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A Quick Reminder About Percentages

We truly hope you are familiar with the following percentage formula: (if not, it's good to have you with us.)

% = Fraction X 100

This formula allows us to alternate between fractions and their percent form. Let's take a look at the following example: 

If we decide to put 25 on the % side, we get the following equation:

25% = fraction X 100 

If we divide the equation by 100, we get: 

25/100 = 1/4 = Fraction

Therefore, 25% is merely another way of presenting 1/4. This formula is sometimes elaborated to include the components of a fraction (nominator and denominator), but for our purposes the formula above is satisfactory.

Percentages and decimal numbers

Many people find it easier to calculate percent changes using decimal numbers. Since a percent is actually a fraction, 1% can be written as 0.01. Therefore, increasing a number by 1% means multiplying it by (1+0.01)= 1.01, and decreasing a number by 1% means multiplying it by (1-0.01)=0.99. Thus, a percent increase means multiplying by numbers greater than one, and a percent decrease means multiplying by numbers that are smaller than one.

How to calculate % changes without the calculator's % function

To speed up the calculation process, we shall use a different format of the above formula. From now on, when asked to calculate a percent increase in value, use the following formula:
% = [ (value after change/value before change) - 1 ] X 100

When asked to calculate a decrease in value use this formula and then multiply by (-1), or use the +\- sign in your calculator. Take a look at the following simplified example:
"The price of X was 30 and is now 40. What is the percent difference between the two prices..."

In this case it is clear that we are looking for an increase change, so we are looking for the ratio between 40 and 30, which constitutes the fraction in our formula:

[ (40/30) - 1 ] X 100 = 33.33%

If you feel comfortable with numbers you can always skip the multiplication by 100 to get 0.33, and thus conclude that this represents 33%. Here is another example with a decrease in value:
"The price of X was 40 and is now 30. What is the percent difference between the two prices..."

In this case, the new number has decreased in respect to the original. If we use the same formula, we get a negative number:

[ (30/40) -1 ] X 100 = (- 25)%

This still represents the true absolute value we are looking for, so you can simply multiply by (-1) or use the +\- sign in your calculator to get the correct answer. In theory, we could also switch places in the formula:

% = [1- (value before change/value after change)]X 100

However, this formula can slow down the calculation if we are using the simplest calculator, as it will require us for two steps because a subtraction precedes a multiplication. 

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