"Percent" means "hundredths."
If you just remember that, you'll never have to move a decimal point again.
Percent to Fraction to Decimal
1. Say the name of the number you have. Do not use words like "percent" or "point."
2. Write the number in its new form. That's it!
Examples:
a. 37% reads "thirty-seven hundredths." Change to 37/100 or .37 (all three forms have the same name).
b. .25 reads "twenty-five hundredths." Change to 25/100 (reduces to 1/4) or 25%.
c. 9/100 reads "nine hundredths." Change to .09 or 9%.
d. 7/10 reads "seven tenths." Change to hundredths by multiplying both the numerator and denominator by 10. The result of 70/100 reads "seventy hundredths." Change to 70% or .70 (same as .7).
e. 122/200 reads "one-hundred-twenty-two two-hundredths." Change to hundredths by dividing by both the numerator and denominator by two. The result of 61/100 reads "sixty-one hundredths." Change to .61 or 61%.
f. 3/8 reads "three eighths." Not directly scalable to hundredths, so divide 3 by 8. Change the decimal result of .375 to percent by noting that the 7 is in the hundredths place. Answer is 37.5%
g. 1/3 reads "one third." Not directly scalable to hundredths, so divide two by three. Change the decimal result of .333... to percent by noting that the second three is in the hundredths place. Answer is 33.333...% (round where appropriate).
h. 5/6% reads "five-sixths hundredths." Kind of awkward, so instead of using a complex fraction, change "five-sixths hundredths" to "five six-hundredths" by adding two zeroes to the denominator. The result of 5/600 can be reduced to 1/120 or divided to produce .008333... (round as appropriate).
i. 7 2/3% reads "seven and two-thirds hundredths." Once again, rather awkward, so change to the improper fraction 23/3% (7x3+2 for the numerator). "Twenty-three-thirds hundredths" changes to "twenty-three three-hundredths" by adding two zeroes to the denominator. The result of 23/300 can be divided to produce the decimal .07666... (round as appropriate).
Type 1: Finding the percentage
What is 25% of 84?
N = .25 x 84 25 84
N = 21 or N = --- x --
100 1
N = 21
Or note that only the "of" is between the numbers. Just multiply .25 x 84 to get 21.
"25% of 84 is what?" produces the same answer.
On many calculators, the rules for percent are built in. Type "84x25%" (no equal sign). If the screen shows "21," you are probably all set for Type 2 and Type 3, as well.
"Percentage" is the amount that you get, not the rate (that's Type 2).
Type 2: Finding the rate
2 is what percent of 12.5?
The clue is "what percent."
2 = N% x 12.5 2 N 12.5
2 / 12.5 = N% or - = --- x ----
.16 = N% 1 100 1
16% = N
2 x 100 / 12.5 = N
(/ means divide)
16% = N
Or note that the equal sign is between the numbers. You cannot multiply. Divide 2 by 12.5 and multiply by 100 since you are looking for a percent.
"What percent of 12.5 is 2?" produces the same answer. The size and position of the numbers relative to each other is not important. The key is which number is closer to "is" and to "of." (If both numbers are equally close to one keyword, the other will break the tie.) The mnemonic (memory aid) "Is over Of" can be helpful (see Hints).
On a percent-compatible calculator, type "2/12.5%" (no equal sign). 16 in the display means 16%.
The answer is a rate, not a percentage (that's Type 1).
Type 3: Finding the basis
12 is 3% of what number?
The word "number" is optional. It just provides a reminder that the answer is not a percent.
12 = .03 x N 12 3
12 / .03 = N or -- = --- x N
400 = N 1 100
12 x 100 / 3 = N
400 = N
On a percent-compatible calculator, type "12/3%" (no equal sign). 400 in the display is an amount, not a rate (that's Type 2). The calculator doesn't know the difference, but the rules work out the same way for both Type 2 and Type 3).
Fraction examples:
Type 1:
3 1
What is 5 - % of 7 - ?
8 2
First, change both mixed fractions to improper fractions.
43 15
5 x 8 + 3 = -- %, 7 x 2 + 1 = --
8 2
Second, convert the percent (rate) to hundredths (add two zeroes to the denominator).43 43 -- % = --- 8 800Third, cross-cancel (if possible), multiply and simplify (if necessary).
43 15 43 3 129 --- x -- = --- x - = --- 800 2 160 2 320Hints:
Is Inside First Keep as Is -- = ------- for manual calculations or ----- for calculators or ---------- for fractions Of Outside Last Flip Over
For Type 3 divisions, always put the converted rate (percent outside the division box, or last in a fraction problem or calculator.
