## What is a Reciprocal?

In mathematics, the reciprocal, additionally known as multiplicative inverse, is the inverse of a number x. dedetailed as 1/x or x-1. This indicates that the product of a number x and its reciprocal yields 1.

You are watching: What is the reciprocal of 1 2

The inverse of a portion a/b is delisted as (a/b)-1, which is b/a. This post discusses the measures on just how to discover the reciprocal of a number, mixed numbers, fractions and also decimals.

## How to Find Reciprocals?

The reciprocal of a number is simply the number that has actually been flipped or inverted upside-dvery own. This involves transposing a number such that the numerator and denominator are put at the bottom and optimal respectively.

To uncover the reciprocal of a whole number, just convert it right into a fraction in which the original number is the denominator and also the numerator is 1.

*Example 1*

The reciprocal of 2/3 is 3/2.

The product of 2/3 and its reciprocal 3/2 is 1.

2/3 x 3/2 = 1

*Example 2*

The reciprocal of a whole number 7 is 1/7 bereason 7 x 1/7 = 1.

### How to Find the Reciprocal of a Mixed Number?

In order to discover the reciprocal of a blended fractivity, convert it right into improper fraction first and also then use the exact same preeminence we learnt over.

*Example 3*

Find the reciprocal of 4 1/2.

Solution

Convert a mixed fractivity into an improper fractivity as calculated below.4 1/2 = (4 x 2) + 1/ 2

= 9/2

Now flip the numerator and also denominator of 9/2.Therefore, the solution for the reciprocal of 4 1/2 is 2/9.### How to Find the Reciprocal of Decimal Numbers?

Like other numbers, decimal numbers also have actually reciprocals. Calculating the reciprocal of a decimal number deserve to be done in the complying with ways:

It deserve to be provided that separating 1 by a fraction is the very same as multiplying the reciprocal of the number by 1. For example,

5 ÷ 1/4

= 5 x 4/1

= 20

*Example 4*

Solve the adhering to problems:

a. Find the reciprocal of 5

Solution

5 = 5/1

So, the reciprocal of 3 = 1/5

b. Find the reciprocal of 1/4

Solution

To discover the reciprocal of 1/4, invert the numerator and also denominator.

The reciprocal of 1/4 = 4

c. Determine the reciprocal of 10/3

Solution

Step 1:

To discover the reciprocal of 10/3, flip the numerator and denominator. The reciprocal = 3/10.

*Example 5*

If 4/7 of a number x is 84. What is the value of x?

Solution4/7 of a number x = 84Write the mathematical equation:

(4/7) x = 84

Multiply both sides by the reciprocal of 4/7Number x = 84 × 7/4

= 21 × 7= 147And for this reason, the number x is 147.

*Example 6*

A half of the students in a college are boys, 3/5 of these boys take scientific research courses and the remainder take humanities. What fraction of the boys take humanities?

Solution

Fraction of boys in the college = 1/2

Fractivity of boys who take scientific researches = 3/5 of 1/2

= 3/5 × 1/2

= 3 × 1/5 × 2

= 3/10

Therefore, 3/10 of the boys take liberal arts.

*Example 7*

Pedro has actually written three-fifth of his 75 paged research study work. How many kind of pages are left to finish composing his research?

SolutionNumber of pages created = 3/5 of 75= 3/5 × 7

= 45 pages.Number of pperiods left= 75 – 45.= 30 pperiods.

See more: Time Difference Between California And Florida, Is California 4 Hours Behind Florida

*Example 8*

A herd of cows in a farm produces 99 liters of milk daily. If each cow produces one-third of total milk produced in a day. How many type of cows are in the farm if 7700 liters of milk is developed weekly.

SolutionA herd of cows produces 99 liters of milk day-to-day.One cow produces 1/3 of total milk daily = 1/3 of 99Thus, one cow produces 11 liters.Total variety of animals in the farm= (7700/7) ÷ 11= 100 cows