Transcript 16 PERCENTS print

% and the
BASIC PERCENT
EQUATION
MSJC ~ Menifee Valley Campus
Math Center Workshop Series
Janice Levasseur
% Percents %
• Percent means “parts of 100” or “per 100”
• A percent can be written using a percent
sign (%), as a fraction, or as a decimal
Converting a % to a Fraction
• To convert a percent to a fraction,
translate the % symbol:
• Remove the % sign and divide by 100
(“per 100”)
Ex: Convert 27% to a fraction
27%
27

100
 Simplify ? No . . .
done
Ex: Convert 25% to a fraction
25
25% 
100
1

4

Simplify?
Simplify? No . . .
done
YES!
Ex: Convert 130% to a fraction
130
130% 
100
30
1
100
3
1
10
Simplify?
Yes!
Improper
Fraction
Simplify?
Yes!
Simplify? No . . .
done
1
Ex: Convert 3 % to a fraction
1
1
1
Divide
% 3
  100
fractions
3
3
100
1 100 1 1
 
 
3 1
3 100
1

Simplify? No . . .
300
done
Ex: Convert 0.5% to a fraction
0.
5
Divide decimals?
0.5% 
Decimal

Fraction
100
1
  100
2
1 100 1 1
1
 
 

2 1
2 100
200
Simplify?
No . . .
done
Converting a % to a Decimal
• To convert a percent to a decimal,
translate the % symbol:
• Remove the % sign and divide by 100
(“per 100”) or
• Move the decimal point two places to the left
Ex: Convert 27% to a decimal
27% = 27
 100  27.0 =
0.27
Ex: Convert 25% to a decimal
25% = 25
 100  25.0 =
0.25
Ex: Convert 130% to a decimal
130% = 130  100  130.0=
1.30
Ex: Convert 0.5% to a decimal
0.5% = 0.5  100  0.5 = 0.005
1
Ex: Convert % to a decimal
3
• We are starting with a percent written as a
fractional percent
• First convert the fractional percent to a
fraction (drop the % sign and divide by 100)
1
1 1
1
 100  

3
3 100 300
Fraction
form of
the
answer
Ex: cont.
1
300
• Recall: To convert a fraction to
a decimal number, divide the
numerator by the denominator
.0033
300 1.0000
900
1000
900
100
0.003
Converting a Fraction to a %
• To convert a fraction to a percent,
reverse the procedure for converting a
percent to a fraction:
• Multiply by 100 and add the % sign
Ex: Convert ¼ to a percent
1
1
100
 100%  
%
4
4 1
100

%
4
= 25%
Simplify? Yes!
Ex: Convert 1 ½ to a percent
1
3
100
1  100%  
%
2
2 1
300

