# 6.11: Percent Equation to Find Part a

Difficulty Level: At Grade Created by: CK-12
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Marcel needs a new shirt to wear to his sports banquet. When he goes to the mall, he spots a clearance rack and finds a shirt on it he likes. The original price of the shirt is 25, but the yellow ticket clearance price is smudged. If the shirt is marked down by 60%, what is the clearance price? In this concept, you will learn how to use the percent equation to find part a, the amount. ### Guidance Think about the proportion to find the percent of a number \begin{align*}\frac{a}{b}=\frac{p}{100}\end{align*} You can cross multiply \begin{align*}b\end{align*} and \begin{align*}p\end{align*} and \begin{align*}a\end{align*} and 100. Then you can divide the product of \begin{align*}b\end{align*} and \begin{align*}p\end{align*} by 100. Let’s look at a statement that uses this proportion. What is 35% of 6? First, convert the numbers to fractions and fill in the proportion. \begin{align*}\frac{a}{6}= \frac{35}{100}\end{align*} Next, cross multiply and solve for \begin{align*}a\end{align*}. \begin{align*}\begin{array}{rcl} 100 a &=& 35(6)\\ 100 a &=& 210 \\ a &=& 2.1 \end{array}\end{align*} Notice that by dividing by 100, you moved the decimal place two places to the left. This is the same two places that the percent is represented by. This means that if you changed the percent to a decimal FIRST, you could skip a step and use an equation to find the missing value. Take a look at the same problem. What is 35% of 6? First, change 35% to a decimal. \begin{align*}35 \% = 0.35\end{align*} Now, multiply this decimal by 6, the base, and find \begin{align*}a\end{align*}, the amount. Look at this equation. \begin{align*}\begin{array}{rcl} a &=& p \% (b)\\ a &=& 0.35(6)\\ a &=& 2.1 \end{array}\end{align*} Notice that you got the same answer as when you used the proportion. Converting the percent to a decimal first just simplifies the process. Let’s try one more example. What is 32% of 200? To figure this out, first change the percent to a decimal. \begin{align*}32\% = 0.32\end{align*} Next, multiply this decimal by 200. \begin{align*}200 \times 0.32 = 64\end{align*} The answer is 32% of 200 is 64. ### Guided Practice What is 25% of 50? First, change 25% to a decimal. \begin{align*}25\% = 0.25\end{align*} Now use the equation. \begin{align*}\begin{array}{rcl} a &=& p\%(b)\\ a &=& 0.25(50)\\ a &=& 12.5 \end{array}\end{align*} The answer is 25% of 50 is 12.5. ### Examples Use the percent equation to find each amount. Include decimals in your answer. #### Example 1 What is 20% of 16? First, change the percent to a decimal. \begin{align*}20\% = 0.20\end{align*} Next, multiply this decimal by 16. \begin{align*}16 \times 0.20 = 3.2\end{align*} The answer is 20% of 16 is 3.2. #### Example 2 What is 5% of 40? First, change the percent to a decimal. \begin{align*}5\% = 0.05\end{align*} Next, multiply this decimal by 40. \begin{align*}40 \times 0.05 = 2\end{align*} The answer is 5% of 40 is 2. #### Example 3 What is 15% of 65? First, change the percent to a decimal. \begin{align*}15\% = 0.15\end{align*} Next, multiply this decimal by 65. \begin{align*}65 \times 0.15 = 9.75\end{align*} The answer is 15% of 65 is 9.75. ### Follow Up Remember Marcel and his shopping trip? The shirt he wants to buy originally costs25 and is marked down by 60%. But thev yellow clearance ticket is too smudged to read the new price. What is the clearance price of the shirt?

First, if the shirt has been reduced by 60%, its clearance price is \begin{align*}100\% - 60\%\end{align*} or 40% of the original price.

First, change the percent to a decimal.

\begin{align*}40\% = 0.40\end{align*}

Next, multiply this decimal by the original price of 25. \begin{align*}25 \times 0.40 = 10\end{align*} The answer is the clearance price of the shirt is10.

### Explore More

Use the percent equation to find each amount.

1. What is 20% of 18?
2. What is 10% of 30?
3. What is 5% of 90?
4. What is 12% of 27?
5. What is 18% of 30?
6. What is 50% of 88?
7. What is 75% of 12?
8. What is 75% of 90?
9. What is 22% of 40?
10. What is 25% of 60?
11. What is 8% of 15?
12. What is 99% of 200?
13. What is 90% of 12?
14. What is 18.5% of 230?
15. What is 20.5% of 160?

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### Vocabulary Language: English

TermDefinition
Amount In a proportion, the amount is the part of the base that is being calculated.
Base In the context of the percent equation, the base is the part of the whole from which the amount is calculated.
Decimal In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
Inverse Operation Inverse operations are operations that "undo" each other. Multiplication is the inverse operation of division. Addition is the inverse operation of subtraction.
Percent Percent means out of 100. It is a quantity written with a % sign.
Proportion A proportion is an equation that shows two equivalent ratios.

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