Pre-Algebra: Percentages

1.
$$135\%+15\%$$
Solution
2.
$$\frac{24\%}{4}$$
Solution
3.
$$0.25\%\times 2$$
Solution
4.
$$5\%\times 7\%+1.5\%$$
Solution
5.
$$8\%+.5\%$$
Solution

Percentages - Introduction

Percentages are everywhere — they’re used in surveys, sales tax and to predict the chance of rainy days. But what is a percentage? How do you calculate percentages, and how do you convert percentages into decimals when the need arises? Let’s take a look.

What Is a Percentage?

Before we can learn to easily convert percentages, it’s worth breaking down exactly what a percentage is.
Start by looking at the word “percent”. Split it up and it is “per cent” — the cent here means century, but it’s also like the number of “cents” in a dollar: 100. Whenever you write a percentage, what it really means is “X per 100” — so 40 percent would be 40 per 100, or like saying that something happens 40 times out of every 100.

Finding Percentages

Now let’s look at finding percentages — how do you easily calculate percentages or deal with them if they appear in equations?
Let's start with an example. If you need to find 10 percent of a number, since that means one tenth of the number, you can simply divide the number by 10.
Example: Find
$$10$$
percent of
$$50$$
.
Solution: Divide
$$50$$
by
$$10$$
, which is
$$5$$
. Therefore,
$$5$$
is
$$10$$
percent of
$$50$$
.
Let's try a more difficult example.
Example: Find
$$56$$
percent of
$$25$$
.
Solution: We know that
$$25$$
percent is the same as
$$\frac{25}{100}$$
, or
$$\frac{1}{4}$$
. This means we just need to divide
$$56$$
by
$$4$$
, which is
$$14$$
.

Converting Percentages to Decimals

Sometimes it is necessary to convert a percentage to a decimal. This is helpful if you come across percentages inside a math expression, such as
$$110\%+.12$$
. For the percentage term, simply move the decimal two places to the left, and you can simplify the problem.
Example: Simplify the expression
$$110\%+.12$$
Solution:
$$110\%+.12$$
becomes
$$1.10+.12$$
, which yields
$$1.22$$

What's Next

At Cymath, our pre-algebra problems and solutions are designed to help students become confident problem solvers. Need a full solution for percentage problem, use Cymath as a percentage calculator. Want to get more practice? Tackle some of our tougher practice problems. You can also upgrade to Cymath Plus and enjoy additional explanations and steps to make learning even more effective.