What is the reciprocal of 1 2

To get the reciprocal of a fraction, just turn it upside down.

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Multiplying a Fraction by its Reciprocal
Reciprocal of a Mixed Fraction

Like this:

Fractions

A Fraction (such as

) has two numbers:

NumeratorDenominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

To get the reciprocal of a fraction, just turn it upside down.
In other words swap over the Numerator and Denominator.

Examples:

Fraction	Reciprocal
38	8 3
56	6 5
197	7 19
12	21 = 2

That last example was interesting. The reciprocal of 12 is 2

Likewise the reciprocal of 13 is 3 and so on.

Multiplying a Fraction by its Reciprocal

When we multiply a fraction by its reciprocal we get 1:

Reciprocal of a Mixed Fraction

To find the reciprocal of a Mixed Fraction, we first convert it to an Improper Fraction, then turn that upside down.

1. Convert it to an improper fraction: 213 = 6 3 + 1 3 = 7 3
2. Turn it upside down: 37

The Answer is: 37

Reciprocal is the inverse. In other words when a number and its reciprocal are multiplied together, the product is 1.

For a fraction, it means flip the fraction to find the reciprocal.

-1/2 reciprocal = -2/1.

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

As you're interested in reciprocals, we suspect that fraction calculators may also be interesting to you. So why not check out our other tools!

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 you multiply a number by its reciprocal, you'll get 1:

For example, if our chosen number is 5, its reciprocal is 1/5. The multiplication of these two numbers will give us 1:

The name reciprocal comes from Latin, possibly from the phrase reque proque, meaning back and forth. The reciprocal number to x may be denoted simply as 1/x but also as x-1. Thus, raising the number to the power of minus one is the same as finding its reciprocal.

So, in short, how to find the reciprocal of a number?

Reciprocal of a fraction

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

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

To find the reciprocal of a number, divide 1 by the number.

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

To find the reciprocal of a decimal, you need to do the same as before - divide 1 by your decimal number.

Example: the reciprocal of 3.25 is 1/3.25

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

Remember that 0 doesn't have the reciprocal, as 1/0 is undefined.

We hope that, after our explanation, you now understand the concept of a reciprocal. In that case, let's look at two examples to check how this calculator works!

Example 1: What is the reciprocal of 4?

Is your number a fraction? Not this time! Choose No from the drop-down list. (If you really want, you can leave it as the fraction option and then choose 1 as the denominator).
Input the number for which you'd like to find the reciprocal, which is 4.
Tadaa! That's all you need to do! The reciprocal calculator shows that the reciprocal of your number is 0.25, or, as a fraction, 1/4.

Example 2: What is the reciprocal of 1/2?

Again, start with the question: is the number a fraction? Pick Yes this time.
Enter the numerator (top) and denominator (bottom) of your fraction into the appropriate fields. So, in our case, input 1 as the numerator and 2 in the denominator box.
The reciprocal calculator finds the answer - the reciprocal of 1/2 is 2.

0.2. Since we can write 5 as 5/1, if we take the reciprocal, it becomes 1/5, which is 0.2 in decimal form.

3/2 or 1.5. Taking the reciprocal of a fraction means swapping the numerator and the denominator around.

1. 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.

You find 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 5/4 is 4/5.