Learn on PengiBig Ideas Math, Course 2Chapter 6: Percents

Lesson 6: Discounts and Markups

In this Grade 7 lesson from Big Ideas Math, Course 2, Chapter 6, students learn how to calculate discounts and markups using percent of a number to find sale prices, original prices, and selling prices. Students apply two methods — subtracting the discount amount from the original price and multiplying by the remaining percent — as well as working backward from a sale price to find the original price using the percent proportion. Real-world contexts like retail pricing help students connect the concepts of discount and markup to everyday consumer math.

Section 1

Discount

Property

An amount of discount is a percent off the original price.

amount of discount=discount rateoriginal price\text{amount of discount} = \text{discount rate} \cdot \text{original price}
sale price=original priceamount of discount\text{sale price} = \text{original price} - \text{amount of discount}

Section 2

Finding Original Price from Sale Price

Property

When given a sale price and discount percentage, the original price can be found using:

original price=sale priceremaining percentage as decimal\text{original price} = \frac{\text{sale price}}{\text{remaining percentage as decimal}}

Where remaining percentage = 100%discount percentage100\% - \text{discount percentage}

Section 3

Mark-up

Property

The mark-up is the amount added to the wholesale price.

amount of mark-up=mark-up ratewholesale price\text{amount of mark-up} = \text{mark-up rate} \cdot \text{wholesale price}
list price=wholesale price+mark-up\text{list price} = \text{wholesale price} + \text{mark-up}

Book overview

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Chapter 6: Percents

  1. Lesson 1

    Lesson 1: Percents and Decimals

  2. Lesson 2

    Lesson 2: Comparing and Ordering Fractions, Decimals, and Percents

  3. Lesson 3

    Lesson 3: The Percent Proportion

  4. Lesson 4

    Lesson 4: The Percent Equation

  5. Lesson 5

    Lesson 5: Percents of Increase and Decrease

  6. Lesson 6Current

    Lesson 6: Discounts and Markups

  7. Lesson 7

    Lesson 7: Simple Interest

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Discount

Property

An amount of discount is a percent off the original price.

amount of discount=discount rateoriginal price\text{amount of discount} = \text{discount rate} \cdot \text{original price}
sale price=original priceamount of discount\text{sale price} = \text{original price} - \text{amount of discount}

Section 2

Finding Original Price from Sale Price

Property

When given a sale price and discount percentage, the original price can be found using:

original price=sale priceremaining percentage as decimal\text{original price} = \frac{\text{sale price}}{\text{remaining percentage as decimal}}

Where remaining percentage = 100%discount percentage100\% - \text{discount percentage}

Section 3

Mark-up

Property

The mark-up is the amount added to the wholesale price.

amount of mark-up=mark-up ratewholesale price\text{amount of mark-up} = \text{mark-up rate} \cdot \text{wholesale price}
list price=wholesale price+mark-up\text{list price} = \text{wholesale price} + \text{mark-up}

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 6: Percents

  1. Lesson 1

    Lesson 1: Percents and Decimals

  2. Lesson 2

    Lesson 2: Comparing and Ordering Fractions, Decimals, and Percents

  3. Lesson 3

    Lesson 3: The Percent Proportion

  4. Lesson 4

    Lesson 4: The Percent Equation

  5. Lesson 5

    Lesson 5: Percents of Increase and Decrease

  6. Lesson 6Current

    Lesson 6: Discounts and Markups

  7. Lesson 7

    Lesson 7: Simple Interest