The word reciprocal has actually its roots in Latin together the word “reciprocus” an interpretation “returning”. On acquisition reciprocal that an reverse number, it returns to the original number. The mutual of a provided number when multiplied by that number offers one as a product. Thus, the is additionally called the multiplicative inverse.

You are watching: What is the reciprocal of a negative number

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

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

## What is Reciprocal?

According to the reciprocal definition in math, the reciprocal of a number is defined as the expression which when multiplied through the number provides the product as 1. In other words, once the product of two numbers is 1, they are claimed to be reciprocals of every other. The reciprocal of a number is also defined together the division of 1 by the number.

The multiplicative inverse is a commonly-used mutual synonym. You might come throughout this term in the future. They average the same. ## How to find the mutual of a Number?

We are already familiar that the mutual of a number is the station of the offered number and we deserve to easily find it for any type of number by composing 1 end it. We can uncover the mutual of herbal numbers, integers, fractions, decimals, also as mixed fractions. Let"s have actually a look at the table offered below.

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

## Reciprocal of a an unfavorable Number

For any an adverse number -n, reciprocal will be that is inverse v a minus sign with it. Also, because that variable terms, such together -ax2, reciprocal can be calculated and thus, reciprocal will be -1/ax2. The adhering to steps deserve to be complied with to discover the reciprocal of any an adverse number or variable:

Step 1:For any an unfavorable number, do it an improper portion by composing one below it as 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 of a Decimal Number

It"s even less complicated to uncover the reciprocal of a decimal number. To find the reciprocal of a decimal number, simply divide one through the decimal number or write one end the number.

For example, the reciprocal of 9.8 is 1/9.8

## Reciprocal of a Fraction

All fountain consist of a numerator and a denominator. To discover the mutual of a fraction, interchange the numerator and also denominator. The resultant portion is the forced reciprocal. The reciprocal of a fraction, consists of variables can be calculated in the exact same manner

For example, the reciprocal of 7/10 is 10/7 and likewise the reciprocal of a/b is b/a.

## Reciprocal that a blended Number

A mixed fraction or a combined number is a mixture the a totality number and also a proper fraction. This have the right to a mixture of numbers or also variables. Reciprocal of blended fractions are always proper fractions. The complying with steps can be complied with to uncover the mutual of a mixed number:

Step 1: convert the mixed number come an not correct fraction.Step 2: Interchanging the numerator and also denominator. The resultant fraction is the compelled reciprocal.

For example, the reciprocal of (2frac13):

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

Important Points

The mutual of a number is additionally called that is multiplicative inverse.The product of a number and its reciprocal is equal to 1.Reciprocal of a reciprocal provides the original number. Because that example, reciprocal of 5 is 1/5 and reciprocal of 1/5 is 5.Reciprocal the a number x is created as 1/x or x-1.Reciprocal that a mixed fraction can be derived by convert the mixed portion into one improper fraction and identify 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 right into 8 pieces. Tom eats 3 slices that the pizza and leaves the rest. Recognize the reciprocal of the amount of the pizza consumed by Tom.

Solution:

Since Tom ate 3 slices the end of 8, it means he ate 3/8 that the pizza. We need to determine the mutual of 3/8. Let"s interchange the numerator and also the denominator to achieve the reciprocal. The reciprocal of 3/8 is 8/3.

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

Example 2: Daniel bought 4 apples from the market. That ate (1 frac12) apples native the 4 the bought. Recognize the mutual of (1 frac12).

Solution:

To recognize the mutual of (1 frac12), convert the mixed portion into an wrong fraction. (1 frac12)=3/2. Now, discover the mutual of 3/2. Mutual 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. Come verify the answer, we will certainly multiply -9/10 v its reciprocal and also check if the product is 1, -9/10 x -10/9 = 1

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

Show equipment >

go to slidego come slidego come slide Have your child solve real-life obstacles using math
Have your child apply concepts learned in college in the real civilization with the help of ours experts.

Book a totally free Trial Class

## Practice concerns on reciprocal

Show equipment >

go to slidego come slidego come slidego come slidego come slide

## FAQs on reciprocal Definition

### How execute you describe Reciprocal?

The reciprocal of a number is 1 divided by the number. That can additionally be explained as: when the product of two numbers is 1, they are claimed to be reciprocals of each other.

### What is the reciprocal of 1?

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

### Does 0 have a Reciprocal?

No, 0 has no reciprocal. Every numbers have reciprocals, except 0.

### How to uncover Reciprocal the a mixed Number?

The following steps have the right to be followed to discover the reciprocal of a mixed number:

Step 1: transform the combined number to an improper fraction.Step 2: Interchanging the numerator and denominator. The resultant fraction is the forced reciprocal.

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

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

The inverse means opposite operation, together as enhancement and subtraction are inverse operations, vice versa, the reciprocal describes the train station of any type of value, also called the multiplicative inverse.

### What is one more Word because that Multiplicative Inverse?

Reciprocal is an additional word for the multiplicative inverse.

### What is the reciprocal of Infinity?

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

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

The mutual 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 reciprocal of a negative number monitor the steps offered below:

Step 1: for any an unfavorable number, do it one improper fraction by creating one below it.Step 2: Swap or interchange the numerator and also denominator.Step 3: include a an unfavorable sign come the resultant value.

See more: How Are The Ideas In The Following Two Sentences Tied Together

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