Percents and Their Relationships with Fractions and Decimals Study Guide

Into the Unknown

When you see the phrase seven percent, you know to express this mathematically as . What about when you see the phrase what percent? How do you express this mathematically? If you're thinking, "I don't know," then you're right. That's right—when you are asked what percent, you are being asked to determine an unknown value.

Instead of writing "I don't know" in the place of the numbers that you don't know, try using a variable, such as x.

Let's put this into practice. What percent of 250 is 30?

What percent means
of 250 means · 250
is 30 means = 30

· 250 = 30
x · = 30
x · 250 = 30 · 100
x · 250 = 3,000
x = 12

Percent Estimation

Sometimes, it may be quicker for you to estimate a percent value. What if you were asked to estimate 19% of 50?

Use 20% as a "friendlier" percent: 20% of 50 = 10, so 19% of 50 is about 10.

Percent of Change

To find a percent increase or decrease, first find the amount of increase or decrease. Then, use the percent of change formula:

amount change = × original number

Let's put this into play. Find the percent decrease from 4 to 3.

First, determine what the actual decrease is. The decrease from 4 to 3 is 1.

Now, plug the information you know into the percent of change formula:

Now, solve for x:

25 = x

So, the percent decrease from 4 to 3 is 25%.

Purchasing and Percents

Some percent questions involve buying or selling items. A discount is the amount by which the regular price of an item is reduced. A markup is the difference between the price paid by the seller and the increased selling price, which is the amount you pay for the item.

Let's look at a discount question.

A book on your summer reading list originally cost $15, but during a summer sale, it's being sold at a 15% discount.

First, find 15% of $15:

So, the discount is $2.25. Now subtract $2.25 from the original price of $15:

During the sale, you can get the book for $12.75!

Now, on the other side, let's try a markup question.

A local sporting goods store paid $1,300 for a mountain bike. The store has marked the bike up by 30%.

First, find 30% of $1,300:

Now, add this $390 markup to the original price:

The store is selling the mountain bike for $1,690.

Find practice problems and solutions for these concepts at Percents and Their Relationships with Fractions and Decimals Practice Questions.