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Reciprocal Definition Illustrated Mathematics Dictionary

The simple rule of the division is “Multiply the dividend by the reciprocal of the divisor”, simply you need to invert the divisor and multiply It by the dividend. Choose the input type from integer, fraction, or mixed number, enter the values in the calculator, and find the reciprocal in seconds. The reciprocal of a fraction is simply the fraction obtained by interchanging the numerator and the denominator.

Definition of Reciprocal in Math

The reciprocal of a decimal can be found by converting the decimal to a fraction and then taking its reciprocal. Now, swap the numerator and denominator to find the reciprocal. The reciprocal of a fraction is a value which, when multiplied with the given fraction, results in 1. A reciprocal of any non-zero number is simply written as 1 divided by that number. The reciprocal of a fraction is a fraction obtained by switching the values in the numerator and the denominator of the given fraction. You find the inverse of a fraction by exchanging the numerator (top number) with the denominator (bottom number) – taking the reciprocal of the fraction.

Reciprocal: Definition, Rules, Solved Examples, Facts, FAQs

For example, the reciprocal of 9 is 1 divided by 9, i.e. 1/9. Now, if we multiply a number by its reciprocal, it gives a value equal to 1. 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.

Reciprocal of Mixed Fraction:

  1. According to the reciprocal definition in math, the reciprocal of a number is defined as the expression which when multiplied by the number gives the product as 1.
  2. The following video will show how to find the reciprocal of fractions.
  3. In mathematics, it’s used as a noun in a more specific way to refer to the number by which another number must be multiplied to get a result of one.
  4. However, when you divide by a fraction you flip the fraction over so the numerator is on the bottom and the denominator is on top.

It is also expressed by the number raised to the power of negative one and can be found for fractions and decimal numbers too. 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. You can perform the manual calculations as we have done above, or for convenience, you can use the reciprocal fraction calculator.


The reciprocal of a non-zero number allows us to express division by a number as multiplication by its reciprocal. Tom eats 3 slices of the pizza and leaves the rest. Determine the reciprocal of the quantity of the pizza left by Tom. Using the additive inverse works for cancelling out because a number added to its inverse always equals 0. In fact, any number you can come up with has an additive inverse.

In math, the reciprocal of any quantity can be defined as 1 divided by that quantity. Notice that the reciprocal of a number that’s already a fraction is just a flipped fraction. Reciprocal actions are often those that return the furniture and fixtures in accounting favor. Reciprocal relationships are based on alternating actions or a mutual exchange of something. In personal relationships, this often involves kind gestures and displays of emotion that are done in response to similar actions.

Superb Owl Words

There is no value or number which, when multiplied with 0, results in 1. Taking the reciprocal of a fraction means swapping the numerator and the denominator around. The number zero (0) does not have a reciprocal. Because, if any reciprocal number is multiplied by 0, it will not give the product as 1.

This video shows how to find the reciprocal of a whole number. The following diagram shows how to get the reciprocal of a fraction, whole number and mixed number. Scroll down the page for more examples and solutions on using reciprocals. A reciprocal in math is one divided by the number in question (also known as the multiplicative inverse).

The other name of reciprocal is multiplicative inverse. Inverse means opposite and reciprocal means https://accounting-services.net/ equality. A reciprocal is a type of inverse but inverse is not necessarily a reciprocal.

For any number ‘a’, the reciprocal will be 1/a. If the given number is multiplied by its reciprocal, we get the value 1. Using exponents, given a number, n, the reciprocal can also be written as n-1. Raising any expression to the power of -1 is the equivalent of taking its reciprocal. Reciprocal is another word for the multiplicative inverse.

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