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### Course: Praxis Core Math > Unit 1

Lesson 2: Number and quantity- Rational number operations | Lesson
- Rational number operations | Worked example
- Ratios and proportions | Lesson
- Ratios and proportions | Worked example
- Percentages | Lesson
- Percentages | Worked example
- Rates | Lesson
- Rates | Worked example
- Naming and ordering numbers | Lesson
- Naming and ordering numbers | Worked example
- Number concepts | Lesson
- Number concepts | Worked example
- Counterexamples | Lesson
- Counterexamples | Worked example
- Pre-algebra word problems | Lesson
- Pre-algebra word problems | Worked example
- Unit reasoning | Lesson
- Unit reasoning | Worked example

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# Percentages | Lesson

## What are percentages?

A $100$ . Percent means parts per hundred.

**percentage**is a ratio whose second term isWe 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 $\mathrm{\%}$ 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 $p\mathrm{\%}$ of $b$ , then:

This equation can be rearranged to show $a$ or $b$ in terms of the other values:

In word problems involving percentages, remember that the sum of all parts of the whole is $100\mathrm{\%}$ . For example, if a teacher has graded $60\mathrm{\%}$ of an assignment, then they have not graded $100-60\mathrm{\%}=40\mathrm{\%}$ of the assignment. $60\mathrm{\%}$ and $40\mathrm{\%}$ are $100\mathrm{\%}$ .

**complementary percentages**: they add up to## 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:

- Find the difference between the initial and final values.
- Divide the difference by the initial value.
- Convert the quotient to a percentage.

We can calculate the percent change, the initial value, or the final value given the other two. To do so, we:

- Write an equation that relates the initial and final values using a percentage.
- Plug in the known values.
- Solve for the unknown quantity.

## Your turn!

## Things to remember

Percent means parts per hundred.

A shortcut for converting percentages to decimals is to remove the $\mathrm{\%}$ symbol and move the decimal point left $2$ places.

If $a$ is $p\mathrm{\%}$ of $b$ , then:

The sum of all parts of the whole is $100\mathrm{\%}$ .

When calculating a percent change from an initial value to a final value:

- Find the difference between the initial and final values.
- Divide the difference by the initial value.
- Convert the quotient to a percentage.

To calculate the percent change, the initial value, or the final value given the other two, we:

- Write an equation that relates the initial and final values using a percentage.
- Plug in the known values.
- Solve for the unknown quantity.

## Want to join the conversation?

- shouldn't the equation be initial - final

- —————— x 100

initial(9 votes) - can some one exsplain this to me(3 votes)
- umm i got something wrong but its right(5 votes)
- 😐no, you got it wrong😐(0 votes)

- why is it so hard(2 votes)
- this thing might be great for my math works at school(1 vote)
- why are you making school SO HARD!(1 vote)
- Why are you making school sooo hard!(1 vote)
- quentin bought shares on the stock exchange worth$3240..over the 10 years the share increased by 400% question(1 vote)
- How do I find Percent of change?(0 votes)
- Can we just simplify this,i literally understand this please help i can't😭!(0 votes)