How To Multiply Percentages Using Decimals and Fractions

Calculating percentages can help you in your daily life. Common examples of when you may need to multiply percentages are for calculating sales tax or discounts, leaving tips, earning a commission or determining interest. Knowing how to multiply percentages is a useful skill for personal use and work, especially if you need to solve percentage problems without using a calculator.

In this article, we’ll discuss percentages, including how to multiply them, how to convert percentages into decimals and fractions and how to multiply a percent by another percent, a whole number, a decimal and a fraction.

What is a percentage?

A percentage, or percent, is a proportion between two numbers expressed in hundredths. A percentage is often used to define a fractional part of a whole. Sometimes you'll see it referred to as "per one hundred," "for every 100" or "out of 100."

Percents are a common mathematical term and used frequently in basic math, statistics, probability and other mathematical calculations. Many industries use percentages on a daily basis. For example, in the finance industry, you use percents to find the rate of return, market shares, interest rates and growth trends. Consumers encounter percents every time they go shopping, since the store applies sales tax to their bill as a percentage.

Related: Basic Math Skills: Definitions, Examples and How To Improve Them

Multiplying with percentages

When you have a math problem that requires you to multiply one or more percentages, you must first convert the percentage into a decimal or fraction. You cannot calculate a multiplication math problem correctly without first making this conversion.

In most cases, unless the direction specify, it doesn't matter whether you convert the percentages into decimals or fractions. Unless there is a reason to use one over the other, it is a personal preference and you may choose either.

By itself, a percent is just a representation of a part of a whole. When multiplying percents by another number, the operation creates a new value equal to the given percent of the original number.If the percentage amount is under 100, the product will be less than the original number. For example, 50% x 300 = 150. If the percentage amount is over 100, the product will be greater than the original number. For example, 200% x 300 = 600.

Related: How To Calculate Percent

How to convert a percent to a decimal

The process for changing a percent into a decimal is simple, just follow these steps:

1. Start with a percentage

Locate the percentage you want to convert to a decimal. For this math problem, use the value 78%.

2. Divide by 100

Take the percentage 78% and set up a division problem to divide it by 100.

78%/100 = .78

Anytime you divide by 100, you move the decimal point two places to the left. This little trick will help you convert percentages to decimals very quickly. Instead of setting up a division problem, just find the decimal point and move it two places to the left.

3. Remove the percentage sign

The last step is to double-check that you removed the percentage sign. Once you divide the percent by 100, the percentage sign no longer applies because the value is now a decimal instead of a percentage. Here are some examples of converting a percent to a decimal:

65% = .65

13.45% = 0.1345

279% = 2.79

Related: How To Calculate Percentage, Percentage Change and Percentage Difference

How to convert a percent to a fraction

The process for changing a percent into a fraction is simple, just follow these steps:

1. Start with a percentage

Locate the percentage you want to convert to a decimal. For this math problem, use the value 78%.

2. Divide by 100

Take the percentage 78% and set up a division problem in the form of a fraction to divide it by 100.

78/100

Remember that the fraction bar separating the two numbers is actually a division symbol. However, instead of working out the division problem to get a decimal value, we are going to leave the division problem as a fraction and reduce it if possible.

78/100 = 39/50

If the percentage is not a whole number, you can multiply both the top and the bottom of the fraction by 10 for each number after the decimal point. For example:

62.5/100 = 625/1000

3. Remove the percentage sign

The last step is to double-check that you removed the percentage sign. Once you place the percent over 100, the percentage sign no longer applies because the value is now a fraction instead of a percentage. Here are some examples of converting a percent to a decimal:

28% = 7/25

325% = 13/4 or 3 1/4

1.76% = 176/10000

Related: How To Calculate Percentages in 3 Easy Steps (With Examples)

How to multiply percentages

When you multiply a percentage by another percentage, you must convert both of the percentages into decimals or fractions before you can multiply. Here are the steps:

1. Convert

Take the math problem and decide whether you want to convert both percentages into decimals or fractions. So you can see it both ways, this example will show both conversions.

For decimals:

If the math problem is 25% x 32%, convert the percentages into decimals.

25% = .25

32% = .32

For fractions:

If the math problem is 25% x 32%, convert the percentages into fractions.

25% = 25/100 = 1/4

32% = 32/100 = 8/25

2. Substitute

Now that you've converted the percentages into either decimals or fractions, substitute the new values into the problem.

For solving as decimals:

.25 x .32 = ?

For solving as fractions:

1/4 x 8/25 = ?

3. Solve

The last step is to do the multiplication operation and multiply the two numbers together for a final answer. If you're using fractions, remember to check if you can reduce the final answer.

For solving as decimals:

.25 x .32 = .08

For solving as fractions:

1/4 x 8/25 = 8/100 = 2/25

Related: How To Calculate Average Percentage: Formula and Examples

How to multiply a percentage by a whole number

When you multiply a percentage by a whole number, you must convert the percentage into either a decimal or a fraction before you can multiply. Here are the steps:

1. Convert

Take the math problem and decide whether you want to convert both percentages into decimals or fractions. So you can see it both ways, this example will show both conversions.

For solving with a decimal:

If the math problem is 66% x 5, convert the percentage into a decimal.

66% = .66

For solving with a fraction:

If the math problem is 66% x 5, convert the percentage into a fraction.

66% = 66/100 = 2/3

2. Substitute

Now that you've converted the percentage into either a decimal or a fraction, substitute the new values into the problem.

For solving with a decimal:

.66 x 5 = ?

For solving with a fraction:

2/3 x 5 = ?

3. Solve

The last step is to do the multiplication operation and multiply the two numbers together for a final answer. If you are using fractions, remember to check if you can reduce the final answer.

For solving with a decimal:

.66 x 5 = 3.3

For solving with a fraction:

2/3 x 5 =2/3 x 5/1 = 10/3 = 3 1/3

Read more: How To Calculate Percentage of a Number (With Examples)

How to multiple a percentage by a decimal

When you multiply a percentage by a decimal, you must convert the percentage into a decimal before you can multiply. In this case, it wouldn't make sense to convert the percentage into a fraction. Here are the steps:

1. Convert

Take the math problem and convert the percentage into a decimal.

If the math problem is $1.60 x 275%, convert the percentage into a decimal.

275% = 2.75

2. Substitute

Now that you've converted the percentage into a decimal, substitute the new value into the problem.

$1.60 x 2.25 = ?

3. Solve

The last step is to do the multiplication operation and multiply the two numbers together for a final answer. Since this example uses money, remember to keep the dollar symbol on your final answer.

$1.60 x 2.25 = $3.60

Related: How To Calculate Percentage Difference

How to multiple a percentage by a fraction

When you multiply a percentage by a fraction, you must convert the percentage into a fraction before you can multiply. In this case, it wouldn't make sense to convert the percentage into a decimal. Here are the steps:

1. Convert

Take the math problem and convert the percentage into a fraction.

If the math problem is 45% x 8/15, convert the percentage into a fraction.

45% = 45/100 = 9/20

2. Substitute

Now that you've converted the percentage into a fraction, substitute the new value into the problem.

9/20 x 8/15 = ?

3. Solve

The last step is to do the multiplication operation and multiply the two numbers together for a final answer. Since this example uses a fraction, remember to reduce your final answer.

9/20 x 8/15 = 72/300 = 6/25