The word reciprocal has actually its root in Latin as the word “reciprocus” an interpretation “returning”. On taking reciprocal of an reverse number, it returns to the original number. The mutual of a given number when multiply by that number provides one as a product. Thus, the is also called the multiplicative inverse.

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In math, mutual can simply be identified as the inverse of a number or a value. Because that a real number n, reciprocal is 1/n, such as reciprocal the 3 is 1/3. Similarly, reciprocal of 5 is 1/5 and so on. What is the mutual of 0? What is the reciprocal of decimal number? Let"s learn about it all in this lesson.

 1 What is Reciprocal? 2 How to find the reciprocal of a Number? 3 Reciprocal of a negative Number 4 Reciprocal that a Decimal Number 5 Reciprocal that a Fraction 6 Reciprocal that a blended Number 6 FAQs on reciprocal Definition

## What is Reciprocal?

According to the reciprocal definition in math, the reciprocal of a number is identified as the expression which once multiplied by the number offers the product as 1. In various other words, when the product of 2 numbers is 1, they are stated to be reciprocals of each other. The mutual of a number is likewise defined as the division of 1 by the number.

The multiplicative inverse is a commonly-used mutual synonym. You may come throughout this term in the future. They median the same.

## How to discover the reciprocal of a Number?

We are already familiar the the reciprocal of a number is the inverse of the offered number and we can easily discover it for any type of number by composing 1 over it. Us can uncover the reciprocal of herbal numbers, integers, fractions, decimals, also as mixed fractions. Let"s have actually a look in ~ the table given below.

TypeReciprocalExample
Natural Number x1/xReciprocal that 4 is 1/4
Integer x, x≠0 1/xReciprocal that -4 is -1/4
Fraction x/y, x,y≠0y/xReciprocal of 2/7 is 7/2
Decimal (x)1/xReciprocal that 0.1 is 1/0.1

## Reciprocal of a negative Number

For any an unfavorable number -n, reciprocal will certainly be its inverse v a minus authorize with it. Also, because that variable terms, such as -ax2, reciprocal deserve to be calculated and thus, reciprocal will certainly be -1/ax2. The complying with steps deserve to be adhered to to uncover the mutual of any an adverse number or variable:

Step 1:For any an unfavorable number, make it an improper fraction by creating one below it together the denominator.Step 2: Interchange the numerator and also denominator.Step 3: add a an unfavorable sign to the resultant value.

For example, the mutual of -31 is -1/31.

## Reciprocal that a Decimal Number

It"s even simpler to find the reciprocal of a decimal number. To find the reciprocal of a decimal number, simply divide one through the decimal number or compose one end the number.

For example, the reciprocal of 9.8 is 1/9.8

## Reciprocal of a Fraction

All fractions consist the a numerator and also a denominator. To find the mutual of a fraction, interchange the numerator and denominator. The resultant portion is the required reciprocal. The reciprocal of a fraction, consisting of variables can be calculated in the exact same manner

For example, the mutual of 7/10 is 10/7 and an in similar way the mutual of a/b is b/a.

## Reciprocal the a mixed Number

A mixed portion or a blended number is a mixture of a totality number and a appropriate fraction. This deserve to a mixture of number or also variables. Mutual of blended fractions are constantly proper fractions. The following steps have the right to be adhered to to uncover the mutual of a mixed number:

Step 1: transform the blended number to an wrong fraction.Step 2: Interchanging the numerator and also denominator. The resultant portion is the required reciprocal.

For example, the mutual of (2frac13):

The improper form of (3frac12) is 7/2The mutual of 7/2 is 2/7.

Important Points

The reciprocal of a number is likewise called that multiplicative inverse.The product the a number and also its reciprocal is equal to 1.Reciprocal of a reciprocal offers the initial number. For example, reciprocal of 5 is 1/5 and also reciprocal that 1/5 is 5.Reciprocal that a number x is created as 1/x or x-1.Reciprocal of a mixed portion can be obtained by converting the mixed portion into an improper fraction and determining its reciprocal.
Important Topics
Whole Numbers
Natural Numbers
Integers
Multiplicative Inverse
Numerator
Denominator
Fractions
Improper Fractions
Reciprocal Functions

## Solved instances on Reciprocal

Example 1: A pizza is sliced into 8 pieces. Tom eats 3 slices that the pizza and also leaves the rest. Determine the mutual of the amount of the pizza eaten by Tom.

Solution:

Since Tom ate 3 slices out of 8, it implies he ate 3/8 of the pizza. We need to identify the reciprocal of 3/8. Let"s interchange the numerator and the denominator to acquire the reciprocal. The mutual of 3/8 is 8/3.

Therefore, 8/3 is reciprocal of the quantity of pizza consumed by Tom.

Example 2: Daniel purchase 4 apples from the market. The ate (1 frac12) apples native the 4 the bought. Determine the reciprocal of (1 frac12).

Solution:

To recognize the mutual of (1 frac12), convert the mixed portion into an improper fraction. (1 frac12)=3/2. Now, discover the reciprocal of 3/2. Reciprocal of 3/2 is 2/3.

Therefore, 2/3 is mutual of (1 frac12).

Example 3: Find the reciprocal of -9/10. Verify her answer.

Solution:

The reciprocal of -9/10 is -10/9. To verify the answer, we will certainly multiply -9/10 v its reciprocal and check if the product is 1, -9/10 x -10/9 = 1

Therefore, -10/9 is reciprocal of -9/10.

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## Practice questions on mutual

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## FAQs on reciprocal Definition

### How perform you define Reciprocal?

The reciprocal of a number is 1 separated by that number. It can additionally be explained as: when the product of two numbers is 1, lock are said to be reciprocals of each other.

### What is the reciprocal of 1?

The reciprocal of 1 is 1. To identify the mutual of 1, divide 1 by 1. (1/1 = 1)

### Does 0 have a Reciprocal?

No, 0 has no reciprocal. All numbers have actually reciprocals, except 0.

### How to find Reciprocal of a combined Number?

The following steps have the right to be complied with to discover the mutual of a mixed number:

Step 1: transform the combined number to an not correct fraction.Step 2: Interchanging the numerator and denominator. The resultant portion is the forced reciprocal.

For Example, mutual of (3frac12) = 2/7.

### What is the Difference between Reciprocal and also Inverse?

The inverse means the opposite operation, together as addition and subtraction room inverse operations, whereas the reciprocal refers to the train station of any type of value, also called the multiplicative inverse.

### What is an additional Word for Multiplicative Inverse?

Reciprocal is one more word for the multiplicative inverse.

### What is the mutual of Infinity?

The reciprocal of infinity is zero (0). (1/∞=0)

### What is the reciprocal of a Decimal Number?

The reciprocal of a decimal is one split by the decimal number or one end the number.

### How to uncover the mutual of a negative Number?

To find the mutual of a negative number follow the steps given below:

Step 1: because that any negative number, make it an improper fraction by creating one below it.Step 2: Swap or interchange the numerator and denominator.Step 3: include a an adverse sign to the result value.

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For example, mutual of -9 is -1/9.