Notes: Percent/Decimal/Fraction Conversions

  • To change a percent to a decimal: move the decimal two places to the left and drop the percent sign.
  • To change a percent to a fraction: Put the number over 100, drop the percent sign. Reduce the fraction on the calculator.
  • To change a decimal to a percent: move the decimal two places to the right, add a percent sign.
  • To change a fraction to a percent: First change the fraction to a decimal, then change the decimal to a percent.
  • To change a fraction to a decimal: Divide. (Numeratordenominator).

Percent/Decimal/Fraction Conversions Practice

Leave fractions and mixed numbers is reduced form.

Fraction or Mixed Number / Decimal / Percent
0.9
.88
2.4
34%
235%
4%

Notes on Solving Percents

Formulas:

Examples:

1.)What is 30% of 120?

Set up as a proportion

Cross multiply 100 * x = 120 * 30

100x = 3,600

x = 36

2.)9 is what percent of 45?

Set up as a proportion

Cross Multiply 45 * x = 9 * 100

45x = 900

x = 20

3.)18 is 9% of what number?

Set up as a proportion

Cross Multiply 9 * x = 18 * 100

9x = 1,800

x = 200

4.)Mrs. Brown has 50 students in her math class. If 40% of the students have a calculator, how many students have a calculator?

50 is the total, 40 is the percent

Cross Multiply 100 * x = 40 * 50

100x = 300

x = 2020 students have calculators.

5.) Brittany paid $6.00 in sales tax for a table. The tax rate is 5%. What is the purchase price of the table (before tax)?

$6.00 is the part, 5 is the percent

Set up a proportion.

Cross Multiply5x = 6 * 100

5x = 600

x = 120$120.00 is the purchase price

6.) In a shipment of 2000 auto parts, 120 are found to be defective. What percent are defective?

120 is the part, 2000 is the total

Set up a proportion

Cross Multiply2000x = 120 * 100

2000x = 12000

x = 66% defective

Percent Practice

1. What is 70% of 500?

2. 4 is 80% of what number?

3. 7 is what percent of 28?

4. A mechanic has an income of $350 per week. Twenty percent of the income is deducted for income tax payment, what is the amount of the income tax?

Numeric problem______Answer: ______

5. A fast food company uses 6% of its budget for advertising. If the amount spent on advertising is $480.00, what is the total budget of the fast food company?

Numeric problem______Answer: ______

6. On a test, Alice had 60% of the problems correct. If she did 30 problems correctly, how many questions were on the test?

Numeric problem______Answer: ______

7. There are 180 grams of acid in 900 grams of a solution. What percent of the solution is acid?

Numeric problem______Answer: ______

8. There were 1200 students that took the entrance exam to trade school. If 960 students passed the entrance exam, what percent passed the exam?

Numeric problem______Answer: ______

Notes on Percent Increase and Percent Decrease

When solving percent increase and decrease problems, you will use the formula: .

This is different from “percent of” problems. The notes for “percent of” will include the formulas: and .

EXAMPLES:

1. Find the missing values.

Original Value / New Value / Amount of Change (Difference) / Percent Change
$50 / $60

To find the percent change (either percent increase or percent decrease):

  1. Find the difference between the two values (original and new value).
  2. Put the values into the formula: . Put x in for the unknown value.
  3. If the value went up, it will be a percent increase. If the value went down from the original value, it will be a percent decrease.

$60 - $50 = $10 = difference

Gives:

Now cross-multiply to solve.

50x = $10 * 100

50x = 1000

x = 20

Original Value / New Value / Change (Difference) / Percent Change
$50 / $60 / $10 / 20% increase

2. Find the missing values.

Original Value / New Value / Change (Difference) / Percent Change
$50 / $30

$40 - $30 = $10

40x = 10 * 100

40x = 1000

x = 20

Original Value / New Value / Change (Difference) / Percent Change
$40 / $30 / 10 / 25% decrease
  1. Tom was making $15 per hour. He received a 4% increase. What is his new hourly wage?

We do not know his new pay rate. But the formula does not have a place to plug in “new value,” so assign x as the difference.

x = difference

Cross multiply.

100x = 15 * 4

100x = 60

x = $0.60 = differenceThis is Tom’s pay raise.

So, how much is he making now (the new value)?

$15 + $.60 = $15.60 per hour

Practice Percent Increase/Decrease

Find the missing values.

Original Value / New Value / Amount of Change / Percent Change
1. $60 / $90
2. $90 / $63
3. $50 / $40
4. $40 / $50

Answers

Original Value / New Value / Amount of Change / Percent Change
1. $60 / $90 / 90 – 60 = 30 /
2. $90 / $63 / 90 – 63 = 27 /
3. $50 / $40 / 50 – 40 = 10 /
4. $40 / $50 / 50 – 40 = 10 /