Interest: ________ _________ _________
/ x \/ x \/ = \
Time on Compounding Principal Rate of Interest Balance
Deposit Period (Initial Interest (Paid) (New
Deposit) /\ Principal)
\ + / \ = /
Alternate form ______________
(for compatibility / x \
with rest of topics): / \
Balance Principal Interest \Rate of
(New (Initial (Paid) /Interest
Principal) Deposit / \ = /
\ = /\ + /
Discount: ___________________ ___________________
/ x \/ = \
/ _______ ____________________ \
/ / x \/ = \ \
List Price Rate of % Paid Discount Net Price
(Original Discount + / (Saved) (Sale Price)
\ \ =100% / /\ /
\ = / \ + /
Commission: ____________________ ___________________
/ x \/ = \
/ ________ ____________________ \
/ / x \/ = \ \
Sales Rate of % to Commission Net
\ Commission + Company /\ Proceeds
\ \ =100% / / \ /
\ = / \ + /
Profit: ____________________ ___________________
/ x \/ = \
/ ________ ____________________ \
/ / x \/ = \ \
Sales Rate of Rate of Cost Profit Rate of
\ Cost Profit /\ (Markup) Markup / /
\ \ + (Rate of / \ / \ on Cost / \ / /
\ \=100%/ Markup / \ + / \ = /|
\ on Sales) / \ /
\ = / \ x /
Generic: ______________________ ____________________
/ x \/ = \
/ _______ ________________________ \
/ / x \/ = \ \
Total Rate + % Remainder Percentage Remainder % Ratio
\ \ =100% / /\ / \ /|
\ = / \ + / \ = / /
\ x /
If you've learned the patterns, you don't really need the formulas. But here they are, anyway, just for reference. The formulas are laid out in the same order as they would be typed on a calculator. The techniques for using a percent-compatible calculator, as mentioned above, apply here. The primary formulas (the ones that are essential to the pattern) are marked with an asterisk (*). The percent formulas that involve multiplication or division are marked according to type, as shown above.
Interest:
* (1) Principal x Rate x Compounding Period = Interest
(2) Interest / Principle / Compounding Period = Rate
(3) Interest / Rate / Compounding Period = Principal
Interest / Principal / Rate = Compounding Period
* Principal + Interest = Balance
Balance - Principal = Interest
Balance - Interest = Principal
Discount:
* (1) List x Rate = Discount
(2) Discount / List = Rate
(3) Discount / Rate = List
(1) List x % Paid = Net
(2) Net / List = % Paid
(3) Net / % Paid = List
* Discount + Net = List
List - Discount = Net
List - Net = Discount
* Rate + % Paid = 100%
100% - Rate = % Paid
100% - % Paid = Rate
Commission:
* (1) Sales x Rate = Commission
(2) Commission / Sales = Rate
(3) Commission / Rate = Sales
(1) Sales x % to Company = Net Proceeds
(2) Net Proceeds / Sales = % to Company
(3) Net Proceeds / % to Company = Sales
* Commission + Net Proceeds = Sales
Sales - Commission = Net Proceeds
Sales - Net Proceeds = Commission
Profit and Loss:
* (1) Sales x Rate of Cost = Cost
(2) Cost / Sales = Rate of Cost
(3) Cost / Rate of Cost = Sales
(1) Sales x Rate of Profit = Profit
(2) Profit / Sales = Rate of Profit
(3) Profit / Rate of Profit = Sales
* Cost + Profit = Sales
Sales - Cost = Profit
Sales - Profit = Cost
* Rate of Cost + Rate of Profit = 100%
100% - Rate of Cost = Rate of Profit
100% - Rate of Profit = Rate of Cost
* (1) Cost x Rate of Markup on Cost = Profit
(2) Profit / Cost = Rate of Markup on Cost
(3) Profit / Rate of Markup on Cost = Cost
Generic:
* (1) Total x Rate = Percentage
(2) Percentage / Total = Rate
(3) Percentage / Rate = Total
(1) Total x % Remainder = Remainder
(2) Remainder / Total = % Remainder
(3) Remainder / % Remainder = Total
* Percentage + Remainder = Total
Total - Percentage = Remainder
Total - Remainder = Percentage
* Rate + % Remainder = 100%
100% - Rate = % Remainder
100% - % Remainder = Rate
* (1) Percentage x % Ratio = Remainder
(2) Remainder / Percentage = % Ratio
(3) Remainder / % Ratio = Percentage
Last updated 6/2/97 - 2/14/2003.