The word reciprocal has its roots in Latin together the word “reciprocus” meaning “returning”. On acquisition reciprocal of an inverted number, it return to the initial number. The mutual of a offered number when multiply by that number provides one as a product. Thus, that is additionally called the multiplicative inverse.

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

 1 What is Reciprocal? 2 How to discover the mutual of a Number? 3 Reciprocal the a an unfavorable Number 4 Reciprocal of a Decimal Number 5 Reciprocal that a Fraction 6 Reciprocal the a blended Number 6 FAQs on mutual Definition

What is Reciprocal?

According to the reciprocal definition in math, the reciprocal the a number is defined as the expression which once multiplied through the number provides the product as 1. In other words, when 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 reciprocal synonym. You might come across this term in the future. They average the same.

How to find the mutual of a Number?

We are currently familiar the the mutual of a number is the train station of the provided number and we deserve to easily find it for any number by creating 1 end it. Us can find the mutual of organic numbers, integers, fractions, decimals, too as mixed fractions. Let"s have a look in ~ the table given below.

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

Reciprocal of a an unfavorable Number

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

Step 1:For any an adverse number, make it one improper portion by writing one below it together the denominator.Step 2: Interchange the numerator and denominator.Step 3: include a an adverse sign to the resultant value.

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

Reciprocal the a Decimal Number

It"s even easier to discover the mutual of a decimal number. To find the reciprocal of a decimal number, simply divide one through the decimal number or compose one over the number.

For example, the reciprocal of 9.8 is 1/9.8

Reciprocal of a Fraction

All fountain consist the a numerator and also a denominator. To find the mutual of a fraction, interchange the numerator and also denominator. The resultant portion is the forced reciprocal. The mutual of a fraction, consisting of variables have the right to be calculate in the same manner

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

Reciprocal the a combined Number

A mixed portion or a blended number is a mixture the a entirety number and also a suitable fraction. This have the right to a mixture of number or even variables. Mutual of combined fractions are constantly proper fractions. The complying with steps can be followed to uncover the reciprocal of a mixed number:

Step 1: convert the mixed number to an improper fraction.Step 2: Interchanging the numerator and denominator. The resultant portion is the compelled reciprocal.

For example, the mutual of $$2\frac13$$:

The improper kind of $$3\frac12$$ is 7/2The mutual of 7/2 is 2/7.

Important Points

The mutual of a number is also called that is multiplicative inverse.The product of a number and its reciprocal is equal to 1.Reciprocal of a reciprocal gives the original number. For example, mutual of 5 is 1/5 and also reciprocal that 1/5 is 5.Reciprocal of a number x is written as 1/x or x-1.Reciprocal of a mixed portion can be derived by convert the mixed portion into an improper fraction and identify its reciprocal.
Important Topics
Whole Numbers
Natural Numbers
Integers
Multiplicative Inverse
Additive Inverse
Additive train station Calculator
Numerator
Denominator
Fractions
Improper Fractions
Reciprocal Functions

Solved instances on Reciprocal

Example 1: A pizza is sliced into 8 pieces. Tom eats 3 slices of the pizza and also leaves the rest. Identify the reciprocal of the quantity of the pizza eaten by Tom.

Solution:

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

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

Example 2: Daniel purchase 4 apples indigenous the market. That ate $$1\tfrac12$$ apples from the 4 that bought. Determine the mutual of $$1\tfrac12$$.

Solution:

To recognize the reciprocal of $$1\tfrac12$$, convert the mixed portion into an improper fraction. $$1\tfrac12$$=3/2. Now, uncover the mutual of 3/2. Mutual of 3/2 is 2/3.

Therefore, 2/3 is mutual of $$1\tfrac12$$.

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 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.

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FAQs on reciprocal Definition

How carry out you define Reciprocal?

The reciprocal of a number is 1 split by the number. That can also be explained as: when the product of 2 numbers is 1, castle are claimed to be reciprocals of every other.

What is the reciprocal of 1?

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

Does 0 have a Reciprocal?

No, 0 has no reciprocal. All numbers have reciprocals, other than 0.

How to uncover Reciprocal that a blended Number?

The complying with steps deserve to be adhered to to uncover the mutual of a mixed number:

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

For Example, reciprocal of $$3\frac12$$ = 2/7.

What is the Difference in between Reciprocal and also Inverse?

The inverse means the contrary operation, together as addition and subtraction room inverse operations, whereas the reciprocal describes the train station of any kind of value, also called the multiplicative inverse.

What is an additional Word because that Multiplicative Inverse?

Reciprocal is an additional 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 separated by the decimal number or one end the number.

How to uncover the reciprocal of a negative Number?

To find the reciprocal of a an unfavorable number monitor the steps given below:

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

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