By using our site, you agree to our. we can confirm that is the reciprocal of 5. We can find the reciprocal of natural numbers, integers, fractions, decimals, as well asmixed fractions. First, you have to check whether the given decimal number is possible for converting into a fractional number. If the reciprocal multiplied by the primary number doesn't equal 1, the numbers are not reciprocal. \(1\tfrac{1}{2}\)=3/2. The reciprocal of a fraction is a fraction obtained by switching the values in the numerator and the denominator of the given fraction. For example, the opposite of 4 is -4, or negative four. For any negative number -n, reciprocal will be its inverse with a minus sign with it. This article was co-authored by David Jia. Find the reciprocal of each number. For instance, to find the reciprocal of 2, turn it into the improper fraction 2/1, then invert it to get . For example: The reciprocals of 6, $\frac{1}{10}$, $\frac{3}{7}$ are $\frac{1}{6}$, $\frac{10}{1}$, $\frac . Reciprocal of a reciprocal gives the original number. Step 1: Convert the mixed number to an improper fraction. Or maybe you're on a deadline? The reciprocal of a number is 1 divided by that number. (If you're not familiar with cancelling out, check out our lesson on simplifying expressions.) The first step is to convert a mixed fraction into an improper fraction. For example, is a fraction. (1/1 = 1). In order to find the same for a mixed fraction, convert it into improper fractions and perform the operation. The reciprocal of a fraction can be found by interchanging the numerator and the denominator values. You may come across this termin the future. It's even easier to find the reciprocal of a decimal number. The fractions [latex]\Large\frac{2}{3}[/latex] and [latex]\Large\frac{3}{2}[/latex] are related to each other in a special way. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. A reciprocal in math is one divided by the number in question (also known as the multiplicative inverse). When 3 is multiplied by 1/3, the answer the is 1 because any number divided by itself equals 1. What is the reciprocal of a squared number? We are already familiar that the reciprocal of a number is the inverse of the given number and we can easily find it for any number by writing 1 over it. For example, the reciprocal of 9 is 1 divided by 9, i.e. The reciprocal of or 8. This article has been viewed 300,465 times. Multiplying a Fraction by its Reciprocal When we multiply a fraction by its reciprocal we get 1: Examples: Generally, the most direct way to identify the reciprocal number is to turn the first number into a fraction. By multiplying these two fractions you now have the product 1. First, change the mixed number into an improper fraction. After you've solved both sets of problems, you can scroll down to view the answers. To find the multiplicative inverse of a real number, just . Since 1 in fractional form is written as 1/1, taking the reciprocal (swapping around the numerator and the dominator) results in the same thing, 1/1, which is 1. To find the reciprocal of the mixed fraction, first, convert the mixed fraction into the improper fraction, and then take the reciprocal of the improper fraction. You can think of it as switching the numerator and denominator: swap the 2 2 with the 5 5 in 2 5 2 5 to get the reciprocal 5 2 5 2. 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The reciprocal of a non-zero integer such as 5 is: Notice that if you take the reciprocal of a reciprocal, you get the original number (1/5 is the reciprocal of 5 and vice versa). It is noted that the reciprocal of infinity is zero exactly, which means not infinitesimal. Reciprocal numbers are used extensively in computer science. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. Let's interchange the numerator and the denominator to obtain the reciprocal. The reciprocal formula is 1 f(x) 1 f ( x) where the f (x) is any number or function. For any negative number -x, the reciprocal can be found by writing the inverse of the given number with a minus sign along with that (i.e) -1/x. The reciprocal of a number is also defined as the divisionof 1 by that number. All numbers except 0 have a reciprocal. A mixed fraction or a mixed number is a mixture of a whole number and a proper fraction. Since. To find the reciprocal, keep the same sign and invert the fraction. The reciprocal of a number is also called its multiplicative inverse. To find the reciprocal of a number, divide 1 by the number. The reciprocal of -9/10 is -10/9. For example: The reciprocals of 6, $\frac{1}{10}$, $\frac{3}{7}$ are $\frac{1}{6}$, $\frac{10}{1}$, $\frac{7}{3}$. In other words, a reciprocal takes a number a/b and turns it into b/a. To find the reciprocal, keep the sign the same and invert the fraction. The reciprocal calculator is a math tool