# 6.7: Proportions to Find Base b

**At Grade**Created by: CK-12

Have you ever tried to figure out a part of a whole? There are many different ways to do this, but you can use proportions. Take a look.

Kelsey bought a box of chocolates from the candy store. There were 6 caramels in the box. This was 25% of the total chocolates in the box.

How many chocolates were there in the box?

Six is 25% of what number?

**This Concept is all about using the cross products of proportions to find a base. You will be able to solve this problem by the end of the Concept.**

### Guidance

You have solved problems where you needed to find the percent. You have solved problems where you needed to find the amount. Now we are going to use cross products to solve for the base.

**When you see the words “OF WHAT NUMBER?” you know that you are going to be solving for \begin{align*}b\end{align*}, the base.**

33 is 15% of what number?

**Remember that the number following the word “of” is the base. Since there is no number there, we need to find the base \begin{align*}(b)\end{align*}. 33 is the amount \begin{align*}(a)\end{align*} and 15 is the percent \begin{align*}(p)\end{align*}.**

\begin{align*}\frac{a}{b}& =\frac{p}{100}\\ \frac{33}{b}& =\frac{15}{100}\\ 15b& =3,300\\ \frac{15b}{15}& =\frac{3,300}{15}\\ b& =220\end{align*}

**Our answer is 220.**

Six students in Miss Lang’s third period math class got A’s on their math test. This was 24% of the class. How many students are in Miss Lang’s third period math class?

**We can think of this problem as “6 is 24% of what number?” First, let’s set up the proportion.**

\begin{align*}\frac{6}{b}=\frac{24}{100}\end{align*}

**Next, we use cross products to solve for \begin{align*}b\end{align*}.**

\begin{align*}24b& =600\\ b& =600 \div 24\\ b & = 25\end{align*}

**There are 25 students in the third period math class.**

Practice finding the base in the following problems.

#### Example A

6 is 25% of what number?

**Solution: 24**

#### Example B

12 is 8% of what number?

**Solution: 150**

#### Example C

22 is 11% of what number?

**Solution: 200**

Here is the original problem once again.

Kelsey bought a box of chocolates from the candy store. There were 6 caramels in the box. This was 25% of the total chocolates in the box.

How many chocolates were there in the box?

Six is 25% of what number?

To figure this out, let's write a proportion.

\begin{align*}\frac{6}{x} = \frac{25}{100}\end{align*}

Now we can cross multiply and solve.

\begin{align*}25x = 600\end{align*}

\begin{align*}x = 24\end{align*}

**There were 24 chocolates in Kelsey's box.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Percent
- a part of a whole out of 100

- Proportion
- formed by two equal ratios or two equivalent fractions

### Guided Practice

Here is one for you to try on your own.

6 is 17% of what number?

**Answer**

To figure this out, let's write a proportion.

\begin{align*}\frac{6}{x} = {17}{100}\end{align*}

Now we cross multiply and divide.

\begin{align*}17x = 600\end{align*}

\begin{align*}35.29\end{align*}

In this answer, we can round to the nearest whole number.

**Our answer is approximate. It is 35.**

### Video Review

Here is a video for review.

- This is a James Sousa video about solving proportions to find the base.

### Practice

Directions: Find each missing base.

1. 5 is 10% of what number?

2. 7 is 10% of what number?

3. 10 is 20% of what number?

4. 16 is 40% of what number?

5. 8 is 25% of what number?

6. 14 is 50% of what number?

7. 25 is 5% of what number?

8. 4 is 80% of what number?

9. 18 is 25% of what number?

10. 9 is 3% of what number?

11. 15 is 20% of what number?

12. 18 is 13% of what number?

13. 15 is 12.5% of what number?

14. 18 is 55% of what number?

15. 22 is 5.5% of what number?

### Image Attributions

Here you'll learn to use cross products of proportions to find base, b.