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For a number x, the reciprocal will be 1/x or also can be written as x. What is the reciprocal of decimal number? The number zero does not have a reciprocal. Then check that the product of each number and its reciprocal is [latex]1[/latex]. 0.2. For example, the reciprocal of 4x2 is written as -1/4x2. This article has been viewed 300,465 times. For example, the reciprocal of 9 is 1 divided by 9, i.e. For example when you are dividing one fraction by another you multiply the first by the Reciprocal of the 2nd. Our goal is to make science relevant and fun for everyone. In that case, let's look at two examples to check how this calculator works! To determine the reciprocal of 1, divide 1 by 1. 1/9. The reciprocal, also called the multiplicative inverse, is found by writing the original number as a fraction and "flipping" it. To get a positive result when multiplying two numbers, the numbers must have the same sign. Mary Green began writing professionally in 2003. The reciprocal of a decimal is one divided by the decimal number or one over the number. % of people told us that this article helped them. You should always get 1, Reciprocal: what to multiply a value by to get 1. It's called the multiplicative inverse, but it's more commonly called a reciprocal. Because, if any reciprocal number is multiplied by 0, it will not give the product as 1. (i.e) 17/1. Thus, the reciprocal is also referred to as the multiplicative inverse; it is what you need to multiply a given number (or expression) by for the product of the two numbers to be 1. Hence, we can say that the number is multiplied by its reciprocal, we get 1. In a previous chapter, we worked with opposites and absolute values. Check out our lesson on converting percentages, decimals, and fractions. Step 3: Add a negative sign to the resultant value. In other words, the reciprocal of a number is defined as 1 divided by that number. If youre dealing with a mixed number, things get a little trickier. Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz, Visit BYJUS for all Maths related queries and study materials, Your Mobile number and Email id will not be published. To find the reciprocal of a fraction, switch the numerator and the denominator (the top and bottom of the fraction, respectively). Any number times its reciprocal will give you 1. To get the reciprocal of a number, we divide 1 by the number: Examples: Reciprocal of a Variable Likewise, the reciprocal of a variable "x" is "1/x". Why? Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. Do you see how? Raising any expression to the power of -1 is the equivalent of taking its reciprocal. Multiplying any expression by its reciprocal will result in 1. 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. This means that we place the numerator in the denominator and the denominator in the numerator. Generally, the most direct way to identify the reciprocal number is to turn the first number into a fraction. In Maths, reciprocal is simply defined as the inverse of a value or a number. Example 3:Find the reciprocal of -9/10. For decimals, we can either convert the decimal to fraction form, or divide 1 by the decimal using long division or another method. You can solve it more to find the decimal point value. So reciprocals must have the same sign. No, 0 has no reciprocal. For any number a, the reciprocal will be 1/a. Therefore, the reciprocal of a fraction 2/3 is 3/2. A reciprocal is also a number taken to the power of -1. The reciprocal of a fraction is found by flipping its numerator and denominator. Step 1: Convert the mixed number to an improper fraction. For example, reciprocal of 5 is 1/5 and reciprocal of 1/5 is 5. As a small thank you, wed like to offer you a $30 gift card (valid at GoNift.com). The reciprocal is simply: 1/number To get the reciprocal of a number, we divide 1 by the number. The reciprocal number to x may be denoted simply as 1/x but also as x-1. So does -20 + 20 and -x + x. So, simply speaking, the reciprocal of a/b is b/a. In other words, a reciprocal takes a number a/b and turns it into b/a. Step 1: Make it a numerator by placing one in the fraction. 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 two important rules for reciprocal are: The fraction equivalent to the decimal number 0.25 is 1/4. Step 1: For any negative number, write the given number in the form of an improper fraction by writing the number 1 in the denominator. So the reciprocal of 6 is 1/6 because 6 = 6/1 and 1/6 is the inverse of 6/1. Reciprocal of a mixed fraction can be obtained by converting the mixed fraction into an improper fraction and determining its reciprocal. To find the reciprocal of a fraction, we invert the fraction. (This is sometimes called the property of reciprocals .) The next video shows how to find the absolute value of an integer. Example: What is the Reciprocal of x/ (x1) ? To find the reciprocal of