Multiplicative Shortcuts for Markups and Discounts
Multiplicative Shortcuts for Markups and Discounts is a Grade 7 math skill in Reveal Math Accelerated, Unit 3: Solve Problems Involving Percentages, where students compute the final price after a markup or discount in a single multiplication step by using a scale factor (e.g., multiplying by 1.25 for a 25% markup or by 0.80 for a 20% discount) instead of two separate steps. This efficiency technique is widely used in financial and commercial contexts.
Key Concepts
You can calculate the final price of an item after a markup or discount in a single step by multiplying the original price by a factor based on the percent change. Let $p$ represent the percent markup or discount written as a decimal.
Common Questions
How do you use a multiplicative shortcut for a markup?
Add the markup percent to 100% to get the scale factor, then multiply the original price. For example, a 25% markup means multiplying by 1.25. If the original price is $40, the new price is 40 x 1.25 = $50.
How do you use a multiplicative shortcut for a discount?
Subtract the discount percent from 100% to get the scale factor, then multiply. For a 20% discount, the scale factor is 0.80. A $60 item discounted 20% costs 60 x 0.80 = $48.
Why is the one-step method faster than the two-step method?
The two-step method finds the amount of markup or discount first, then adds or subtracts. The one-step method combines both operations into a single multiplication, saving time and reducing errors.
What is Reveal Math Accelerated Unit 3 about?
Unit 3 covers Solve Problems Involving Percentages, including percent of a number, percent change, percent error, markup, discount, and simple interest applications.