The word reciprocal has its root in Latin together the word “reciprocus” definition “returning”. On taking reciprocal that an turning back number, it returns to the initial number. The reciprocal of a provided number when multiply by that number offers one together a product. Thus, that is likewise called the multiplicative inverse.

You are watching: Does every number have a reciprocal

In math, mutual can simply be defined as the inverse of a number or a value. Because that a actual number n, mutual is 1/n, such together reciprocal the 3 is 1/3. Similarly, mutual 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 around it every in this lesson.

1. | What is Reciprocal? |

2. | How to find the mutual of a Number? |

3. | Reciprocal of a negative Number |

4. | Reciprocal the a Decimal Number |

5. | Reciprocal of a Fraction |

6. | Reciprocal the a mixed Number |

6. | FAQs on reciprocal Definition |

## What is Reciprocal?

According come the reciprocal definition in math, the **reciprocal of a number** is defined as the expression which as soon as multiplied by the number provides the product as 1. In various other words, once the product of 2 numbers is 1, lock are said to be reciprocals of each other. The reciprocal of a number** **is likewise defined as the division of 1 by that number.

The multiplicative inverse is a commonly-used reciprocal synonym. You might come throughout this term in the future. They typical the same.

## How to uncover the mutual of a Number?

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

TypeReciprocalExample

Natural Number x | 1/x | Reciprocal that 4 is 1/4 |

Integer x, x≠0 | 1/x | Reciprocal the -4 is -1/4 |

Fraction x/y, x,y≠0 | y/x | Reciprocal that 2/7 is 7/2 |

Decimal (x) | 1/x | Reciprocal of 0.1 is 1/0.1 |

## Reciprocal of a an unfavorable Number

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

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

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

## Reciprocal of a Decimal Number

It"s even simpler to discover the reciprocal of a decimal number. To find the reciprocal of a decimal number, simply divide one by the decimal number or write one over the number.

For example, the mutual of 9.8 is 1/9.8

## Reciprocal that 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 fraction is the forced reciprocal. The mutual of a fraction, consist of of variables can 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 that a combined Number

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

Step 1: convert the mixed number come an wrong fraction.Step 2: Interchanging the numerator and also denominator. The resultant portion is the required reciprocal.

For example, the reciprocal of (2frac13):

The improper type of (3frac12) is 7/2The mutual of 7/2 is 2/7.**Important Points**

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 the the pizza. We require to identify the reciprocal of 3/8. Let"s interchange the numerator and the denominator to obtain the reciprocal. The mutual of 3/8 is 8/3.

Therefore, 8/3 is mutual of the amount of pizza eaten by Tom.

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

**Solution:**

To determine the mutual of (1 frac12), convert the mixed portion into an improper fraction. (1 frac12)=3/2. Now, find the reciprocal 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 mutual of -9/10 is -10/9. To verify the answer, we will multiply -9/10 v its reciprocal and check if the product is 1, -9/10 x -10/9 = 1

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

Show solution >

go come slidego come slidego come slide

Have her child fix real-life difficulties using math

Have her child use concepts learned in school in the real people with the aid of our experts.

Book a totally free Trial Class

## Practice concerns on mutual

Show solution >

go come slidego come slidego come slidego come slidego come slide

## FAQs on mutual Definition

### How do you define Reciprocal?

The reciprocal of a number is 1 split by the number. It can additionally be explained as: as soon as the product of 2 numbers is 1, they are said to it is in reciprocals of every other.

### What is the reciprocal of 1?

The reciprocal of 1 is 1. To recognize the mutual of 1, divide 1 through 1. (1/1 = 1)

### Does 0 have a Reciprocal?

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

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

The following steps can be followed to uncover the reciprocal of a blended number:

Step 1: convert the blended number come an improper fraction.Step 2: Interchanging the numerator and denominator. The resultant fraction is the compelled reciprocal.For Example, reciprocal of (3frac12) = 2/7.

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

The inverse means opposite operation, together as addition and subtraction room inverse operations, vice versa, the reciprocal refers to the station of any value, additionally called the multiplicative inverse.

### What is another Word for Multiplicative Inverse?

Reciprocal is another word because that 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 reciprocal of a decimal is one split by the decimal number or one end the number.

### How to discover the mutual of a an unfavorable Number?

To discover the mutual of a an unfavorable number follow the steps provided below:

Step 1: because that any an unfavorable number, make it one improper fraction by writing one below it.Step 2: Swap or interchange the numerator and denominator.Step 3: include a negative sign to the resultant value.See more: How Did Oyster Crackers Get Their Name )? Access To This Page Has Been Denied

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