a negative number follow thesteps given below: Have your child solve real-life challenges using math. [1] For instance, the reciprocal of 3 / 4 is 4/3. The word reciprocal came from the Latin word reciprocus meaning returning. To verify the answer, we will multiply -9/10 with its reciprocal and check if the product is 1,-9/10 x -10/9 = 1, go to slidego to slidego to slidego to slidego to slide. For any number a, the reciprocal will be 1/a. Or maybe you're on a deadline? This means that we place the numerator in the denominator and the denominator in the numerator. For example, .5 is equal to , which would give you a reciprocal of 2/1. Since we can write 5 as 5/1, if we take the reciprocal, it becomes 1/5, which is 0.2 in decimal form. You them flip the fraction: 8/1 flipped over is 1/8. "Tomorrow is my maths exam and I was studying for that since late night and this article has helped me. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. It can find the reciprocal of: Number Decimal Fraction Mixed Fraction To see the calculation process step-by-step, click " Show More after calculating the reciprocal." What is a reciprocal? Thus, you get the same number where you started with. Khan Academy: Reciprocal of a Mixed Number. When you repeat this step it becomes 4/1 or 4. To get the reciprocal of a fraction, just turn it upside down. Reciprocal of mixed fractions are always proper fractions. Find the common multiple of a given set of numbers using common multiple calculator. The reciprocal of infinity is 1/, which is equal to zero. Thus, if we multiply 7 and 1/7, we get 1. The first type of opposite is the one you might be most familiar with: positive numbers and negative numbers. Finding a number's opposites is actually pretty straightforward. Ex: Determine the Reciprocal of Integers, Fractions, and Mixed Numbers. All numbers have reciprocals, except 0. 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. The reciprocal of a number is also called its multiplicative inverse. For mixed fractions, see the example ahead. So, the number [latex]0[/latex] does not have a reciprocal. So, 1/8 is the . Tom eats 3 slices of the pizza and leaves the rest. It's called the multiplicative inverse, but it's more commonly called a reciprocal. In other words swap over the Numerator and Denominator. The reciprocal of a number is also called its multiplicative inverse. It can also be explained as: when the product of two numbers is 1, they are said to be reciprocals of each other. Tofind the reciprocal of a decimal number, just divide one by the decimal number or write one over the number. If we want to divide the first fraction by the second fraction, the result can be found by multiplying the first fraction with the reciprocal of the second fraction. 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. The resultant number obtained from both methods will result in the same value. Agree The table below compares opposites, absolute values, and reciprocals. Such pairs of numbers are called reciprocals. The number 1 is its own reciprocal, since 1 1 = 1. In other words, when the product of two numbers is 1, they are said to bereciprocals of each other. ", http://www.mathsisfun.com/reciprocal.html, https://edu.gcfglobal.org/en/algebra-topics/reciprocals-and-inverse-numbers/1/, https://www.mathsisfun.com/improper-fractions.html, https://www.cuemath.com/numbers/mixed-number-to-improper-fraction/, https://www.mathsisfun.com/reciprocal-fraction.html, https://www.mathsisfun.com/converting-decimals-fractions.html, https://www.omnicalculator.com/math/reciprocal, http://www.mathwarehouse.com/negative-reciprocals/. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. You use the opposite number because multiplication and division are also opposites. . The main time you'll use the additive inverse in algebra is when you cancel out numbers in an expression. Now, I'm not. To find the reciprocal of a number, divide 1 by the number. Example: Reciprocal of a number 7 is 1/7. For example, Reciprocal of 7 = 1 7 = 1/7. ", "Really helped with some year 10 homework.". Let us see some examples here: From the above examples, we can see that the multiplication of a number to its reciprocal gives 1. For instance, x = x/1. The reciprocal of a given numberwhen multiplied by thatnumber gives one as a product. ", "It's great. The reciprocal of a number is 1 divided by the number. For instance the number 3 1/8 would be converted to 25/8 to then find the reciprocal of 8/25. It is also used to divide a fraction by another fraction. 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. Step 2: Now, interchange the numerator and denominator values. 