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How to Find the Reciprocal Download ArticleExplore this Article methods 1 Finding the Reciprocal of a Fraction or Whole Number 2 Finding the Reciprocal of a Mixed Number 3 Finding the Reciprocal of a Decimal Other Sections Questions & Answers VideoWATCH NOW Tips and Warnings Related Articles References Article Summary Co-authored by David Jia
Last Updated: November 23, 2025 References
Download Article ARTICLE VIDEO X
This article was co-authored by David Jia. 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. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been viewed 342,580 times.
Reciprocals are helpful in all sorts of algebraic equations. For example when you are dividing one fraction by another you multiply the first by the Reciprocal of the 2nd. You might also need reciprocals when finding equations of lines.
Steps
Method 1 Method 1 of 3:
Finding the Reciprocal of a Fraction or Whole Number
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1 Find the reciprocal of a fraction by flipping it. The definition of "reciprocal" is simple. To find the reciprocal of any number, just calculate "1 ÷ (that number)."[1]X Expert Source David JiaAcademic TutorExpert Interview For a fraction, the reciprocal is just a different fraction, with the numbers "flipped" upside down (inverted).[2]XResearch source
For instance, the reciprocal of 3/4 is 4/3.
Any number times its reciprocal will give you 1.
2 Write the reciprocal of a whole number as a fraction. Again, the reciprocal of a number is always 1 ÷ (that number).[3]XResearch source For a whole number, write that as a fraction; there's no point in calculating it out to a decimal.
For instance, the reciprocal of 2 is 1 ÷ 2 = 1/2.
Advertisement Method 2 Method 2 of 3:
Finding the Reciprocal of a Mixed Number
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1 Identify a mixed number. Mixed numbers are part whole number and part fraction, such as 24/5.[4]XResearch source There are two steps to finding the reciprocal of a mixed number, explained below.
2 Change it to an improper fraction.[5]X Expert Source David JiaAcademic TutorExpert Interview Remember, the number 1 can always be written as (number)/(the same number), and fractions with the same denominator (lower number) can be added together.[6]XResearch source Here's an example with 24/5:
24/5
= 1 + 1 + 4/5
= 5/5 + 5/5 + 4/5
= (5+5+4)/5
= 14/5.
3 Flip the fraction. Once the number is written entirely as a fraction, you can find the reciprocal just like you would with any fraction: by flipping it.[7]XResearch source [8]X Expert Source David JiaAcademic TutorExpert Interview
In the example above, the reciprocal of 14/5 is 5/14.
Advertisement Method 3 Method 3 of 3:
Finding the Reciprocal of a Decimal
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1 Change it to a fraction if possible. You might recognize some common decimal numbers that can easily be turned into fractions.[9]XResearch source For instance, 0.5 = 1/2, and 0.25 = 1/4. Once in fraction form, just flip the fraction to find the reciprocal.
For instance, the reciprocal of 0.5 is 2/1 = 2.
2 Write out a division problem. If you can't change it to a fraction, calculate the reciprocal of that number as a division problem: 1 ÷ (the decimal). You can use a calculator to solve this, or continue on to the next step to solve it by hand.[10]XResearch source
For example, you can find the reciprocal of 0.4 by calculating 1 ÷ 0.4.
3 Change the division problem to use whole numbers. The first step to dividing decimals is to move the decimal point until all the numbers involved are whole numbers. As long as you move the decimal point the same number of spaces for both numbers, you'll get the correct answer.
For example, you can take 1 ÷ 0.4 and rewrite it as 10 ÷ 4. In this case, you've moved each decimal place one space to the right, which is the same as multiplying each number by ten.
4 Solve the problem using long division. Use long division techniques to calculate the reciprocal. If you calculate it for 10 ÷ 4, you'll get the answer 2.5, the reciprocal of 0.4.
