Six PERCENTS
360 payments @ $979.68 = $352,684.80
15 yrs Interest $88,799.40
180 payments @ $1343.33 = $241,884.00
$363.65 extra a month saves $110,885.40
12
Chapter 6