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# Percent of a Number

## Use multiplication and proportions to find the percent of a number.

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MCC6.RP.3c - Percent of a Number

Remember Sam and the floor? Well, after finishing her sweeping, Sam had to mop the floor. Here is what she discovered about cleaning fluid.

Sam is surprised that it takes so much cleaning fluid to mop the floor. Now it is a big floor, but after Sam finishes mopping, she discovers that she has used 25% of the 20 gallons of fluid.

How many gallons of fluid are left?

To answer this question, you will need to know how to find the percent of a number.

Pay attention to this Concept and you will know how to calculate the answer at the end of it.

### Guidance

Percents are found in real life all around us. We work with percents every day. In fact, they are so common that sometimes we don’t even realize that we are using them. This Concept takes what we have learned about percents and applies it in some different real world situations. Let’s begin by learning how to find the percent of a number.

We can find the percent of another number. When we find the percent of a number, we want to figure out what part of the number is equal to the amount of the percent.

What is 10% of 25?

This is an example where we are looking for the percent of a number. We want to figure out 10% of 25. Said another way, we want to find a part of 25 that is the same as ten percent.

How can we figure out this problem?

We can figure out the percent of a number in two different ways. One is to use a proportion and one is to use key words and multiplication. Let’s look at using a proportion first.

How can we find the percent of a number using a proportion?

Remember that a proportion is created when two ratios are equal. We can compare the percent out of 100 with a part of another number. We know that we need to find 10% of 25. The percent is out of 100 so we can write our first ratio by changing 10% into a fraction.

\begin{align*}10\% =\frac{10}{100}\end{align*}

Next, we change the 25 into a proportion. Now we are looking for what part of 25 is equal to 10%, so that is going to be what we need to find out of 25. Here is what it looks like.

\begin{align*}\frac{x}{25}\end{align*}

Our proportion is \begin{align*}\frac{10}{100}=\frac{x}{25}\end{align*}.

That’s correct! We solve the proportion to find our answer. Do you remember how to solve the proportion? We can do this by using cross products.

Next, we can write an equation.

\begin{align*}100x = 250\end{align*}

To solve this equation, we have to think "What times 100 is equal to 250?" We could also use the inverse operation of "times 100", and divide 250 by 100.

\begin{align*}x = 250 \div 100\end{align*}

\begin{align*}250 \div 100 = 2\underleftarrow{50.} = 2.5\end{align*}

Our answer is \begin{align*}2.5\end{align*}

Let’s review the steps of using a proportion!!

We can also use key words and multiplication to find the percent of a number.

What is 10% of 25?

First, we look for any key words that mean an operation. The word “OF” means multiplication, so we are going to use multiplication to find an answer. Next, we turn 10% into a decimal.

10% = .10

We are looking for 10% of 25, so we multiply the decimal .10 times 25 to find our answer.

\begin{align*}25\\ \underline{\times \ \ .10}\\ 00\\ \underline{+ \ \; 25 \ }\\ 250\end{align*}

Finally we put the decimal point into our product. We have two decimal places in .10 so we put it in two places counting from right to left.

Our answer is \begin{align*}2.5\end{align*}.

Notice that our answers are the same!! You can use either way to find the correct answer!!

It is time for you to practice a few of these on your own.

#### Example A

What is 10% of 54?

Solution: \begin{align*}5.4\end{align*}

#### Example B

What is 25% of 80?

Solution: \begin{align*}20\end{align*}

#### Example C

What is 5% of 78?

Solution: \begin{align*}3.9\end{align*} which could be rounded to \begin{align*}4\end{align*}

Remember Sam and the cleaning fluid? Here is the original problem once again.

Sam is surprised that it takes so much cleaning fluid to mop the floor. Now it is a big floor, but after Sam finishes mopping, she discovers that she has used 25% of the 20 gallons of fluid.

How many gallons of fluid are left?

To solve this problem, Sam will need to find 25% of 20. Here is how we can set up the problem.

What is 25% of 20?

First, we convert the percent to a decimal.

\begin{align*}25% = .25\end{align*}

Now we multiply \begin{align*}.25 /times 20\end{align*}.

Our answer is 5. Which means that 5 gallons were used.

How much is left?

We can subtract 5 from 20.

If Sam used 25% of 20 gallons, then she used 5 gallons, so there are 15 gallons of cleaning fluid left.

### Vocabulary

Here are the vocabulary words in this Concept.

Percent
a part of a whole 100, written using a % sign.
Proportion
two equal ratios.

### Guided Practice

Here is one for you to try on your own.

What is 15% of 200?

To figure this out, we change 15% to a decimal by moving the decimal point.

15% becomes .15

Next, we multiply .15 times 200.

### Video Review

Here is a video for review.

### Practice

Directions: Find the percent of each number.

1. What is 2% of 10?

2. What is 5% of 50?

3. What is 10% of 30?

4. What is 25% of 18?

5. What is 20% of 36?

6. What is 11% of 40?

7. What is 8% of 80?

8. What is 15% of 45?

9. What is 20% of 100?

10. What is 25% of 250?

11. What is 4% of 60?

12. What is 5% of 85?

13. What is 2% of 18?

14. What is 15.5% of 90?

15. What is 20.5% of 70?

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