We can find the reciprocal of any number, but we cannot apply the reciprocal condition on zero, since it will give an indefinite value. The fraction equivalent to the decimal number 0.25 is 1/4. Therefore, we can have a reciprocal for all real numbers but not for zero. To find the reciprocal of a Mixed Fraction, we first convert it to an Improper Fraction, then turn that upside down. To get the reciprocal of a fraction, just turn it upside down. In other words swap over the Numerator and Denominator.

• In a previous chapter, we worked with opposites and absolute values.
• If you want then you can solve to get a decimal number value in step 3.
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• In other words, if you have a number ‘a,’ its reciprocal is denoted as ‘1/a’.

If n is a real number, then its reciprocal will be 1/n. It means that we have to convert the number to the upside-down form. 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. Finding the reciprocal of fractions is a little different than whole numbers and negative numbers as there are numerators and denominators in the fractions.

Learning Outcomes

The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. 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. So this way by the multiplicative inverse property we can find the reciprocal https://kelleysbookkeeping.com/ of whole number. Similar to the reciprocal of a whole number we can also find the reciprocal of a negative number. To find the reciprocal of the negative number, we divide 1 by the negative number and simplify it further. The reciprocal of a number is also known as the multiplicative inverse of that number.

• In the following video we will show more examples of how to find the reciprocal of integers, fractions and mixed numbers.
• Reciprocal of a Fraction is the fraction obtained by interchanging the numerator and denominator of the given fraction.
• Using the additive inverse works for cancelling out because a number added to its inverse always equals 0.
• It is important to leave space between the whole number and the fraction part of a mixed number.

Hence, it returns its original value, if we take the reciprocal of an inverted number. In this article, we are going to learn the definition of reciprocal, how to find the reciprocal of numbers, fractions and decimals with many examples. The second type of https://business-accounting.net/ opposite number has to do with multiplication and division. It’s called the multiplicative inverse, but it’s more commonly called a reciprocal. If you’re wondering how to find the reciprocal, we’re here to help with this easy-to-use reciprocal calculator.

Practice Questions on Reciprocal Function

The reciprocal functions can be easily identified with the following properties. A negative reciprocal is a kind of reciprocal that has a negative sign before the number. The negative reciprocal is specially designed to find the reciprocal of negative numbers and fractions.

What Is the End Behavior of a Reciprocal Function?

Reciprocal math is simply math that involves the use of reciprocals, which are fractions that are flipped over. This video shows how to use reciprocals when dividing by a fraction and when solving an algebraic equation with a coefficient that is fraction. Since finding the reciprocal of a real number is reduced to division, the result of such a division can be either a terminating decimal or a repeating decimal. If, when dividing, you end up with a remainder of zero, then you have a terminating decimal.

Which of the following is the reciprocal of $21\times5$?

Notice that the reciprocal of a number that’s already a fraction is just a flipped fraction. 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.

Definition of Reciprocal in Math

The reciprocal is defined as the multiplicative inverse of a number. In other words, the reciprocal of a number is defined as 1 divided by that number. The product of a given number https://quick-bookkeeping.net/ and its reciprocal will always give the value 1. Now, you get the fraction and do the same operation for finding the reciprocal by flipping the numerator and the denominator.

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This video shows how to find the reciprocal of a whole number. For example, the reciprocal of 4 is one fourth (1/4 or 0.25), and the reciprocal of 0.5 is 1 divided by 0.5, or 2. The most important application of reciprocal is that it is used in division operation for fractions. If we want to divide the one fraction by the second fraction, we can find it by multiplying the first fraction with the reciprocal of the second fraction. In other words, we turn the number upside down, or interchange the numerator and denominator. 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.