Reciprocal Calculator

How to Use the ‘Reciprocal Calculator’?

Follow these steps to use the reciprocal calculator:

Step 1: Select the type of number using the dropdown menu.

Step 2: Enter the particular type of number into the input box provided.

Step 3: Click on the ‘Solve’ button to obtain the reciprocal of the number entered in the input box.

Step 4: Click on the ‘Show Steps’ button to view the steps used while finding the reciprocal of numbers.

Step 5: Click on the $fra1$ button to enter new inputs and start again.

Step 6: Click on the ‘Example’ button to find the reciprocal of different numbers.

Step 7: Click on the ‘Explore’ button to learn the relationship between a number and its reciprocal. Select numbers with the use of sliders and verify the relationship.

Step 8: When on the ‘Explore’ page, click on the ‘Calculate’ button to return to the calculator.

What Is the Reciprocal of a Number?

The reciprocal of a number is defined as a number that when multiplied by the given number results in one as the product. Hence, the reciprocal of a number is also called the ‘multiplicative inverse’ of the number.

On the other hand, when the product of two numbers is 1, the numbers are the reciprocals of each other.

For example, $5 \times \frac{1}{5} = 1 $

So, the reciprocal of 5 is $ \frac{1}{5}$ and, the reciprocal of $ \frac{1}{5}$ is 5.

How to Find the Reciprocal of a Number?

One divided by the given number gives us the reciprocal of a number.

$fra1$

Follow these steps to find the reciprocal of different numbers.

For Integers:

Step 1: Write the integer as a fraction

Step 2: Invert the numerator and the denominator

For Decimals:

Step 1: Add 1 in the denominator of the number

Step 2: Invert the numerator and the denominator

Step 3: Convert the decimal into a fraction

Step 4: Reduce or simplify the fraction

Step 5: Convert the fraction into decimal form

For fractions:

Step 1: Invert the numerator and the denominator

For mixed numbers:

Step 1: Convert the mixed number into an improper fraction

Step 2: Invert the numerator and the denominator

Let us understand these steps with the help of a few examples.

Solved Examples

Example 1: Find the reciprocal of the fraction $ \frac{5}{4}$

Solution:

Invert the numerator and the denominator,

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So, the reciprocal of $ \frac{5}{4}$ is $ \frac{4}{5}.$

Example 2: Find the reciprocal of 16.

Solution:

Write 16 as a fraction $ \frac{16}{1}$

Invert the numerator and the denominator,

$fra3$

So, the reciprocal of 16 is $ \frac{16}{1}$

Example 3: Find the reciprocal of the fraction $ \frac{4}{9}.$

Solution:

Invert the numerator and the denominator,

$fra4$

So, the reciprocal of $ \frac{4}{9}$ is $ \frac{9}{4}.$

Example 4: Find the reciprocal of 1.5.

Solution:

Add 1 in the denominator of the number.

$ \frac{1.5}{1}$

Invert the numerator and denominator,

$fra5$

Convert the decimal into a fraction.

$ \frac{1}{1.5} = \frac{10}{15}$

Reduce (Simplify) the fraction.

$ \frac{10}{15} = \frac{2}{3}$

Convert the fraction into decimal form.

$ \frac{2}{3} = 0.666$

So, the reciprocal of 1.5 is 0.666.

Example 5: Find out the reciprocal of $ 2\text{ }\frac{4}{5}.$

Solution:

Convert mixed number into an improper fraction.

$ 2\text{ }\frac{4}{5}=\frac{14}{5}$

Invert the numerator and the denominator,

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So, the reciprocal of $ 2\text{ }\frac{4}{5}\text{ }is\text{ }\frac{5}{14}.$

Step 2: Invert the numerator and the denominator

Step 3: Reduce or simplify the fraction if required

Reciprocal Calculator