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Course: Praxis Core Math > Unit 1

Lesson 2: Number and quantity
Test prep
Praxis Core Math
Lessons
Number and quantity
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Percentages | Lesson

Google Classroom

What are percentages?

A percentage is a ratio whose second term is 100. Percent means parts per hundred.
p% is equivalent to:
  • p:100
  • p100
We can use equivalent forms of percentages interchangeably and choose the one(s) that best suit our purpose. Typically, the fraction and decimal equivalents of percentages are best suited for calculations.
A shortcut for converting percentages to decimals is to remove the % symbol and move the decimal point 2 places to the left.
Percentages are useful because we tend to have a better intuitive understanding of something out of 100 than fractions and decimals. That's good because in the real world, we're surrounded by percent calculations: a waiter's tip, income tax, results of surveys, etc.

What skills are tested?

  • Using percent relationships to calculate percentages and values
  • Solving word problems involving percentages
  • Solving word problems involving percent increases and decreases

How do we calculate percentages?

For two numbers in a percent relationship, we can find either number or the percentage given the other two values. If a is p% of b, then:
p=ab×100
This equation can be rearranged to show a or b in terms of the other values:
a=p100×bb=a(p100)=100×ap
In word problems involving percentages, remember that the sum of all parts of the whole is 100%. For example, if a teacher has graded 60% of an assignment, then they have not graded 100−60%=40% of the assignment. 60% and 40% are complementary percentages: they add up to 100%.

How do we calculate percent changes?

We're often asked to calculate by what percent a quantity changes relative to an initial value: the percent discount on jeans, the percent increase in the amount of potato chips in a bag, etc. When calculating a percent change from an initial value to a final value:
  1. Find the difference between the initial and final values.
  2. Divide the difference by the initial value.
  3. Convert the quotient to a percentage.
%change=final−initialinitial×100
We can calculate the percent change, the initial value, or the final value given the other two. To do so, we:
  1. Write an equation that relates the initial and final values using a percentage.
  2. Plug in the known values.
  3. Solve for the unknown quantity.

Your turn!

TRY: TAKING A PERCENTAGE
What is 30% of 40 ?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

TRY: CALCULATING A PERCENTAGE
What percent of 20 is 12 ?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
%

TRY: USING COMPLEMENTARY PERCENTAGES
Tara has read 95% of the books she owns. If Tara owns 160 books, how many of her books has she not read?
Choose 1 answer:

TRY: CALCULATING PERCENT INCREASE
The price of a particular model of headphones was $7 in 2016. In 2018, the price of the same model of headphones was $10. What is the approximate percent increase in the price of the headphones?
Choose 1 answer:

Things to remember

Percent means parts per hundred.
p%=p100
A shortcut for converting percentages to decimals is to remove the % symbol and move the decimal point left 2 places.
If a is p% of b, then:
p=ab×100a=p100×bb=a(p100)=100×ap
The sum of all parts of the whole is 100%.
When calculating a percent change from an initial value to a final value:
  1. Find the difference between the initial and final values.
  2. Divide the difference by the initial value.
  3. Convert the quotient to a percentage.
%change=final−initialinitial×100
To calculate the percent change, the initial value, or the final value given the other two, we:
  1. Write an equation that relates the initial and final values using a percentage.
  2. Plug in the known values.
  3. Solve for the unknown quantity.

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