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A percent is a ratio of a part to the whole set. What makes a percent special is that the ratio is always given as a certain number of parts out of 100.

In this section, you will use a percent bar model to represent different percents of a given number. You will also think about different ways to calculate a percent or to use a percent to calculate a part or the whole.

A percent bar model consists of the following components.

In this model, 0 is at the left end of the percent bar, and 100%, or the whole set, is at the right end of the percent bar. The vertical line marking the part, which is n% of the whole, indicates the proportion of the percent bar representing the part.

Suppose that a store is having a sale on all merchandise. Depending on the type of item, shoppers will receive a particular discount.

Interactive exercise. Assistance may be required. Use the percent bar contained in the interactive below to set up and solve the percent problems that follow. Click on the image to open the interactive, which will open in a new browser tab or window.

Enter the amount of the whole in the box in the upper right portion of the interactive.
Drag the point marked on the percent bar to adjust the part.
Use the information about the part and the percent to answer the question.

Interactive popup. Assistance may be required.

Need additional directions?

Use the interactive to answer the following questions.

All shoes are marked at a 40% discount. If the original price of a pair of shoes is $90, how much of a discount will Sheila receive if she purchases the pair of shoes?
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Check Your Answer

Sheila will receive a $36 discount.
All belts are marked at a 25% discount. If the original price of a belt is $45, how much of a discount will Ricardo receive if he purchases the belt?
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Ricardo will receive a $11.25 discount.

What is the discounted price of the pair of shoes that Sheila wants to purchase and the discounted price of the belt that Ricardo wants to purchase?

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Check Your Answer

Sheila's shoes	Ricardo's belt
The original price is $90, and she will receive a discount of $36. $90 − $36 = $54	The original price is $45, and he will receive a discount of $11.25. $45 − $11.25 = $33.75

What part of the percent bar represents the discounted price, as opposed to the amount of discount?
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The discount is represented by the left-hand portion of the percent bar, and the discounted price is represented by the right-hand portion of the percent bar.
At this same store, jackets are discounted 25%. Jason received a $30 discount on a jacket that he purchased. What was the original price?
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Use the percent bar model shown below. How many pieces that represent 25% will you need in order to make 100%?

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Check Your Answer
There are four 25%-sized pieces in 100% so you will need four $30 pieces.

Jason’s jacket was originally priced at $120.
Simone purchased a backpack with an original price of $60 that was marked with a discount of $20. What was the percent discount on Simone’s backpack?
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Use the percent bar model shown below. What part of $60 is $20?

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$20 is 1 over 3 1 3 of $60, since 20 over 60 20 60 = 1 over 3 1 3 . We know that 1 over 3 1 3 can be written as 331 over 3 1 3 %.

Simone received a 331 over 3 1 3 % discount.

Pause and Reflect

How could you use a proportion to show the information in the percent bar?

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A proportion uses two equivalent ratios: Amount of Discount over Original Price Amount of Discount Original Price and Percent of Discount over 100 Percent of Discount 100 . The percent bar visually illustrates the proportion, since the two quantities for one ratio are above the percent bar and below the percent bar.

If you know the percent, how could you convert the percent to a decimal, and then use the decimal number to solve the problem?

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If you need to determine the part of the whole, multiply the percent (as a decimal) by the whole. If you need to determine the size of the whole, divide the percent (as a decimal) by the part.

Practice

The Broadford Middle School football team scored 225 points last season. Of those, 60% were scored with field goals. How many points did the football team score with field goals?
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Need a hint?
Set up and solve a proportion.

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Check Your Answer

Field Goal Points over Total Points Field Goal Points Total Points = 60 over 100 60 100 = x over 225 x 225

135 points were scored with field goals.
According to the nutrition facts label on a bag of snack mix, 8 grams of protein is 16% of the recommended daily value for the amount of protein that a person should eat in one day. What is the total amount of protein recommended for a person to eat in one day?
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Set up and solve a proportion.

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Check Your Answer
Snack Mix over Total Snack Mix Total = 16 over 100 16 100 = 8 over x 8 x

50 grams of protein are recommended in one day.
At a local park, there are 48 ducks. Of these, 30 are mallards. What percent of ducks at the local park are mallards?
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Set up and solve a proportion.

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Check Your Answer
Mallards over Total Mallards Total = 30 over 48 30 48 = x over 100 x 100

62.5% of the ducks at the local park are mallards.