How Are Percentages Used?

What are percents used for?

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  1. Learners will be able to describe what a percent is.
  2. Learners will be able to identify several instances in which percents are used and why.
  3. Learners will be able to estimate percents using benchmarking.
When we go out to eat, why do you think we're expected to leave a tip that's a percent of the bill instead of a set amount?

What is a percent?

When kids first start learning about percents in school, one of the biggest mistakes they make is not realizing that a percent can't be treated the same way any other number can. A sale for 30% off doesn't mean you just subtract $30.

Percentages actually work a lot more like fractions, acting as a part compared to a whole. To understand how percents work, we have to look at what the word actually means. The word "percent" can be broken into two parts: per, meaning "for every" and cent, meaning "100."

The word percent can be broken into per, meaning for every, and cent, meaning 100.

In the situation of our 30% off sale, we'd treat 30% as 30 for every hundred. Instead of just subtracting $30 like kids initially try to do, we'd actually subtract $30 for every $100 of the price.

If we were buying a $100 pair of shoes, 30% off would mean we'd save $30. But if the shoes were $200, we'd save $60, since we'd save $30 for every $100.

Two pairs of shoes marked down 30%

Because the $200 shoes cost more, the buyer saves more. But 30% is taken from both prices, so one deal isn't necessarily better than another.

Percents in the Real World

While some math concepts show up for the first time in school, by the time percents come up in sixth grade, most of us already have context for them. Here are some places you might find percents in the real world.

1. A phone battery

  • Your phone battery might not show what percent or the battery remains by default, but most phones these days have the option. We know our battery is full when it's at 100%, and when it drops below a certain point, we know it's time to get the charger. But having 50% remaining doesn't translate to having 50 minutes left - it just means you've used about half of your battery so far.

2. A sale in your favorite store

  • We're also accustomed to seeing sales advertised using percents. We might see a sale for 25% or even 50% off from time to time, but just like the phone battery it isn't a direct translation meaning you'll save $25 or $50. The amount you save will depend on how much your purchases originally cost.

3. Paying a tip in a restaurant

  • Tipping isn't customary in every country, but in the US, it's common to tip your waiter for the service they provide during a meal. A waiter who serves a table of six people who all order appetizers, entrees, desserts, and drinks will likely do substantially more work than one who serves a table of two that just orders an appetizer. In this case, the first table with all their food would have a much higher bill than the second table. Since it's customary to leave a tip that's a percentage of the bill, the bigger table would leave more money for their waiter than the smaller table.

Try it!

Visit your favorite online retailer. What examples of percentages can you find?

In daily life, it's common practice for retailers, banks, and businesses to use percents to calculate their profits and discounts. One of the reasons they're so common is because they're fair.

Percents are calculated based on original costs, meaning the more you spend, the higher they come out to be. It makes sense for a bank to charge a client more for a larger loan, or for a retailer to give a more substantial discount to someone spending a lot of money. But using a percent means that every customer spends or saves the same fraction of their original cost, allowing each customer to be treated fairly.

Two bills, one for $14.94 and another for $127.83 with tip included

Using percentages for discounts also helps businesses balance savings for the customer with profits for their company. Consider the scenario below.

You are a business owner. Would you rather give a customer spending $100 a $50 discount or a customer spending $1000 a $50 discount? Why?

In the scenario, it's up to you as the business owner, but most people would probably choose to give the discount to the customer spending $1000. The more a customer spends, the bigger a discount the business can afford to give. Because of this, most companies tend to give a percentage discount, allowing customers to save a fraction of the price based on their spending.

Using Estimation

There are lots of ways to calculate the percent of a number, but one of the simplest is a method called benchmarking. In benchmarking, we use easy-to-find percents to estimate more complicated ones.

A chart describing how to find 10%, 25%, and 50%

Once you learn the patterns to find the benchmark percents, you can use them to estimate tougher ones. Consider the following scenarios.

You're out shopping and you only have $20 in cash to spend. You add up the cost of the items in your cart and get $17.00. Do you have enough cash for the cost of your items AND the 7% tax?
We haven't learned how to find 7% in this lesson, but we did learn about a benchmark percent that's pretty close. How could you use what we've learned to decide if you have enough cash?
You see a sweatshirt for sale in a store for $30.00. A sign above the rack tells you the sweatshirt is 30% off! How much will the sweatshirt cost?
How can you use your benchmark percents to estimate the cost of the sweatshirt?
Your boss calls you into her office and tells you you're getting a 20% raise! If you made $40,000 before, what will your new salary be?
How can you use benchmark percents to find your new salary?

When is it okay to use estimation?

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