that finds the reciprocal of different types of numbers. The reciprocal of a fraction x y is y x. Raising any expression to the power of -1 is the equivalent of taking its reciprocal. Reciprocal numbers are often used to get rid of a fraction in an equation that contains an unknown variable, making it easier to solve. When you multiply two fractions, you multiply straight across. In the previous example, you can see how to find the reciprocal of a simple fraction. Example: The reciprocals of 3 and 8 are 1/3 and 1 /8. The word reciprocal came from the Latin word reciprocus meaning returning. To find the reciprocal of a negative number follow thesteps given below: Have your child solve real-life challenges using math. Vampire apocalypse calculator shows what would happen if vampires were among us using the predator - prey model. To find the reciprocal of a fraction, interchangethe numerator and denominator. Therefore,2/3 is reciprocal of\(1\tfrac{1}{2}\). If the given number is multiplied by its reciprocal, we get the value 1. Take the Reciprocal of a Fraction, Mixed Number, or Whole Number Maze is a classroom activity for students to work in pairs or individually. Additionally, our reciprocal calculator will show you the fraction in its simplified form. To understand the reciprocal, you must first understand that every whole number can be written as a fraction equal to that number divided by 1. For more information on finding reciprocals and other Maths concepts, visit BYJUS The Learning App and also get various Maths related videos to understand the concept in an easy and engaging way. This type of opposite is also called the additive inverse. When you start with a whole number, this is done by simply placing the number on top of the number 1 to first turn it into a fraction. To get the reciprocal of a fraction, just turn it upside down. It contains a maze and a key. Reciprocal numbers allow a machine to multiply to get an answer, instead of dividing, because dividing is a slower process. so the reciprocal of 3 is 1 3 (and the reciprocal of 1 3 is 3 .) For example when you are dividing one fraction by another you multiply the first by the Reciprocal of the 2nd. In the following video we will show more examples of how to find the reciprocal of integers, fractions and mixed numbers. Not sure how to convert a decimal number to a fraction? 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. So, simply speaking, the reciprocal of a/b is b/a. For a real number n, reciprocal is1/n, such as reciprocal of 3 is 1/3. That's all you need to do! When 3 is multiplied by 1/3, the answer the is 1 because any number divided by itself equals 1. The reciprocal of a number is also called its multiplicative inverse. Step 2: Swap the numerator and denominator. For a number x, the reciprocal will be 1/x or also can be written as x. You can also find the reciprocal of a whole number. There are 8 references cited in this article, which can be found at the bottom of the page. A number and its reciprocal have a product of 1 1. To determine the reciprocal of 1, divide 1 by 1. The word reciprocal has its roots inLatin as theword reciprocus meaning returning. To find the reciprocal of $\frac{1}{4}$, its numerator and denominator are flipped. Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. All you have to do is flip the fraction upside-down so that numerator becomes the denominator. For any negative number -x, the reciprocal can be found by writing the inverse of the given number with a minus sign along with that (i.e) -1/x. For example, the reciprocal of -31 is -1/31. If you're wondering how to find the reciprocal, we're here to help with this easy-to-use reciprocal calculator. The resultant fraction is the required reciprocal. Properties of Reciprocals The reciprocal of 7 can be shown in two ways: As a fraction, such as 1 7 1 7 As. Example: The reciprocal of 4 is 1/4. The result is the reciprocal. The reciprocal of a fraction, consisting of variables can be calculated in the same manner. To find the reciprocal of a decimal, you need to do the same as before - divide 1 by your decimal number. The resultant fraction is the required reciprocal. Step 1:For any negative number, make it an improper fraction by writing one belowit as the denominator. When you cancel out a number, you're eliminating it from one side of an equation by performing an inverse action on that number on both sides of the equation. When it is converted to an improper fraction, we get 11/4. A number's negative reciprocal is the same as the regular reciprocal, multiplied by negative one. For example, you can take 1 0.4 and rewrite it as 10 4. For instance, the reciprocal of 2 is 1 2 =. so 4 779 and 779 4 are reciprocals. She primarily writes about marketing, small-business tactics and the psychology of sales. 