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Question What is the reciprocal of a squared number? Donagan Top Answerer It is 1 divided by the squared number. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 31 Helpful 49
Question What is the reciprocal of 8? Community Answer 1/8. Since every whole number is invisibly divided by 1 (in this case, 8/1), you just interchange the numerator and denominator, putting the denominator over the numerator and there is your reciprocal, 8/1. In other words, a reciprocal takes a number a/b and turns it into b/a. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 28 Helpful 36
Question What is the reciprocal of a+b? Donagan Top Answerer 1 / (a+b). Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 33 Helpful 48
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A number's negative reciprocal is the same as the regular reciprocal, multiplied by negative one.[11]XResearch source For instance, the negative reciprocal of 3/4 is -4/3. Thanks Helpful 3 Not Helpful 3
The number 0 does not have a reciprocal, since 1 ÷ 0 is undefined.[12]XResearch sourceThanks Helpful 0 Not Helpful 0
The number 1 is its own reciprocal, since 1 ÷ 1 = 1. Thanks Helpful 8 Not Helpful 7
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Co-authored by: David Jia Math Tutor This article was co-authored by David Jia. 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. This article has been viewed 342,580 times. 28 votes - 56% Co-authors: 19Updated: November 23, 2025 Views: 342,580 Categories: Multiplication and Division | FractionsArticle SummaryX
Finding the reciprocal of a fraction is simple. All you have to do is flip the fraction upside-down so that numerator becomes the denominator. For example, the reciprocal of ¾ would be 4/3. You can also find the reciprocal of a whole number. Give the number a denominator of 1, then invert it. For instance, to find the reciprocal of 2, turn it into the improper fraction 2/1, then invert it to get ½. If you’re dealing with a mixed number, things get a little trickier. First, change the mixed number into an improper fraction. To do this, multiply the whole number by the denominator of the fraction, then add the product to the numerator. The resulting number will become the numerator in your improper fraction. Then, invert the fraction to find the reciprocal. For instance, 2 ½ is the same as 5/2, and the reciprocal is 2/5. To find the reciprocal of a decimal, convert the decimal to a fraction first if you can, then invert it. For example, .5 is equal to ½, which would give you a reciprocal of 2/1. If you want to learn when you need to use reciprocals, keep reading the article!Did this summary help you?YesNo
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Download Article Explore this Article methods 1 Finding the Reciprocal of a Fraction or Whole Number 2 Finding the Reciprocal of a Mixed Number 3 Finding the Reciprocal of a Decimal Other Sections Questions & Answers VideoWATCH NOW Tips and Warnings Related Articles References Article Summary Co-authored by David Jia 
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Co-authored by: David Jia Math Tutor This article was co-authored by David Jia. 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. This article has been viewed 342,580 times. 28 votes - 56% Co-authors: 19 Updated: November 23, 2025 Views: 342,580 Categories: Multiplication and Division | Fractions Article SummaryX
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563 
1 Find the reciprocal of a fraction by flipping it. The definition of "reciprocal" is simple. To find the reciprocal of any number, just calculate "1 ÷ (that number)."[1] For a fraction, the reciprocal is just a different fraction, with the numbers "flipped" upside down (inverted).[2] 
2 Write the reciprocal of a whole number as a fraction. Again, the reciprocal of a number is always 1 ÷ (that number).[3] For a whole number, write that as a fraction; there's no point in calculating it out to a decimal. 
1 Identify a mixed number. Mixed numbers are part whole number and part fraction, such as 24/5.[4] There are two steps to finding the reciprocal of a mixed number, explained below. 
2 Change it to an improper fraction.[5] Remember, the number 1 can always be written as (number)/(the same number), and fractions with the same denominator (lower number) can be added together.[6] Here's an example with 24/5: 
3 Flip the fraction. Once the number is written entirely as a fraction, you can find the reciprocal just like you would with any fraction: by flipping it.[7] [8] 
1 Change it to a fraction if possible. You might recognize some common decimal numbers that can easily be turned into fractions.[9] For instance, 0.5 = 1/2, and 0.25 = 1/4. Once in fraction form, just flip the fraction to find the reciprocal. 
2 Write out a division problem. If you can't change it to a fraction, calculate the reciprocal of that number as a division problem: 1 ÷ (the decimal). You can use a calculator to solve this, or continue on to the next step to solve it by hand.[10] 
3 Change the division problem to use whole numbers. The first step to dividing decimals is to move the decimal point until all the numbers involved are whole numbers. As long as you move the decimal point the same number of spaces for both numbers, you'll get the correct answer. 
4 Solve the problem using long division. Use long division techniques to calculate the reciprocal. If you calculate it for 10 ÷ 4, you'll get the answer 2.5, the reciprocal of 0.4. Advertisement 
Donagan Top Answerer It is 1 divided by the squared number. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 31 Helpful 49 
Community Answer 1/8. Since every whole number is invisibly divided by 1 (in this case, 8/1), you just interchange the numerator and denominator, putting the denominator over the numerator and there is your reciprocal, 8/1. In other words, a reciprocal takes a number a/b and turns it into b/a. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 28 Helpful 36 