Have you ever tried to solve problems involving percents? Take a look at this dilemma.

“You know,” Cameron started to say in study hall. “I think we should shoot for 55 or 60% attendance at football games and not just 50%. I mean think about it, we should all go and support the team. After all, some of us hope to play football at the high school someday!”

The other four kids at the table looked up from their work to discuss the suggestion. Carla was the first to speak.

“I think that’s a good point. I mean if we attend their games, maybe other middle school kids will do the same thing when we are at the high school.”

“Yes, but some kids need a ride or have other things to do,” Jeremy argued.

“Well I’m not saying everyone. I am saying 55 or 60%,” Cameron said.

“How many is that?” Jeremy asked.

“I can figure it out easy,” Cameron said.

On his paper he wrote these equations:

What is 55% of 380?

What is 60% of 380?

**Before Cameron solves these problems, let’s look at what he wrote. Cameron used the a statement that could be written into a “percent equation”. We can use the percent equation instead of a proportion. The percent equation can be helpful when you look for a percent, a base or a part of the base. Let’s look at how we can use the percent equation before we solve this problem.**

### Guidance

You can use the proportion \begin{align*}\frac{a}{b}=\frac{p}{100}\end{align*} to solve a percent problem. We can also solve percent problems by using an equation. In this Concept, we will use a proportion to create a different kind of equation that will help us solve percent problems differently.

**When we solve the proportion \begin{align*}\frac{a}{b}=\frac{p}{100}\end{align*}, we use cross products to find the missing variable. However, even if we leave it in terms of the variables, we can still use cross multiply.**

\begin{align*}\frac{a}{b} &= \frac{p}{100}\\ 100 a &= pb\\ a &= \frac{pb}{100}\\ a &= .01pb\end{align*}

If we change the percent to a decimal by moving the decimal point two places to the left, then there is no need to multiply \begin{align*}p\end{align*} by .01 as we will have already accounted for the coefficient of .01 by moving the decimal point.

**Okay, let’s go through it again. Look at what we just wrote.**

We wrote the same thing we just didn’t include values. The variables stayed and we multiplied them.

**The key is that if we change the percent to a decimal, then all we have to do is to multiply it by the base and we will be able to figure out the value of \begin{align*}a\end{align*}.**

Take a look at this situation.

**What is 85% of 90?**

To figure this out, first we change the 85% into a decimal. “OF” is a key word meaning multiply, so we multiply the decimal .85 times 90.

\begin{align*}.85 \times 90 = 76.5\end{align*}

**This is our answer.**

*Some of you may find that this is much simpler than using a proportion! Either way is correct just be sure that you know what are looking for with each equation.*

**What is 7% of 900?**

First, let’s change 7% into a decimal.

7% = .07

Next, we multiply it by 900. Notice the key word “of” which means that we multiply.

\begin{align*}900 \times .07 = 63\end{align*}

**Our answer is 63.**

Because percents are all around us in the real – world, you will need to know how to use the percent equation to solve many different types of practical problems. Remember these key words as you work through percent problems.

“Of” means multiply

“what percent” means you are looking for a percent-you will need to convert the decimal to a percent at the end of the problem.

“Is” means equals

“Of what number” means the base is missing-it means you look for the whole.

*Write these key words down in your notebooks.*

#### Example A

What is 22% of 100?

**Solution: 22**

#### Example B

What is 8% of 57?

**Solution: 4.56**

#### Example C

What is 17% of 80?

**Solution: 13.6**

Now let's go back to the dilemma from the beginning of the Concept.

**Now let’s take the two questions and write two equations that we can use to solve those equations.**

**What is 55% of 380? Becomes \begin{align*}x= .55(380)\end{align*}**

**What is 60% of 380? Becomes \begin{align*}x= .60(380)\end{align*}**

**Next, we solve each equation for the part of the whole.**

**55% of 380 = 209 students**

**60% of 380 = 228 students**

**These are our two answers.**

### Vocabulary

- Percent
- a part of a whole out of 100.

### Guided Practice

Here is one for you to try on your own.

What is 19% of 300?

**Solution**

To figure this out, we can use the percent equation.

First, convert the percent to a decimal.

\begin{align*}19\% = .19\end{align*}

Next, multiply.

\begin{align*}.19 \times 300 = 57\end{align*}

**This is our answer.**

### Video Review

### Practice

Directions: Solve each percent problem. You may round your answers to the nearest tenth when necessary.

- How much is 15% of 73?
- What is 70% of 5?
- What is 3% of 4 million?
- What is 18% of 30?
- What is 22% of 56?
- What is 19% of 300?
- What is 21% of 45?
- What is 34% of 250?
- What is 33% of 675?
- What is 3% of 700?
- What is 11% of 955?
- What is 14% of 55?
- What is 37% of 17?
- What is 20% of 9?
- What is 2% of 180?