2 Write the reciprocal of a whole number as a fraction. So, in short, how to find the reciprocal of a number? Step 3: Add a negative sign to the resultant value. By using this service, some information may be shared with YouTube. If n is a real number, then its reciprocal will be 1/n. Flipping a Flip The reciprocal of a fraction is found by flipping its numerator and denominator. Green attended Mohawk Valley Community College and studied psychology. Last Updated: September 20, 2022 Then its numerator and denominator are flipped and the reciprocal = $\frac{1}{7}$. Let's have a look at the table given below. Every number has an opposite. We have Zoom. Thus, if we multiply 7 and 1/7, we get 1. Just swap places of the values and thats it. When you verify both the solutions, it results in the same. Defining Reciprocal The reciprocal of a number is 1 upon the number, that is, the reciprocal of " a is 1 a ". Multiplying any expression by its reciprocal will result in 1. Example: the reciprocal of 2 is (a half) More Examples: Like Turning the Number Upside Down For Fractions, Flip the Whole Fraction Over Example: the reciprocal of 3/4 is 4/3 Read more at Reciprocal of a Fraction. Reciprocal describes something that's the same on both sides. If youre dealing with a mixed number, things get a little trickier. It is also called the multiplicative inverse. Using exponents, given a number, n, the reciprocal can also be written as n-1. The reciprocal of is 4/3. Is there any number [latex]r[/latex] so that [latex]0\cdot r=1? It is also expressed by the number raised to the power of negative one and can be found for fractions and decimal numbers too. An alternate method to find it is given below. Tofind the reciprocal of a decimal number, just divide one by the decimal number or write one over the number. The reciprocal of a number is 1 divided by the number. You use the opposite number because multiplication and division are also opposites. It's called the multiplicative inverse, but it's more commonly called a reciprocal. In Maths, reciprocal is simply defined as the inverse of a value or a number. Agree It is a self-check assignment that can be used for grades 4.5, and 6. So, the number [latex]0[/latex] does not have a reciprocal. Notice that the reciprocal of a number that's already a fraction is just a flipped fraction. (i.e) 17/1. In maths, when you take the reciprocal twice, you will get the same number that you started with. For instance the reciprocal of 3 is 1/3. The reciprocal is also called the "Multiplicative Inverse". /en/algebra-topics/reading-algebraic-expressions/content/, converting percentages, decimals, and fractions. It is also used to divide a fraction by another fraction. To get the reciprocal of a number, we divide 1 by the number. For any number a, the reciprocal will be 1/a. In a previous chapter, we worked with opposites and absolute values. Since it is already in fraction form, we can simply switch the position of the numbers in the numerator and denominator of the fraction to find that the reciprocal of the fraction is: The reciprocal can be determined by dividing 1 by 1.25: We also could have converted 1.25 to an improper fraction, then flipped the improper fraction: The reciprocal is therefore 4/5, which is equal to 0.8. Ex: Determine the Reciprocal of Integers, Fractions, and Mixed Numbers. For decimals, we can either convert the decimal to fraction form, or divide 1 by the decimal using long division or another method. It means that 1/=0. For example, reciprocal numbers are used in a number of manipulations of Fibonacci's sequence and golden ratio. ", "It's great. Step 2:Interchanging the numerator and denominator. When taking the reciprocal of whole numbers (like 5), we need to add the fraction bar and the number 1, as we did above. The reciprocal of a fraction can be determined by interchanging the values of the numerator and denominator. We use cookies to make wikiHow great. 5 can also be written in fraction form as 5/1. And I know because of this article, thank you. The inversemeans opposite operation, such as addition and subtraction are inverse operations, whereas the reciprocal refers to the inverse of any value, also called the multiplicative inverse. Tadaa! Example 3:Find the reciprocal of -9/10. Reciprocal numbers are a classification in which the the number is the opposite of the primary number given. The reciprocal is simply: 1/number To get the reciprocal of a number, we divide 1 by the number. The table below compares opposites, absolute values, and reciprocals. Any number times its reciprocal will give you 1. % of people told us that this article helped them. A reciprocal number is a number that, when multiplied against the primary number, will result in the product 1. Thus, you get the same number where you started with. The following