How to Multiply or Divide Two Percentages

Co-authored by David Jia

Last Updated: March 22, 2024 References

Do you have two percentages that you wish to multiply together, or divide? Multiplying and dividing percents is different from adding or subtracting them. You cannot remove the percent sign from each number and multiply or divide the numbers by each other; you will need to convert the percentages to decimal or fraction. Therefore, this process takes more work than adding or subtracting percentages, but it can still be completed in minutes.

Things You Should Know

You can make things easier by converting percentages into decimals or fractions before you multiply or divide them.
Convert the percentages into a decimal by moving the decimal point 2 spaces to the left. Then, multiply and divide them like normal numbers.
Rewrite the percentages as fractions over 100, then simplify the fractions until you can’t reduce them anymore. Then, multiply or divide the fractions.

Method 1

Method 1 of 4:

Multiplication: Converting the Percentages to Decimal

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Do this by moving the decimal point two spaces to the left, or dividing them by 100.^{[1]
X
Research source} For example, 30% and 70% would be 0.3 and 0.7 as decimals.
2
Multiply the decimals. The multiplication of decimals is similar to that of whole numbers, with a few differences.^{[2]
X
Research source}
- Remember that you do not need to line up the decimal point while you multiply, as you will be ignoring the decimal points as you do so. When you have your product, you will then count the total number of values behind the decimal point, and move the decimal point that number of places.
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If you had 0.25 as your product, for instance, you would multiply it by 100 to get a product of 25%.

Method 2

Method 2 of 4:

Multiplication: Converting the Percentages to Fractions

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$Step 1 Rewrite both percentages as fractions with a denominator of 100.$

For example, if you had 50% and 25%, you would rewrite them as 50/100 and 25/100. Then simplify as needed;^{[3]
X
Research source} in the given example, 50/100 would simplify to 1/2, and 25/100 would simplify to 1/4.
$Step 2 Multiply the fractions...$

Multiply the fractions. Remember that when multiplying fractions, the denominators do not have to be the same; you will multiply the numerators and denominators.^{[4]
X
Research source} In the example above, 1/2 x 1/4 would equal 1/8, or 0.125.
In the example above, your percentage value would be 12.5%, since 0.125 x 100 equals 12.5%.

Method 3

Method 3 of 4:

Dividing: Converting the Percentages to Decimal

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Do this by moving the decimal point two spaces to the left, or dividing them by 100. For example, 20% and 80% would be 0.2 and 0.8 as decimals.
Divide the first decimal by the second one. To do this, move the decimal point the number of spaces it would take to make the number whole, then divide as usual.^{[5]
X
Research source} In the example given above, 0.2/0.8 would give you a quotient of 0.25, since 2 divided by 8 equals 0.25.
Then add a percent (%) sign so others know that the number is being compared to 100.

Method 4

Method 4 of 4:

Dividing: Converting the Percent to a Fraction

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$Step 1 Rewrite the percentages as fractions with a denominator of 100.$

For instance, if you had 80%, and 25%, you would get the fractional values of 80/100 and 25/100.
Simplify as needed. In the example given above, 80/100 would simplify to 4/5, and 25/100 would simplify to 1/4.
$Step 3 Divide the fractions...$

Divide the fractions. To do this, multiply the first fraction by the reciprocal of the second one (flip the second fraction over).^{[6]
X
Research source} In the example given above, you would multiply 4/5 by 4/1 (or 4) to get 16/5.
If you're simplifying an improper fraction, it's best to convert it to a decimal rather than a mixed number, as converting a mixed number to percentage takes more work.
In the example given above, you would multiply 16/5 (or 3.2) by 100 to get 320%.

Expert Q&A

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Question

How can compute percentages in real-life situations?

David Jia
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David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

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Expert Answer

So simplify percentage computations in real-life scenarios by streamlining the process by combining multiple steps into one. For instance, when calculating a tip for a $20 restaurant meal at 15%, instead of separately finding 15% of $20 and then adding it back, directly multiply $20 by 1.15. This approach eliminates unnecessary calculations and provides the final amount in one step. Extend this method to more complex scenarios, such as factoring in a 9% tax, a 15% tip, and a 20% discount on a $20 restaurant meal. Instead of performing multiple steps, efficiently compute the total amount by multiplying $20 by 1.09 for the tax, then by 1.15 for the tip, and finally by 0.8 for the 20% discount. By incorporating these percentages into a single calculation, you can easily arrive at an accurate total without unnecessary intermediary steps.

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How do I multiply negative decimals ?

Donagan

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Multiply the numbers as usual. If you're multiplying two negative decimals, the answer will be positive.

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How do I divide a whole number and a percentage?

Donagan

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First convert the percentage to a decimal, then perform the division.

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