Calculating percentages

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Writing and Evaluating Algebraic Expressions Worksheets

The guidance below will help you work through percentage calculation problems including those found on the percentage worksheets page.

As you guide your child you should also take the opportunity to explain the importance and relevance of percentage calculations: pay rises, allowance rises, interest rates, discounts on sale items etc. Learning is always improved when the relevance of what is being learned is appreciated.

What is a percentage?

Percent means “for every 100” or "out of 100." The (%) symbol as a quick way to write a fraction with a denominator of 100. As an example, instead of saying "it rained 14 days out of every 100," we say "it rained 14% of the time."

Percentages can be written as decimals by moving the decimal point two places to the left:

Decimals can be written as a percentages by moving the decimal point two places to the right:

Formula for calculating percentages

The formulas for calculating percentages or for converting from percentages are relatively simple.

To convert a fraction or decimal to a percentage, multiply by 100:

To convert a percent to a fraction, divide by 100 and reduce the fraction (if possible):

Examples of percentage calculations

The following two examples show how to calculate percentages.

1) 12 people out of a total of 25 were female. What percentage were female?

2) The price of a $1.50 candy bar is increased by 20%. What was the new price?

3) The tax on an item is $6.00. The tax rate is 15%. What is the price without tax?

Similar types of problems to those in the examples above are solved in a series of three mini-lessons on Calculating with Percent. These are listed below.

 #1: Introduction

 #2: Calculating with Percent e.g. 12% of 80 is?

 #3: Calculating with Percent e.g. 6 out of 8 is what % and 15 is 30% of what?

Percentage Chart

This Percentage Chart shows what 15% of $1 through $100 is although it is customizable so you can set the percentage and the numbers to whatever you want.

Find 1% - The Unitary Method

Handy Tip: A good way of finding percentages is to start by finding what 1% is.Example: What is 6% of 31?

Find 1%.
Divide by 100 (or move the decimal
point two places to the left)
31 ÷ 100 = .31
We now know what 1% is. We just need to
multiply it by 6 to find 6%
.31 x 6 = 1.86

6% of 31 is 1.86

You can practice calculating percentages by first finding 1% (and/ or finding 10%) and then multiplying to get your final answer using this Calculating Percentages in Two Steps Worksheet. There are also more percentage worksheets here too.

Common error when finding a percentage

Since percentages are often thought of as parts of a larger whole thing, there can be a tendency to divide instead of multiply when faced with a problem such as "find 35% of 80." As the example below shows, after converting the percent to a decimal, the next step is to multiply, not divide.

error whening finding percentages by dividing instead of multiplying the decimal conversion

An understanding of percent allows students to estimate to check whether their answer is reasonable. In this example, knowing that 35% is between one-quarter and one-half would mean the answer should be somewhere between 20 and 40.