How To Find The Reciprocal Of A Fraction

Reciprocal Estimator

Created past Hanna Pamuła , PhD candidate

Reviewed by

Steven Wooding and Jack Bowater

Final updated:

Jan 07, 2022

Table of contents:

What is a reciprocal?
How to discover the reciprocal?
Examples: what is the reciprocal of 4 and 1/ii?
FAQ

If yous're wondering how to find the reciprocal, we're hither to help with this easy-to-use reciprocal calculator.
Below, you can find an caption of what a reciprocal is and examples of how to calculate and find the reciprocals, be it the reciprocal of a fraction or a number.

Equally you're interested in reciprocals, we suspect that fraction calculators may exist interesting to you as well. So why not check out our other tools!

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What is a reciprocal?

A reciprocal in math is one divided by the number in question (also known as the multiplicative inverse).

The reciprocal of x = 1/x

Alternatively, you can say that if y'all multiply a number past its reciprocal, yous'll become 1:

explanation what is a reciprocal: number (x) * reciprocal (1/x) = 1

For case, if our chosen number is 5, then its reciprocal is 1/5. The multiplication of these two numbers will requite us ane:

5 * i/v = 5 * 0.ii = ane

The name reciprocal comes from Latin, perhaps from the phrase reque proque pregnant dorsum and forth. The reciprocal number to x may be denoted simply as one/x, just likewise every bit x^-i . Thus, raising the number to the power of minus one is the same as finding its reciprocal.

How to observe the reciprocal?

So, in curt, how to notice the reciprocal of a number?

Reciprocal of a fraction

To notice the reciprocal of a fraction, switch the numerator and the denominator (the top and bottom of the fraction, respectively). And then, simply speaking, the reciprocal of a/b is b/a.

Example: the reciprocal of 3/4 is four/3
Reciprocal of a number

To find the reciprocal of a number, split i past the number.

Example: the reciprocal of 7 is 1/7
Reciprocal of a decimal

To find the reciprocal of a decimal, yous need to exercise the aforementioned as earlier - divide 1 by your decimal number.

Instance: the reciprocal of 3.25 is one/3.25

Additionally, our reciprocal calculator will show you lot the fraction in its simplified form.

Call up that 0 doesn't take the reciprocal, as 1/0 is undefined.

Examples: what is the reciprocal of 4 and 1/2?

We hope that, subsequently our explanation, you now understand the concept of a reciprocal. In that instance, let'southward look at two examples to check how this reciprocal estimator works!

Instance ane: What is the reciprocal of 4?

Is your number a fraction? Not this time! Cull No from the drop-downwards list. (If you really want, you can exit it every bit the fraction pick and then choose one as the denominator).
Input the number for which you lot'd like to observe the reciprocal, which is 4.
Tadaa! That'south all you need to do! The reciprocal figurer shows that the reciprocal of your number is 0.25, or, as a fraction, 1/4.

Instance ii: What is the reciprocal of i/2?

Again, start with the question is the number is a fraction? Choice Yes this fourth dimension.
Enter the numerator (top) and denominator (lesser) of your fraction into the appropriate fields. So, in our case, input one as the numerator and 2 in the denominator box.
The reciprocal computer finds the respond - the reciprocal of 1/2 is 2.

FAQ

What is the reciprocal of 5?

0.two. Since we tin write v every bit 5/i, if we take the reciprocal, it becomes one/v, which is 0.2 in decimal form.

What is the reciprocal of 2/iii?

three/two or i.v. Taking the reciprocal of a fraction means swapping the numerator and the denominator around.

What is the reciprocal of ane?

1. Since ane in partial course is written as 1/i, taking the reciprocal (swapping around the numerator and the dominator) results in the same thing, 1/1, which is 1.

How exercise yous find the inverse of a fraction?

Y'all detect the inverse of a fraction by exchanging the numerator (top number) with the denominator (bottom number) – taking the reciprocal of the fraction. For example, the inversion of the fraction 5/iv is 4/five.

Hanna Pamuła , PhD candidate

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