Percent of a Whole

Percents are the ratio of a number and 100. Percents are used in many different applications. Percents are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by 12% from last year, or that the number of jobless claims has increase by 5% this quarter over last quarter.

Unemployment rate as percent by year between 2004 and 2014.

We regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.

Before we dissect the methods for finding percent change of a quantity, let’s learn the basics of finding percent of a whole.

For example, if we knew a gas tank held 14 gallons, and wanted to know how many gallons were in [latex]\frac{1}{4}[/latex] of a tank, we would find [latex]\frac{1}{4}[/latex] of 14 gallons by multiplying:

[latex]\frac{1}{4}\,\cdot \,14=\frac{1}{4}\,\cdot \,\frac{14}{1}=\frac{14}{4}=3\frac{2}{4}=3\frac{1}{2}\,\,\,\text{gallons}[/latex]

Likewise, if we wanted to find 25% of 14 gallons, we could find this by multiplying, but first we would need to convert the 25% to a decimal:

[latex]25\%\,\,\text{of}\,\,14\,\,\,\text{gallons}=0.25\,\cdot \,14=3.5\,\,\,\text{gallons}[/latex]

The following video contains an example that is similar to the one above.

From the previous example, we can identify three important parts to finding the percent of a whole:

• the percent,  has the percent symbol (%) or the word “percent”
• the amount, the amount is part of the whole
• and the base, the base is the whole amount

The following examples show how to identify the three parts: the percent, the base, and the amount.

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

The following video provides more examples that describe how to identify the percent, amount, and base in a percent problem.

In the next section, you will use the parts of a percent problem to find the percent increase or decrease of a quantity by writing and solving equations.