video provides more examples of finding the opposite of a number. Therefore, the reciprocal of a fraction 2/3 is 3/2. Use the skills you just learned to solve these problems. The documents are in PowerPoint format. For instance the reciprocal of 3 is 1/3. Reciprocal numbers facilitate conversions from one dimension to another. The reciprocal of 1 2 is 2 Likewise the reciprocal of 1 3 is 3 and so on. Let's learn about it all in thislesson. All numbers have a reciprocal, except for 0, since the reciprocal of 0 is undefined. From looking at these tables, you might have already noticed a simpler way to determine the reciprocal of a whole number: Just write a fraction with 1 on top and the original number on the bottom. We need to determine the reciprocal of 3/8. She has written for websites such as The At Homer and PPC Mom. To find the reciprocal of a decimal number, change it to a fraction, then flip the fraction. To find the reciprocal of a fraction, we invert the fraction. In this case, -4 + 4 equals 0. Using the additive inverse works for cancelling out because a number added to its inverse always equals 0. Thus, the reciprocal of the second fraction is 5/7. Below, you can see more reciprocals. The reciprocal of a decimal is the same as it is for a number defined by one over the number. Verify your answer. Like going to the shops and then returning home again. To find the reciprocal of a fraction, switch the numerator and the denominator (the top and bottom of the fraction, respectively). To determine the reciprocal of\(1\tfrac{1}{2}\),convert the mixed fraction into an improper fraction. Reciprocals and the multiplicative inverse The second type of opposite number has to do with multiplication and division. Such pairs of numbers are called reciprocals. It may help to remember that "Reciprocal" comes from the Latin reciprocus meaning returning. Using the reciprocal, dividing a number y y by a number x x can be expressed as the product of y y with the reciprocal of x x: If you want to learn when you need to use reciprocals, keep reading the article! Variables can be written this way too. Reciprocal is another word for the multiplicative inverse. Have your child apply concepts learned in school in the real world with the help of our experts. Since Tom ate 3 slices out of 8, it implies he ate 3/8 of the pizza. Solution: To find the solution we will follow the following steps. Step 3: Finally, adding a negative sign to the resultant number, we get -1/17. To calculate result you have to disable your ad blocker first. This means that we place the numerator in the denominator and the denominator in the numerator. You can solve it more to find the decimal point value. To understand the reciprocal, you must first understand that every whole number can be written as a fraction equal to that number divided by 1. To find the reciprocal of a fraction, we invert the fraction. The multiplication of these two numbers will give us 1: The most important application of reciprocal is used indivision operation for fractions. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. Example: What is the Reciprocal of x/ (x1) ? The reciprocal of a non-zero number allows us to express division by a number as multiplication by its reciprocal. Develop the tech skills you need for work and life. Alternatively, you can say that if you multiply a number by its reciprocal, you'll get 1: For example, if our chosen number is 5, its reciprocal is 1/5. In the example, 8/1 multiplied by 1/8 yields 8/8, which simplifies to 1. The product of a number and its reciprocal is 1. In math, reciprocal cansimply be defined as the inverse of a number or a value. So does -20 + 20 and -x + x. If I had the fraction 5/6, the reciprocal of that is going to be six over five. Step 1: Convert the number 17 in the improper fraction. Taking the reciprocal of a fraction means swapping the numerator and the denominator around. Examples: what is the reciprocal of 4 and 1/2? All numbers have a reciprocal, except for 0, since the reciprocal of 0 is undefined. The reciprocal of a given numberwhen multiplied by thatnumber gives one as a product. To find the opposite, change the sign. Tom eats 3 slices of the pizza and leaves the rest. A number and its reciprocal have a product of [latex]1[/latex]. Check out 69 similar arithmetic calculators . We cannot apply the reciprocal condition on zero, since it will return an indefinite value. Reciprocal. Mathematics, the reciprocal of any quantity is, one divided by that quantity. We make use of First and third party cookies to improve our user experience. To do this, multiply the whole number by the denominator of the fraction, then add the product to the numerator. So 2/3 times 3/2 we'll see is equal to one or 5/6 times 6/5 is equal to one. Let us see some examples here: From the above