PERCENT CONVERTING A PERCENT TO A FRACTION

[Pages:3]PERCENT

PERCENT Percent means "per hundred."

50% = 0.50, 100% = 1.00, 150% = 1.50, 200% = 2.00, etc.

CONVERTING A PERCENT TO A FRACTION Drop the percent symbol, and write the percent as the numerator of a fraction that has a denominator of 100. Then reduce the fraction, if possible.

% 0.01 1 100

P% = P x 0.01 = P 1 P 100 100

CONVERTING A FRACTION TO A PERCENT

P One method is to set the fraction equal to 100 , solve the percent proportion for P, and then write the answer as P%.

Another method is to multiply both numerator and denominator by a number that makes the new denominator 100 (ie. building fractions).

A third method is to convert the fraction to a decimal and then convert the decimal to a percent (which we will see next).

CONVERTING A DECIMAL TO A PERCENT Move the decimal place two places to the right, and attach the percent symbol(%) to the number.

CONVERTING A PERCENT TO A DECIMAL Move the decimal two places to the left, and remove the percent symbol.

THE PERCENT PROPORTION

A= P The percent proportion is B 100 , where

P represents the number with the percent symbol(%) or with the word percent; B represents the whole amount, or the base; it usually follows the expression "percent of"; A represents the part of the whole (or the amount) that we're concerned with.

THE THREE TYPES OF PERCENT PROBLEMS 1. Finding a percent of a number (solving for A).

"What is P% of B?" 2. Finding what percent one number is of another (solving for P).

"A is what percent of B?" 3. Finding a number when a percent of it is given (solving for B).

"A is P% of what number?"

FINDING A FRACTIONAL PART OF A NUMBER 1. If the fractional part is expressed as a fraction, multiply the fraction times the number. 2. If the fractional part is expressed as a decimal, multiply the decimal times the number. 3a. If the fractional part is expressed as a percent, change the percent to a fraction or decimal then multiply. 3b. If the fractional part is expressed as a percent, you can use the percent proportion and solve for A.

SOLVING APPLIED PROBLEMS THAT INVOLVE PERCENT Read and study the problem carefully, and decide which of THE THREE TYPES OF PERCENT PROBLEMS it matches. Then solve.

PERCENT INCREASE OR DECREASE For percent increase (or decrease) problems, in the percent proportion

P is the percent of increase (or decrease), A is the amount of increase (or decrease), and B is the original amount.

AMOUNT OF INCREASE (OR MARKUP) 1. We can first find the amount of the increase (if the markup is P%, the amount of the markup is P% of the original amount) and then add this amount to the original amount.

2. We can add the percent of the increase to 100% and then find that percent of the original amount.

Ex: You buy a shirt that costs $20. Your "markup" will be the sales tax of 6.5% that you have to pay. Method 1: First, find 6.5% of $20 --> (0.065)($20) = $1.30 Now, add this amount to the original amount. --> $20 + $1.30 = $21.30

Method 2: First, add the percent increase to 100% --> 100% + 6.5% = 106.5% Now, find this "new" percent of the original amount --> (1.065)($20) = $21.30

AMOUNT OF DECREASE (OR DISCOUNT) 1. We can first find the amount of the decrease (if the discount is P%, the amount of the discount is P% of the original amount) and then subtract this amount to the original amount.

2. We can subtract the percent of the decrease from 100% and then find that percent of the original amount.

Ex: You buy a shirt with an original cost of $20 at a "15% Off" sale. Method 1: First, find 15% of $20. --> (0.15)($20) = $3.00 Now, subtract this amount from the original amount. --> $20 - $3.00 = $17.00

Method 2: First, subtract the percent decrease from 100%. --> 100% - 15% = 85% Now, find this "new" percent of the original amount. --> (0.85)($20) = $17.00

REAL LIFE EXAMPLE Ex: You work at Orange Park mall where sales tax is 7%. Since you work at the mall, you get a 10% discount. You buy $125 (ticket price) worth of "stuff." How much did you PAY (SPEND)?

First, take off your discount. --> (0.90)($125) = $112.50 Now, add your sales tax. --> (1.07)($112.50) = $120.375 = $120.38

Notice, this is equal to ($125)(0.90)(1.07), and (0.90)(1.07) = 0.963 = 96.3%. Therefore, your 10% discount equates to you PAYING (SPENDING) 3.7% off the ticket price. Not, 3% =10% - 7%, which you might have thought.

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