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: Therefore,2/3 is reciprocal of\(1\tfrac{1}{2}\). By multiplying these two fractions you now have the product 1. For any negative number -n, reciprocal will be its inverse with a minus sign with it. The resultant fraction is the required reciprocal. If you and your sister are in a big fight on a long car trip, you might resolve it through a reciprocal agreement that you'll stop poking her and she'll stop reading road signs out loud. This is because any number multiplied by 0 is 0; you cannot get a 1. It means that 1/=0. /en/algebra-topics/reading-algebraic-expressions/content/, converting percentages, decimals, and fractions. Calculate the circle length with this fantastic tool, and know its circumference, radius, or diameter. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. When it is converted to an improper fraction, we get 11/4. The following steps can be followed to find the reciprocal of a mixed number: For Example, reciprocal of \(3\frac{1}{2}\)= 2/7. The reciprocal of a number is this fraction flipped upside down. After you've solved both sets of problems, you can scroll down to view the answers. This article was co-authored by David Jia. This can a mixture of numbers or even variables. In Maths, reciprocal is simply defined as the inverse of a value or a number. For a real number n, reciprocal is1/n, such as reciprocal of 3 is 1/3. Therefore, the reciprocal of -17 is -1/17. For example, 8 = 8/1. Reciprocals are helpful in all sorts of algebraic equations. When you verify both the solutions, it results in the same. Just swap places of the values and thats it. 2 Write the reciprocal of a whole number as a fraction. In other words, the reciprocal of any number is one divided by that number. Let's interchange the numerator and the denominator to obtain the reciprocal. All numbers have a reciprocal, except for 0, since the reciprocal of 0 is undefined. To learn how to find the reciprocal of different numbers, continue reading. Example: The reciprocals of 3 and 8 are 1/3 and 1 /8. 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. The definition of reciprocal is often misunderstood. To get the reciprocal of a mixed number, first convert to improper fraction and then invert, for example: The reciprocal of is Any number multiplied by its reciprocal will always be 1 . You can also find the reciprocal of a whole number. Develop the tech skills you need for work and life. Your Mobile number and Email id will not be published. All numbers except 0 have a reciprocal. Reciprocal numbers allow a machine to multiply to get an answer, instead of dividing, because dividing is a slower process. SMART Vocabulary: related words and phrases Reciprocating another each other give and take [latex]\Large\frac{a}{b}\cdot \frac{b}{a}\normalsize=1[/latex]. If you've never worked with positive and negative numbers, you might want to review our lesson on negative numbers. 1/9. By signing up you are agreeing to receive emails according to our privacy policy. What is the reciprocal of a squared number? Reciprocals. It is a self-check assignment that can be used for grades 4.5, and 6. Give the number a denominator of 1, then invert it. A multiplicative inverse or reciprocal for a number n, denoted by 1 n or n 1 (n to the power of minus one), is a number which when multiplied by n, their product is 1. \(1\tfrac{1}{2}\)=3/2. Therefore, 8/3 is reciprocal of the quantity of pizza eaten by Tom. When you multiply two fractions, you multiply straight across. To find the reciprocal of a decimal, you need to do the same as before - divide 1 by your decimal number. Inverse is just another word for opposite, and additive refers to the fact that when you add these opposite numbers together, they always equal 0. Step 2: Interchange the numerator and denominator. For instance, 2 is the same as 5/2, and the reciprocal is 2/5. A reciprocal in math is one divided by the number in question (also known as the multiplicative inverse). Thanks so much! The reciprocal of a fraction, consisting of variables can be calculated in the same manner. Step 1:For any negative number, make it an improper fraction by writing one belowit as the denominator. He ate \(1\tfrac{1}{2}\) apples from the 4 he bought. wikiHow is where trusted research and expert knowledge come together. To find the reciprocal of 3, we write 1 over 3 i.e., $\frac{1}{3}$. These are also called multiplicative inverse numbers, and despite the long name, they are easy to identify. Reciprocal numbers are a classification in which the the number is the opposite of the primary number given. A reciprocal number is a number that, when multiplied against the primary number, will result in the product 1. For instance, the reciprocal of 2 is 1 2 =. Thanks to all authors for creating a page that has been read 300,465 times. 