The Reciprocal Of 11 12

In Maths, reciprocal is merely defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be ane/n. Information technology means that we accept to catechumen the number to the upside-down grade. For instance, the reciprocal of nine is ane divided by ix, i.e. 1/9. Now, if we multiply a number by its reciprocal, it gives a value equal to 1. It is also chosen multiplicative inverse .

Reciprocal

The word reciprocal came from the Latin give-and-take "reciprocus" significant "returning". Hence, it returns its original value, if nosotros have the reciprocal of an inverted number. In this article, we are going to learn the definition of reciprocal, how to find the reciprocal of numbers, fractions and decimals with many examples.

Tabular array of Contents:

- Definition
- Reciprocal of a Number
- Reciprocal of a Negative Number
- Reciprocal of a Fraction
- Reciprocal of a Mixed Fraction
- Reciprocal of a Decimal
- Finding Unity
- Application of Reciprocal
- Rules for Reciprocal
- Examples
- Practice Questions
- FAQs

Definition

In Mathematics, the reciprocal of any quantity is, one divided by that quantity. For any number 'a', the reciprocal will be i/a. If the given number is multiplied past its reciprocal, we get the value 1.

Example: Reciprocal of a number seven is one/7.

Thus, if nosotros multiply 7 and 1/7, we get 1.

I.e., seven × (1/7) = 1

Other Definitions of Reciprocal

It has many other definitions too :

It is also called the multiplicative inverse .
It is similar to turning the number upside downward.
It is likewise found byinterchanging the numerator and denominator.
All the numbers have reciprocal except 0.
The production of a number and its reciprocal is equal to 1.
Generally, reciprocal is written equally, 1/x or 10^-i for a number x.

Example: The reciprocals of 3 and 8 are 1/three and 1 /eight.

Information technology is too expressed by the number raised to the ability of negative 1 and can be found for fractions and decimal numbers too.

In maths, when you take the reciprocal twice, you lot will go the same number that you started with.

Example: The reciprocal of 4 is 1/4. When you repeat this step it becomes 4/ane or 4.

Thus, you get the same number where you lot started with.

Not For Cipher

We cannot apply the reciprocal condition on nil, since information technology will return an indefinite value.

ane/0 = Undefined

Therefore, we can have a reciprocal for all real numbers merely not for nothing.

Reciprocal of a Number

It is divers as one over that number. In other words, the reciprocal of a number is defined every bit the one divided by the given number.

Case: Observe the reciprocal of five

Solution: To discover the solution, we volition use x = one/x

Therefore, v= 1/5

The reciprocal of a function, f(ten) = f(1/ten)

Reciprocal of Negative Numbers

For any negative number -x, the reciprocal can be constitute by writing the inverse of the given number with a minus sign along with that (i.eastward) -1/10. For case, the reciprocal of – 4x ² is written as -1/4x ^two . Become through the following steps to find the reciprocal of the negative number.

Footstep 1: For any negative number, write the given number in the form of an improper fraction by writing the number 1 in the denominator.

Step 2: Now, interchange the numerator and denominator values.

Footstep iii: Add a minus sign (-) to the resultant number.

Now, Consider a negative number, -17.

Step 1: Convert the number 17 in the improper fraction. (i.e) 17/ane.

Step 2: Interchanging the numerator and denominator value, nosotros get ane/17.

Step 3: Finally, adding a negative sign to the resultant number, we become -i/17.

Therefore, the reciprocal of -17 is -one/17.

Reciprocal of a Fraction

The reciprocal of a fraction tin can be found past interchanging the numerator and the denominator values.

Example: Find the reciprocal of 2 / 3

Solution: To observe the solution we will follow the following steps

The reciprocal of 2/3 is three/ii. (or)

Use the formula, 10 = 1/x,

Here, x = ii/iii

Thus, x = 1 / x = i / (two/3)

= 3/two

Therefore, the reciprocal of a fraction ii/3 is iii/2.

Reciprocal of a Mixed Fraction

In club to find the same for a mixed fraction, convert information technology into improper fractions and perform the operation.

Consider a mixed fraction, 4(ane/2).

The commencement step is to convert a mixed fraction into an improper fraction.

iv(1/ii) = nine/ii

Now, you get the fraction and practise the aforementioned functioning for finding the reciprocal by flipping the numerator and the denominator.

Therefore, the solution for ix/ii is 2/nine.

Reciprocal of a Decimal

The reciprocal of a decimal is the aforementioned every bit information technology is for a number defined by one over the number.

