Welcome to Shopping and Spending with Percentages, your second course in this learning path! In the first course, you built a strong foundation with percent conversions, benchmark mental math, and the three core percent problem types. Now we put those skills to work in real shopping and spending situations.
This first lesson focuses on one of the most common uses of percentages you will encounter: calculating discounts and sale prices. By the end, you will be comfortable finding how much you save and what you actually pay when a store offers a percent off.
Before we jump into calculations, let's make sure the idea behind a discount is crystal clear. When a store tag reads "25% off," it means the store is removing 25 out of every 100 units of currency from the original price. As you may recall from previous lessons, a percent is simply a number out of 100, so "25% off" tells us exactly what fraction of the price is being taken away.
This leads to two natural questions every shopper wants answered:
- How much money do I save? (the discount amount)
- How much do I actually pay? (the sale price)
We will learn two methods that answer both questions, and you can pick whichever feels more natural for a given situation.
The most straightforward approach has two short steps. First, find the discount amount by multiplying the original price by the discount percent written as a decimal. Then, subtract that discount from the original price to get the sale price.
Let's walk through an example. A jacket is priced at $80 and the store is running a 15% off sale.
Step 1 — Discount amount:
The discount saves us $12.
Step 2 — Sale price:
Here is another way to think about the same problem. If a store takes 15% off, that means we are paying the remaining 85% of the price. We can jump straight to the sale price in a single step by multiplying the original price by that remaining percent.
Using the same $80 jacket:
To make the relationship between the two methods concrete, let's look at one more example with both approaches next to each other. A pair of sneakers costs $60 and is marked 20% off.
Both paths arrive at the same sale price of $48. The only difference is which value you calculate first. Method 1 naturally gives you the discount amount, while Method 2 gives you the sale price. You can always find the other value with a simple subtraction.
As you practice, keep these pointers in mind:
- Always start from the original price. The discount percent applies to the original price, not to any other number.
- Convert the percent to a decimal before multiplying. For example, 30% becomes 0.30, not 30.
- Check reasonableness. If an item is 25% off, you should pay less than the original but more than half. A quick mental estimate can catch arithmetic errors.
A helpful sanity check is to glance at the discount percent itself. A small percent like 10% should trim only a little off the price, while a large percent like 70% should leave only a small amount to pay. If your answer doesn't match that intuition, double-check your arithmetic.
In this lesson, we explored two reliable methods for calculating discounts and sale prices. The subtract-the-discount method finds the savings first and then subtracts, while the remaining-percent shortcut jumps straight to what you pay. Both produce the same result, so choose whichever fits the question you need to answer.
Up next, you will put these methods into action with hands-on practice problems that mirror real store scenarios. You will work through guided examples, compute discount amounts on your own, find final sale prices, and even compare deals across different items — so get ready to do some savvy shopping with numbers!