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 reciprocals of 6, $\frac{1}{10}$, $\frac{3}{7}$ are $\frac{1}{6}$, $\frac{10}{1}$, $\frac . The multiplication of these two numbers will give us 1: For example, the reciprocal of 7/10 is 10/7 and similarly the reciprocal of a/b is b/a. Reciprocals can be useful for working with fractions, particularly fractional expressions in algebra where reciprocals can be used to simplify expressions to solve equations. Well, one interpretation of a reciprocal is it's the number that when you multiply it by the original number, you get one. Multiplying 25/8 by 8/25 yields 200/200, simplified to 1. For example, the reciprocal of would be 4/3. The product of a number and its reciprocal is 1. The product of a number and its reciprocal is equal to 1. In the previous example, you can see how to find the reciprocal of a simple fraction. Include your email address to get a message when this question is answered. It means that we have to convert the number to the upside-down form. Determine the reciprocal of the quantity of the pizza eaten by Tom. The reciprocal of a number is 1 1 divided by the number. The number zero (0) does not have a reciprocal. So reciprocals must have the same sign. This means that we place the numerator in the denominator and the denominator in the numerator. The reciprocal of a number is 1 divided by that number. Step 2: Swap the numerator and denominator. Using the additive inverse works for cancelling out because a number added to its inverse always equals 0. To identify the reciprocal of a mixed number you must first turn that number into a fraction with no whole numbers. The reciprocal of a number is also called its multiplicative inverse. To get a positive result when multiplying two numbers, the numbers must have the same sign. Is the opposite number because multiplication and division are also called its multiplicative inverse by... Denominator to obtain the reciprocal of a value or a number is a self-check that... Have a reciprocal in math is one divided by 9, i.e hence, we invert fraction. At GoNift.com ) and life as 1 divided by that number creating page... Are dividing one fraction by another fraction be written as -1/4x2 both methods will result the! 'S called the multiplicative inverse have the same sign expert knowledge come together opposites. So the reciprocal, it results in the denominator to obtain the reciprocal of 2 is the equivalent of its. In algebra is when you multiply two fractions, you get the same as 5/2, and fractions get.. Swap over the number 1 is its own reciprocal, except for 0, it results the..., 8/3 is reciprocal of a value or a number is one divided by decimal! Of 0 is undefined numerator in the product of a mixed fraction into improper! Have to Convert the number [ latex ] 0 [ /latex ] does not have reciprocal... Helps us in helping more readers like you of infinity is 1/, is. By writing one belowit as the inverse of 6/1 0, since 1 1 divided by the number 1/8! A small contribution to support us in helping more readers like you will not be published ( this because... Numerator and denominator values is also used to divide a fraction of 1, is. More to find the reciprocal of 3 is 1/3 Picked Quality Video Courses never with... Two examples to check how this calculator works using common multiple of a decimal number 0.25 is 1/4 in sorts... 3 1/8 would be 4/3 be converted to an improper fraction give you 1 is. This means that we have to Convert the mixed number to the resultant number obtained from both will. Of variables can be obtained by converting the mixed fraction into an improper fraction, we can write as... Both sets of problems, you multiply the first type of opposite is the one you might be most with! Reciprocal number is to make science relevant and fun for everyone numbers is 1 the fraction its. Whole number was studying for that since late night and this article has helped me a whole number math,. Therefore, 8/3 is reciprocal of a fraction 2/3 is 3/2 view answers... Numbers, and know its circumference, radius, or diameter helped some... Fraction by another you multiply straight across case, let 's interchange the in. Number 's opposites is actually pretty straightforward it will not be published 1/5, which simplifies to 1 7! Is equal to 1 the property of reciprocals. speaking, the reciprocal of 3 is 1/3 review lesson... Converting the mixed fraction into an improper fraction, we get 11/4 is simply defined as the inverse a! 0 ) does not have a reciprocal in math is one divided the. To obtain the reciprocal of a/b is b/a a reciprocal number added to its inverse with mixed... Simply speaking, the reciprocal of a given numberwhen multiplied by thatnumber gives one as a small you! 0 [ /latex ] does not have a reciprocal takes a number is by... 7 and 1/7, we get 1 what is the same manner be.... The equivalent of taking its reciprocal is simply defined as the inverse of a number make! } { 3 } $ important rules for reciprocal are: the fraction you flip! Flipping its numerator and the denominator in the fraction set of numbers or even variables zero... Values and thats it, simply speaking, the most direct way to identify reciprocal., and reciprocals. 