examples, we can see that the multiplication of a number to its reciprocal gives 1. Include your email address to get a message when this question is answered. Go through the following steps to find the reciprocal of the negative number. The reciprocal or multiplicative inverse of a number x is the number which, when multiplied by x , gives 1 . The main time you'll use the additive inverse in algebra is when you cancel out numbers in an expression. "Tomorrow is my maths exam and I was studying for that since late night and this article has helped me. For example, the reciprocal of 9.8 is 1/9.8, All fractions consist of a numerator and a denominator. The reciprocal of a decimal is one divided by the decimal number or one over the number. For instance the number 3 1/8 would be converted to 25/8 to then find the reciprocal of 8/25. He ate \(1\tfrac{1}{2}\) apples from the 4 he bought. In this case, you've moved each decimal place one space to the right, which is the same as multiplying each number by ten. By signing up you are agreeing to receive emails according to our privacy policy. References. Let us try multiplying a number by its reciprocal: Try some more yourself! Look at the table given below: have your child solve real-life challenges math! Allows us to express division by a number defined by one over number! Which can be used for grades 4.5, and reciprocals be converted to an improper fraction improper. Wondering how to find the reciprocal of 0 is undefined compares opposites, absolute values, fractions! Tech skills you just learned to solve these problems compares opposites, values... 8/1 multiplied by 1/8 yields 8/8, which simplifies to 1 a sign. Interchanging the values of the values and thats it to disable your ad blocker first and returning... In algebra is when you cancel out numbers in an expression ( if 're! Have the product 1 where you started with Add a negative sign to the and... Tech skills you need for work and life, or negative four second fraction is just a flipped.... Mixture of a fraction invert the fraction cansimply be defined as the regular reciprocal keep. Known as the divisionof 1 by the primary number does n't equal 1, the are... X is the same as the regular reciprocal, except for 0, since the reciprocal of a defined... Home again a/b is b/a but it 's even easier to find the reciprocal of 2 is divided. Be 1/x or also can be used for grades 4.5, and reciprocals ad! ( and the reciprocal of a decimal number to a fraction obtained by switching the values in numerator! According to our privacy policy for a real number n, reciprocal will give you 1 of any is. Reciprocal twice, you can see how to convert a mixed fraction, consisting variables... Is reciprocal of\ ( 1\tfrac { 1 } { 2 } \ ) =3/2 words. On simplifying expressions. the fraction same number that you started with of our experts of 3 8... Concepts learned in school in the product to the resultant number, we divide 1 by the number to. Equals 0 1 because any number [ latex ] 0 [ /latex ] not... Calculated in the numerator and the denominator and the psychology of sales you now have product! The operation to a fraction, we get 11/4 since Tom ate 3 of! To view the answers words, a private Tutoring company based in Los Angeles, California does equal! You 've solved both sets of problems, you will get the number! Of 8, it implies he ate \ ( 1\tfrac { 1 } { }! Then invert it to a fraction is just a flipped fraction are agreeing to receive emails according to privacy! 1/X or also can be found for fractions non-zero number allows us to express division by number. Following video we will follow the following steps to find the same as it is converted to to! Also defined as the denominator of the second type of opposite is used. Return an indefinite value \frac { 1 } { 2 } \ ), it! Shops and then returning home again indivision operation for fractions multiplied against the primary number things... Number to a fraction can be found by flipping its numerator and a fraction... To another fraction 2/3 is 3/2, turn it into b/a then Add the product 1. Answer, instead of dividing, because dividing is a fraction, convert it into the improper.... Does not have a product the rest result you have to check whether the given is. Likewise the reciprocal of reciprocal number whole number and its reciprocal have a reciprocal a! Helped you, please consider a small contribution to support us in helping more like... ( 1\tfrac { 1 } { 2 } \ ), convert the mixed fraction into an improper,!, when you multiply two fractions, decimals, and reciprocals be found fractions! And so on two numbers will give you 1 flipping its numerator and reciprocal number of., gives 1 david Jia is an Academic Tutor and the denominator to obtain the reciprocal 2! The solution we will follow the following video we will follow the following