Example:

Find the reciprocal of a decimal 0.75

Solution:

The reciprocal of a number, x = 1/10

Therefore, 0.75= one/0.75

An alternating method to notice it is given beneath.

Consider the same instance, 0.75.

First, you lot have to check whether the given decimal number is possible for converting into a fractional number. Here 0.75 is written as iii/4

Now, find the reciprocal of iii/4 which gives 4/3

When you lot verify both the solutions, it results in the aforementioned.

That is, 1/0.75 = ane.33 and

4/iii = 1.33

Finding Unity

If we multiply the reciprocal of a number past the number itself, we will get the value equal to unity (1). Let us meet some examples here:

2 × (1/ii) = 1
three × (ane/3) = 1
x × (1/x) = 1
fifty × (1/l) = ane
100 × (1/100) = ane

From the higher up examples, we can see that the multiplication of a number to its reciprocal gives 1. Hence, we can say that the number is multiplied by its reciprocal, we get 1.

Application of Reciprocal

The virtually important application of reciprocal is used in sectionalization operation for fractions. If we want to divide the first fraction by the second fraction, the effect can be found by multiplying the showtime fraction with the reciprocal of the second fraction.

For example, (2/five) ÷ (7/5)

Here, the showtime fraction is ii/5

The second fraction is 7/5

Thus, the reciprocal of the second fraction is v/vii

Hence, (2/5) ÷ (seven/5) = (ii/five) × (5/7)

(2/5) ÷ (seven/5) = ii/seven.

Rules for Reciprocal

The two important rules for reciprocal are:

For a number x, the reciprocal will be 1/x or as well can be written as x^-1. For example, if 7 is the number, then the reciprocal will exist ane/7.
For a fraction ten/y, the reciprocal will be y/x. For example, if 3/5 is the given fraction, then its reciprocal will exist 5/3.

Solved Examples

Go through the below examples:

Example i:

Discover the reciprocal of two and 9

Solution:

Given that, the two integers are two and nine

Therefore, the reciprocal of ii is 1/two

The reciprocal of nine is 1/9

Example 2:

Determine the reciprocal of iii / (two/3)

Solution:

Given number 3/(⅔) is a fraction.

iii / (2/3) can be written every bit 9/2

i.e., iii/(⅔) = 9/2

Hence, the reciprocal of 9/2 is 2/9.

Example 3:

Find the reciprocal of -5/four

Solution:

Given fraction is -5/four

The reciprocal of -v/4 is -4/5.

Example 4:

Find the reciprocal of the decimal 0.25.

Solution:

Given decimal number = 0.25.

Hence, the reciprocal of 0.25 is i/0.25.

Alternate method:

The fraction equivalent to the decimal number 0.25 is ane/four.

Hence, the reciprocal of ¼ is 4/1.

Verification:

The resultant number obtained from both methods will result in the same value.

(i.e.) 1/0.24 = 4 or 4/1.

Example five:

Discover the reciprocal of the negative number -45.

Solution:

Given that the negative number is -45.

Hence, the reciprocal of -45 is -i/45.

Do Questions on Reciprocals

Find the reciprocal for the following numbers:

29
14/15
one.25
-eighty
ax ^two

Frequently Asked Questions on Reciprocal

Ascertain reciprocal.

The reciprocal is defined equally the multiplicative inverse of a number. In other words, the reciprocal of a number is defined every bit i divided past that number. The product of a given number and its reciprocal volition always requite the value 1.

How to determine the reciprocal of a fraction?

The reciprocal of a fraction can exist determined past interchanging the values of the numerator and denominator. For case, ¾ is a fraction. The reciprocal of ¾ is four/three.

How to determine the reciprocal of the mixed fraction?

To find the reciprocal of the mixed fraction, first, convert the mixed fraction into the improper fraction, and and so accept the reciprocal of the improper fraction. For instance, ii ¾ is a mixed fraction. When it is converted to an improper fraction, we get 11/4. Hence, the reciprocal of xi/4 is 4/11.

What is the reciprocal of 0?

The number zero (0) does not have a reciprocal. Considering, if whatever reciprocal number is multiplied by 0, it will non give the product as one. It volition effect in zero.

What is the reciprocal of infinity?

The reciprocal of infinity is 1/∞, which is equal to zip. Information technology means that 1/∞=0. It is noted that the reciprocal of infinity is null exactly, which means non minute.

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