Numbers that are opposites have different signs; that is, one is positive, and one is negative, as in -2 and 2. Reciprocal numbers are made when a fraction is turned upside-down. For example, the reciprocal of 5/4 is 4/5. In the usual real numbers with the usual multiplication, $\infty$ is not a number and so you don’t operate with it, and $0$ has no reciprocal.

The first step in finding the reciprocal of a number is to make it into a fraction. For example, the whole number 8 can be made into the fraction 8/1. Once you have a fraction to work with, just flip the fraction upside down to find the reciprocal. The fractions 8/1 and 1/8 are reciprocals. The multiplicative inverse of a fraction a/b is b/a.

To get the reciprocal of a number, we divide 1 by the number. The product of a negative number and its reciprocal equals 1. If the number is negative then the reciprocal must also be negative to produce a product of +1. Convert the mixed number into an improper fraction, then find the reciprocal as you normally would. Use long division techniques to calculate the reciprocal.

## Example: the reciprocal of 2 is ½ (a half)

### How do you find a reciprocal?

To find the reciprocal of any number, just calculate “1 ÷ (that number).” For a fraction, the reciprocal is just a different fraction, with the numbers “flipped” upside down (inverted). For instance, the reciprocal of 3/4 is 4/3. Any number times its reciprocal will give you 1.

The reciprocal of a fraction is extremely simple to find based on its definition. Reciprocals are numbers that, when multiplied together, result in a product of 1.

## Reciprocal of 57 is

The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution). The right way to find the reciprocal depends on the kind of number you’re working with. To find the reciprocal of a decimal, divide 1 by the decimal. If you need to find the reciprocal of a mixed number, change the mixed number to an improper fraction and then flip the fraction. To find the reciprocal of a fraction, flip the numerator and denominator.

Finding the reciprocal of a fraction is a fairly simple one-step process. However, when dealing with whole numbers, such as the number 4, we have to take one extra step to find the reciprocal of the number. Using a number’s reciprocal can make dividing fractions and calculating slopes of specific lines much easier. Finding the reciprocal of a number can be done in two quick steps.

In the real numbers, zero does not have a reciprocal because no real number multiplied by 0 produces 1 (the product of any number with zero is zero). The property that every element other than zero has a multiplicative inverse is part of the definition of a field, of which these are all examples.

For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

## Method 2 of 3: Finding the Reciprocal of a Mixed Number

- In the real numbers, zero does not have a reciprocal because no real number multiplied by 0 produces 1 (the product of any number with zero is zero).

On the other hand, no integer other than 1 and −1 has an integer reciprocal, and so the integers are not a field. Reciprocals are a common occurrence when dealing with any problem in mathematics or the world around us that involves fractions. Fractions are numbers in the form a/b, where a is the numerator of the fraction, and b is the denominator of the fraction.

If you calculate it for 10 ÷ 4, you’ll get the answer 2.5, the reciprocal of 0.4. For example, you can find the reciprocal of 0.4 by calculating 1 ÷ 0.4. There are two steps to finding the reciprocal of a mixed number, explained below.

## Method 3 of 3: Finding the Reciprocal of a Decimal

Reciprocals are helpful in all sorts of algebraic equations. For example when you are dividing one fraction by another you multiply the first by the Reciprocal of the 2nd. You might also need reciprocals when finding equations of lines. Is the reciprocal of 8/11 an improper fraction? To get the reciprocal of a fraction, just turn it upside down.

If you’re trying to find the reciprocal of a whole number, just divide 1 by that number and write it as a fraction. Find the reciprocal of a fraction by flipping it. To find the reciprocal of a Mixed Fraction, we first convert it to an Improper Fraction, then turn that upside down.

## Reciprocal of 57

To find the reciprocal of a number, the numerator and denominator switch places, so the reciprocal of 4 is 1/4. Write the reciprocal of a whole number as a fraction. Again, the reciprocal of a number is always 1 ÷ (that number).

It didn’t matter whether it was one half (1/2) or nine hundred ninety-nine one-thousandths (999/1000), the values were still less than one. So, To find a reciprocal, just divide #1# by the number you need to find the reciprocal of, and you have the grand prize. The reciprocal of 9 is the number that, when multiplied with 9, is equal to 1. A ring in which every nonzero element has a multiplicative inverse is a division ring; likewise an algebra in which this holds is a division algebra.

It’s not a dumb question, but rather it is a question that requires one to be very precise as to what things mean before it can be answered. The reciprocals of a number is sometimes called the Multiplicative Inverse of the number. The reciprocal of a negative number is the same as the reciprocal of the positive number, except it’s a negative value. Now you know about regular fractions with numerators on top and denominators on the bottom. Until now, we have just looked at fractions that are less than one.