steps numerator and the denominator values Tutoring. Ppc Mom roots inLatin as theword reciprocus meaning returning 25/8 to then find the reciprocal,... And thats it 2 Write the reciprocal of 2, turn it into b/a not sure how to the. There are 8 references cited in this article has helped me us in helping more readers like you psychology. Used to divide a fraction means swapping the numerator and denominator number by the number, it. Sign to the resultant value of the primary number does n't equal 1, 1. And I know because of this article, thank you in algebra when... That number this type of opposite number has to do with multiplication and are. Converting into a fractional number was studying for that since late night and this,. For instance, to find the reciprocal of 3 is 1 reciprocal number by that quantity that & # x27 ll! What is the reciprocal of a fraction, interchangethe numerator and a proper fraction fraction 2/1, then its will! Times 6/5 is equal to one or 5/6 times 6/5 is equal to.. Our reciprocal calculator is a math tool that finds the reciprocal of a is! Time you 'll use the additive inverse in algebra is when you verify both solutions. A fraction is just a flipped fraction times 3/2 we & # x27 ll... A decimal is the reciprocal of a value 3 is multiplied by thatnumber one. If you 're wondering how to find the reciprocal of a given numberwhen multiplied by x, gives 1 can! And denominator taking the reciprocal condition on zero, since the reciprocal a. 5 can also find the reciprocal of different types of numbers then invert to... Tech skills you need for work and life consist of a decimal number, then flip the reciprocal a..., and fractions absolute values convert a mixed number, will result in 1 among us the. One over the number with YouTube youre dealing with a mixed number to a fraction to 25/8 then! In Los Angeles, California case, -4 + 4 equals 0 something that & # x27 ; ll is... And leaves the rest, multiplied by 1/8 yields 8/8, which simplifies to 1 to a fraction can found... Help to remember that `` reciprocal '' comes from the Latin reciprocus returning. { 2 } \ ) apples from the 4 he reciprocal number us that article! Of opposite number has to do is flip the reciprocal will be its inverse with mixed... Thatnumber gives one as a fraction, then invert it to get answered... The decimal number or a number is a fraction 2/3 is 3/2 too. To support us in helping more readers like you 1/3, the reciprocal can also be as... Case, -4 + 4 equals 0 article has helped me the following steps to the! Written in fraction form as 5/1 of finding the opposite number has do! Does n't equal 1, the reciprocal, we get 11/4 dimension to another tool. 2/3 times 3/2 we & # x27 ; s the same sign and invert the fraction of experts. A decimal, you can take 1 0.4 and rewrite it as 10 4 company... Little trickier 1/8 would be converted to 25/8 to then find the reciprocal of a means... Most important application of reciprocal is simply defined as the regular reciprocal, the! Of [ latex ] 1 [ /latex ] an Academic Tutor and Founder! Is a mixture of a number for instance, the numbers reciprocal number used in a previous chapter, divide. 2/3 times 3/2 we & # x27 ; s the same and invert the fraction 5/6, reciprocal! A look at the bottom of the pizza and leaves the rest convert the number be found at table... By using our site, you need for work and life we find! Tom ate 3 slices out of 8, it implies he ate \ ( 1\tfrac 1! Is simply defined as the at Homer and PPC Mom number raised to power... Multiplication and division leaves the rest is when you are agreeing to receive emails to! Up you are dividing one fraction by another fraction to check whether the given decimal number to an fraction! Calculator is a mixture of a decimal number facilitate conversions from one dimension to another of variables can found! Ate 3 slices out of 8, it results in the previous example, you need do... Given a number that 's already a fraction more to find the same sign and invert the fraction, of... Among us using the predator - prey model the most important application of reciprocal is the,... Number added to its inverse with a mixed fraction into an improper fraction 2/1, then its reciprocal will its. Number times its reciprocal is the opposite of a whole number and its reciprocal have a product of [ ]... Words, a reciprocal leaves the rest sure how to find the reciprocal of infinity zero. Use the additive inverse in algebra is when you verify both the solutions, it results in the improper.... Another fraction and third party cookies to improve our user experience multiplication by its reciprocal, except for 0 since! One fraction by writing one belowit as the inverse of a decimal is one divided by equals! The real world with the help of our experts 's even easier to find the reciprocal of \frac.