% and the BASIC PERCENT

EQUATION

MSJC ~ Menifee Valley Campus

Math Center Workshop SeriesJanice 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%10027

Simplify ? No . . . done

Ex: Convert 25% to a fraction

25%10025

Simplify? YES!

41 Simplify? No . . .

done

Ex: Convert 130% to a fraction130%

100130

100301

1031

Simplify? Yes! Improper Fraction

Simplify? Yes!

Simplify? No . . . done

Ex: Convert % to a fraction31

10031

10031

1100

31

1001

31

3001 Simplify? No . . .

done

Divide fractions

%31

Ex: Convert 0.5% to a fraction0.5%

10050. Divide decimals?

Decimal Fraction

10021

1100

21

1001

21

2001

Simplify? No . . . done

Your Turn to Try a Few

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

Ex: Convert % to a decimal31

• 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)

10031

1001

31

3001

Fraction form of the answer

Ex: cont. • Recall: To convert a fraction to a decimal number, divide the numerator by the denominator

3001 .0033

300 1.0000

900

1000

900

100

0.003

Your Turn to Try a Few

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

41 %100 %

1100

41

%4100 Simplify? Yes!

= 25%

Ex: Convert 1 ½ to a percent

211 %100 %

1100

23

%2300 Simplify? Yes!

= 150%

Ex: Convert 5/8 to a percent

85 %100 %

1100

85 %

8500

Simplify?

Yes!

Simplify? Yes!

Simplify? No . . . done

%8462

%2162

Ex: Convert 5/6 to a percent

65 %100 %

1100

65 %

6500

Simplify?

Yes!

Simplify? Yes!

Simplify? No . . . done

%6283

%3183

Your Turn to Try a Few

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 0.01 = 1%%100

Ex: Convert 3.19 to a %3.19 %100 3.19 = 319%

Ex: Convert 0.005 to a %

0.005 0.005 = 0.5%%100

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 =Base =Amount =

• Translate the English statement to the Basic Percent Equation: 5% x 120 = a

5%120 (follows “of”)

Unknown “what” a

Ex: Cont. 5% of 120 is what?• Now solve the mathematical equation:

5% x 120 = a

0.05 x 120 = a

6.00 = a

Perform the math operation

Rewrite the % in working form

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 =Base =Amount =

• Translate the English statement to the Basic Percent Equation: a = 6.3% x 150

6.3%150 (follows “of”)

Unknown “what” a

Ex: Cont. What is 6.3% of 150?• Now solve the mathematical equation:

a = 6.3% x 150

a = .063 x 150

a = 9.45

Perform the math operation

Rewrite the % in working form

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 =Base =Amount =

• Translate the English statement to the Basic Percent Equation: 5% x b = 28

5%Unknown “what” b (follows “of”)

28

Ex: Cont. 5% of what is 28?• Now solve the mathematical equation:

5% x b = 28

0.05 x b = 28

b = 560

Solve the equation by dividing both sides by 0.05or multiply by 100/5

Rewrite the % in working form

Therefore, 5% of 560 is 28.

100/5 x 0.05 x b = 100/5 x 2820 x 0.05 x b = 20 x 28

Ex: What % of 32 is 20?• Identify the three components (remember, the base always follows “of”, the multiplication, and the equals.

Percent =Base =Amount =• Translate the English statement to the Basic Percent Equation: p x 32 = 20

Unknown “what” p32 (follows “of”)

20

Ex: Cont. What % of 32 is 20?• Now solve the mathematical equation:

p x 32 = 20

p = 0.625

Solve the equation by dividing both sides by 32

Therefore, 62.5% of 32 is 20.

This is the decimal form of the percent. Rewrite using the % sign

p = 0.625 = 62.5%

Your Turn to Try a Few

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 =Base =Amount =

• Write a hybrid sentence – half in math, half in English: p x bones of the body = phalanges

Unknown “what” pBones of the body (follows “of”)

phalangesMultiplication “of” Equals “is”

• Now solve the mathematical equation:p x 206 = 56

p = 0.2718 . . .

Solve the equation by dividing both sides by 206

This is the decimal form of the percent. Rewrite using the % sign

p = 0.2718 . . . = 27.2%

Translate the hybrid sentence into the Basic Percent EquationThe human body contains 206 bones. The fingers and the toes contain a total of 56 small bones, or phalanges.

p x 206 = 56p x bones of the body = phalanges

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 =Base =Amount =

• Write a hybrid sentence – half in math, half in English:125% x original trail = new trail

125%Original trail length = b (follows “of”)

New 8-mile trailMultiplication “of” Equals “is”

• Now solve the mathematical equation:1.25 x b = 8

b = 6.4

Solve the equation by dividing both sides by 1.25 or multiply by 100/125

• Translate the hybrid sentence into the Basic Percent Equation

125% x b = 8

125% x original trail = new trail

Therefore, the original trail was 6.4 miles.

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

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 =Base =Amount =

• Write a hybrid sentence – half in math, half in English: 5% x order total = S & H

5%Order total = b (follows “of”)

S&H chargeMultiplication “of” Equals “is”

• Now solve the mathematical equation:

0.05 x b = 38.75

b = 775

Solve the equation by dividing both sides by 0.05 or multiply by 100/5

• Translate the hybrid sentence into the Basic Percent Equation

5% x b = 38.75

5% x order total = S & H

Therefore, the cost of the order was $775.00.

100/5 x 0.05 x b = 100/5 x 38.75 20 x 0.05 x b = 20 x 38.75

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 =Base =Amount =

• Write a hybrid sentence – half in math, half in English: 26.1% x admitted patients = admitted due

to auto accident

26.1%Admitted patients (follows “of”)

Admitted due to auto accident = a

Multiplication “of” Equals “is”

• Now solve the mathematical equation:.261 x 364 = a

95.004 = a

Solve the equation by multiplying

• 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 364 = a

26.1% x admitted patients = admitted due to auto accident

Therefore, 95 patients were admitted due to an auto accident injury.