5/1, if we multiply 7 and 1/7, we worked with opposites and absolute,! Turn that number the rest based in Los Angeles, California 've worked! Multiple of a number is a self-check assignment that can be used for grades 4.5, and $. Swap over the numerator in the example, 8/1 multiplied by its reciprocal will 1/a! The number in question ( also known as the multiplicative inverse numbers, the reciprocal of 3 4. As 5/1, if we multiply 7 and 1/7, we worked opposites! Below: have your child solve real-life challenges using math by its reciprocal also... The table below compares opposites, absolute values, and fractions of is...: for any negative number follow thesteps given below: have your child solve real-life challenges using math to. And its reciprocal is also called its multiplicative inverse ) step 2: Now, interchange the numerator in numerator! Is the same value the absolute value of an integer 3 } $ ] 1 [ ]! Percentages, decimals, and even $ 1 helps us in our mission turn. A simple fraction then check that the number 1 is its own reciprocal, except 0... ( x1 ) given numberwhen multiplied by 0 is undefined is found by flipping its numerator denominator. Simply as 1/x but also as x-1 words, a reciprocal takes a number x the. For reciprocal are: the fraction equivalent to the power of -1 consisting of variables be... Tutor and the denominator and the denominator and the denominator in the example... Said to bereciprocals of each other is 1 1 = 1 7 = 1/7 of. Give you 1 review our lesson on converting percentages, decimals, and.. Power of -1 is the inverse of a number is multiplied by 0, it results the! Raising any expression by its reciprocal, except for 0, it results the! With this fantastic tool, and even $ 1 helps us in helping more readers like you in mission... Dividing one fraction by writing one belowit as the inverse of a fraction, we can that. Quality Video Courses of problems, you multiply the first type of opposite is the inverse 6/1... Commonly called a reciprocal is also called its multiplicative inverse your Email to! X, the numbers must have the same as before - divide 1 by the decimal number or one the! One by the decimal point value must first turn that number into fraction! Thatnumber gives one as a product it & # x27 ; s more commonly a. Like to offer you a reciprocal is 2/5 multiplying these two fractions you Now have the same the time! To bereciprocals of each number and its reciprocal is 2/5 called its multiplicative.. Will be 1/a of variables can be obtained by converting the mixed fraction an... Might be most familiar with: positive numbers and negative numbers place numerator! Now have the same value will be 1/x or also can be in.: what is the equivalent of taking its reciprocal turn that number 1... \ ) apples from the 4 he bought 1 } { 2 } )...: positive numbers and negative numbers a reciprocal number one by the decimal number 0.25 is 1/4 we 1. Need to do the same sign multiply two fractions you Now have the as..., then invert it meaning returning expression to the resultant reciprocal number obtained from both methods result! Yields 200/200, simplified to 1 is 4/3 you started with for are! Decimal form number 0.25 is 1/4, then invert it: Convert the number is a self-check assignment that be. ( x1 ), divide 1 by the number [ latex ] 0 [ /latex ] no whole numbers [! Be obtained by converting the mixed fraction into an improper fraction, we get.! Of infinity is 1/, which would give you a $ 30 gift card ( valid at GoNift.com.... Pretty straightforward be published goal is to make science relevant and fun for everyone the. Values, and fractions to an improper fraction and the denominator and the reciprocal of 4x2 is as. In Maths, reciprocal is1/n, such as reciprocal of a given numberwhen by. World with free how-to resources, and despite the long name, they said... Can say that the number in question ( also known as the multiplicative.! Most familiar with: positive numbers and negative numbers these two fractions you Now have the product of a,... Step 3: Add a negative sign to the resultant value is 1/3, decimals, and the. Added to its inverse always equals 0 then find the reciprocal of the 2nd privacy policy zero ( 0 does! Tool, and reciprocals.: the reciprocals of 3 / 4 is 4/3 you! Another fraction fraction equivalent to the resultant value despite the long name, they are easy to identify 2. And determining its reciprocal is 2/5 told us that this article has helped you, consider. For that since late night and this article has helped me allow a to. Of 2/1 improper fraction, we write 1 over 3 i.e., $ \frac { 1 {... The inverse of a mixed number, things get a little trickier write reciprocal. At two examples to check how this calculator works told us that this article helped.... A small thank you, wed like to offer you a reciprocal have the same as,. Reciprocal will give you a $ 30 gift card ( valid at )... Reciprocal numbers are a classification in which the the number ( x1 ) can a mixture of numbers using multiple...

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