GED Mathematical Reasoning: Understanding Percentages

  • The word “percent” means “parts per 100.” So percent is another to represent part of a whole and here’s the symbol we use to denote percent “%”.
  • To transform a percent into a decimal, move the decimal point two places TO THE LEFT. If no decimal point is showing, assume it falls after the right-most digit. This makes sense since percent means “parts per 100” and the word “per” implies division. So when we move the decimal point two places to the left, behind the scenes we’re just dividing the number in the percent by 100.
  • How do I change a fraction into a decimal  (which can then be changed into a percent)? The answer is: Divide the numerator by the denominator.

 

Example 1

What percent of the large square is shaded?

percent1

 

Notice that the large square is divided into 100 equal parts. So to determine the percent of the square that’s shaded, we’ll count the number of shaded parts. 96 out of the 100 parts are shaded; therefore, we can say that “96 parts per 100” are shaded.

What if we wanted to state the percent of the large square that’s NOT shaded? Well, since there are FOUR “parts per 100” that are NOT shaded, that would be 4%.

Notice that the shaded parts combined with the UNshaded parts represent the entire square. And when we add the 96% that’s shaded and the 4% percent that’s NOT shaded, the result is 100%.

For another quick illustration, consider a one dollar bill. One dollar can be divided into 100 equal parts using pennies, since 100 pennies equals one dollar.

1 dollar = 100 pennies

What percent of one dollar does a dime represent?

1 dime = 10 pennies

Well, a dime is equal to ten pennies, which means it represents ten “parts per 100.” So the answer is 10%.

Since we’re talking about money and money is represented using decimals, it may not surprise you to learn that percents and decimals are closely related. In fact, percents are closely related to decimals AND fractions. And when calculating with a percent, we actually need to change the percent into a decimal or fraction.

 

Example 2

How is 45.3% written as a decimal? 

 

To write 45.3% as a decimal, we’ll move the decimal point two places to the left. The result is 0.453. Recall that percent means “parts per 100” and the word “per” implies division. So when we move the decimal point two places to the left, behind the scenes we’re just dividing the number in the percent by 100.

45.3\% = \frac{45.3}{100} = 0.453

 

Example 3

How is 25% written as a fraction in lowest terms?

 

Because “percent” means “parts per 100,” we can read 25% as “25 parts per 100.”

As we just discussed, “per” implies division so “25 parts per 100” can be written in fraction form as \frac{25}{100}. To write \frac{25}{100} in lowest terms, we will divide the numerator and denominator by a common factor of 25, which leads us to the result \frac{1}{4}.

math 159

How do I change a fraction into a decimal  (which can then be changed into a percent)? The answer is: Divide the numerator by the denominator. As an example, let’s change \frac{3}{4} into a decimal.

The easiest way to do this is using a calculator. Simply press 3, then the division key, then 4. The result is 0.75. From there, you can change the decimal into a percent by moving the decimal point two places to the right and adding the percent sign, which results in 75%.

 

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