%
2
= 150%
Simplify? Yes!
Ex: Convert 5/8 to a percent
Simplify?
5
5
100
500
 100%  
%
% Yes!
8
8 1
8
4
 62 % Simplify? Yes!
8
1
 62 % Simplify? No . . .
2
done
Ex: Convert 5/6 to a percent
Simplify?
5
5
100
500
 100%  
%
% Yes!
6
6 1
6
2
 83 % Simplify? Yes!
6
1
 83 % Simplify? No . . .
3
done
Converting a Decimal to a %
• To convert a decimal to a percent,
reverse the procedure for converting a
percent to a decimal:
• Multiply by 100 and add the % sign 
• Move the decimal point two places to the
right
Ex: Convert 0.36 to a %
0.36 100%  0.36 = 36%
Ex: Convert 0.01 to a %
0.01 100%  0.01 = 1%
Ex: Convert 3.19 to a %
3.19 100%  3.19 = 319%
Ex: Convert 0.005 to a %
0.005
 100%
 0.005 = 0.5%
Your Turn to Try a Few
The BASIC PERCENT
EQUATION
• The Basic Percent Equation is given by
Percent x Base = Amount
• The Percent has the percent sign %
• The Base always follows the word “of”
• The other number is the Amount
Ex: 5% of 120 is what?
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals.
Percent = 5%
Base = 120 (follows “of”)
Amount = Unknown “what”  a
• Translate the English statement to the Basic
Percent Equation:
5% x 120 = a
Ex: Cont.
5% of 120 is what?
• Now solve the mathematical equation:
5% x 120 = a
Rewrite the % in working form
0.05 x 120 = a
Perform the math operation
6.00 = a
Therefore, 5% of 120 is 6.
Ex: What is 6.3% of 150?
Identify the three components (remember, the base
always follows “of”, the multiplication, and the equals.
Percent = 6.3%
Base = 150 (follows “of”)
Amount = Unknown “what”  a
• Translate the English statement to the
Basic Percent Equation:
a = 6.3% x 150
Ex: Cont. What is 6.3% of 150?
• Now solve the mathematical equation:
a = 6.3% x 150
Rewrite the % in working form
a = .063 x 150
Perform the math operation
a = 9.45
Therefore, 9.45 is 6.3% of 150.
Ex: 5% of what is 28?
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals.
Percent = 5%
Base = Unknown “what”  b (follows “of”)
Amount = 28
• Translate the English statement to the Basic
Percent Equation:
5% x b = 28
Ex: Cont. 5% of what is 28?
• Now solve the mathematical equation:
5% x b = 28
Rewrite the % in working form
0.05 x b = 28
Solve the equation by
dividing both sides by 0.05
or multiply by 100/5
100/5 x 0.05 x b = 100/5 x 28
20 x 0.05 x b = 20 x 28
b = 560
Therefore, 5% of 560 is 28.
Ex: What % of 32 is 20?
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals.
Percent = Unknown “what”  p
Base = 32 (follows “of”)
Amount = 20
• Translate the English statement to the Basic
Percent Equation: p x 32 = 20
Ex: Cont. What % of 32 is 20?
• Now solve the mathematical equation:
p x 32 = 20
Solve the equation by
dividing both sides by 32
p = 0.625
This is the decimal form of the
percent. Rewrite using the % sign
p = 0.625 = 62.5%
Therefore, 62.5% of 32 is 20.
Ex: The human body contains
206 bones. The fingers and the
toes contain a total of 56 small
bones, or phalanges. What
percent of the bones of the
body are phalanges?
Find the sentence that will be your
equation (percent, base, amount, of, “is”)
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals: What percent
of the bones of the body are phalanges?
Percent = Unknown “what”  p
Base = Bones of the body (follows “of”)
Amount = phalanges
Multiplication “of”
Equals “is”
• Write a hybrid sentence – half in math, half in
English: p x bones of the body = phalanges
Translate the hybrid sentence into the Basic Percent Equation
The human body contains 206 bones. The fingers and the toes contain a total of 56
small bones, or phalanges. p x bones of the body = phalanges
p x 206 = 56
• Now solve the mathematical equation:
p x 206 = 56
Solve the equation by
dividing both sides by 206
p = 0.2718 . . . This is the decimal form of the
percent. Rewrite using the % sign
p = 0.2718 . . . = 27.2%
Therefore, about 27.2% of bones are phalanges.
Ex: The new 8-mile nature trail
is 125% of the length of the
original trail.
How long was the original trail?
Find the sentence that will be your
equation (percent, base, amount, of, “is”)
• Identify the three components (remember, the
base always follows “of”, the multiplication, and the
equals: The new 8-mile nature trail is 125% of the
length of the original trail.
Percent = 125%
Base = Original trail length = b (follows “of”)
Amount = New 8-mile trail
Multiplication “of”
Equals “is”
• Write a hybrid sentence – half in math, half in English:
125% x original trail = new trail
• Translate the hybrid sentence into the Basic
Percent Equation 125% x original trail = new trail
125% x b = 8
• Now solve the mathematical equation:
Solve the equation by dividing both
sides by 1.25 or multiply by 100/125
100/125 x 1.25 x b = 100/125 x 8
1.25 x b = 8
4/5 x 1.25 x b = 4/5 x 8
b = 6.4
32/5 = 6.4
Therefore, the original trail was 6.4 miles.
Ex: A medical supply company
charges 5% of the order total as
a shipping and handling charge.
If the shipping and handling
charge is $38.75, what was the
cost of the order?
Find the sentence that will be your
equation (percent, base, amount, of, “is”)
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals: 5% of the order
total as a shipping and handling charge.
Percent = 5%
Base = Order total = b (follows “of”)
Amount = S&H charge
Multiplication “of”
Equals “is”
• Write a hybrid sentence – half in math, half in
English: 5% x order total = S & H
• Translate the hybrid sentence into the Basic
Percent Equation
5% x order total = S & H
5% x b = 38.75
• Now solve the mathematical equation:
0.05 x b = 38.75 Solve the equation by dividing both
sides by 0.05 or multiply by 100/5
100/5 x 0.05 x b = 100/5 x 38.75
20 x 0.05 x b = 20 x 38.75
b = 775
Therefore, the cost of the order was $775.00.
More Practice:
Ex: 26.1% of the 364 patients admitted
in an emergency room are admitted
due to an auto accident injury.
How many patients are admitted
due to an auto accident injury?
Find the sentence that will be your equation
(percent, base, amount, of, “is”)
• Identify the three components (remember, the base
always follows “of”, the multiplication, and the equals:
26.1% of the 364 patients admitted in an emergency room are admitted due
to an auto accident injury.
Percent = 26.1%
Base = Admitted patients (follows “of”)
Amount = Admitted due to auto accident = a
Multiplication “of”
Equals “is”
• Write a hybrid sentence – half in math, half in
English: 26.1% x admitted patients = admitted due
to auto accident
• Translate the hybrid sentence into the Basic Percent Equation
26.1% of the 364 patients admitted in an emergency room are admitted due to
an auto accident injury.
26.1% x admitted patients = admitted due to auto accident
26.1% x 364 = a
• Now solve the mathematical equation:
.261 x 364 = a
95.004 = a
Solve the equation by
multiplying
Therefore, 95 patients were admitted
due to an auto accident injury.