% and the BASIC PERCENT EQUATION

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and the BASIC PERCENT EQUATION
MSJC Menifee Valley Campus Math Center Workshop
Series Janice Levasseur
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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

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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
No . . . done
Simplify ?
27
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Ex Convert 25 to a fraction
25
Simplify?
YES!
No . . . done
Simplify?
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Ex Convert 130 to a fraction
Yes! Improper Fraction
130
Simplify?
Simplify?
Yes!
Simplify?
No . . . done
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Ex Convert to a fraction
Divide fractions
Simplify?
No . . . done
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Ex Convert 0.5 to a fraction
Divide decimals? Decimal ? Fraction
0.5
No . . . done
Simplify?
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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

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Ex Convert 27 to a decimal
27
? 27.0
0.27
27 100
Ex Convert 25 to a decimal
25
25 100
? 25.0
0.25
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Ex Convert 130 to a decimal
130
? 130.0
1.30
130 100
Ex Convert 0.5 to a decimal
0.5
0.5 100
? 0.5
0.005
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Ex Convert to a decimal

• 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)

Fraction form of the answer
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Ex cont.

• 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
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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

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Ex Convert ¼ to a percent
Simplify?
Yes!
25
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Ex Convert 1 ½ to a percent
Simplify?
Yes!
150
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Ex Convert 5/8 to a percent
Simplify?
Yes!
Simplify?
Yes!
No . . . done
Simplify?
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Ex Convert 5/6 to a percent
Simplify?
Yes!
Simplify?
Yes!
No . . . done
Simplify?
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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

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Ex Convert 0.36 to a
0.36
? 0.36
36
Ex Convert 0.01 to a
0.01
? 0.01
1
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Ex Convert 3.19 to a
3.19
? 3.19
319
Ex Convert 0.005 to a
0.005
? 0.005
0.5
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• Your Turn to Try a Few

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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

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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
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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.
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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
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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.
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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
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Ex Cont. 5 of what is 28?

• Now solve the mathematical equation

Rewrite the in working form
5 x b 28
Solve the equation by dividing both sides by
0.05 or multiply by 100/5
0.05 x b 28
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.
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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
32
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.
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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)
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• 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
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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

Solve the equation by dividing both sides by 206
p x 206 56
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.
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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)
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• 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
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• 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
1.25 x b 8
100/125 x 1.25 x b 100/125 x 8
4/5 x 1.25 x b 4/5 x 8
32/5 6.4
b 6.4
Therefore, the original trail was 6.4 miles.
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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)
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• 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
SH charge
Multiplication of
Equals is

• Write a hybrid sentence half in math, half in
  English

5 x order total S H
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• 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

Solve the equation by dividing both sides by 0.05
or multiply by 100/5
0.05 x b 38.75
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.
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More PracticeEx 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)
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• 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
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• 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
Solve the equation by multiplying
95.004 a
Therefore, 95 patients were admitted due to an
auto accident injury.