Question

What is a reciprocal in math?

Answer 1

Hint: First, we will need to know about the concept of the reciprocal and then we will also check the reciprocals of the numbers.
Reciprocal is more like the fraction’s terms. If the given number is in the form of an integer then the reciprocal will be in the form of fractions.
If the given number is in the form of integers then the reciprocal looks like the form of rational numbers which has ${\displaystyle \frac{p}{q}}$ a format where $p=1$ always in the reciprocal of any integers.

Complete step-by-step solution:
The reciprocal of the number is defined as the number divided by $1$. Since a number can be written as in the form of a fraction with a denominator of one.
Hence which is of the form of the number $3$ can be rewritten as ${\displaystyle \frac{3}{1}}$ and the reciprocal of this number can be represented as ${\displaystyle \frac{1}{3}}$
Thus, the number ${\displaystyle \frac{1}{x}}$ multiplied by the $x$ gives as the product $1$ is known as the reciprocal of the numbers also called the multiplicative inverse.
The reciprocal of a number is defined as Turing the numbers upside down, like reciprocal of the term${\displaystyle \frac{x}{y}}$ is ${\displaystyle \frac{y}{x}}$
The reciprocal of the numbers can be also expressed as ${\displaystyle \frac{1}{n}}$ to $n^{-1}$

Note: We know that ${\displaystyle \frac{3}{4}}=0.75$ in this case, the dividend is exactly divisible after a few steps;
While in the process we get the remainder is zero, such decimal numbers are known as terminating decimals.
Hence its reciprocal value is ${\displaystyle \frac{4}{3}}=1.333...$ and thus the values and its reciprocals values are not always the same
Now, look at this ${\displaystyle \frac{2}{3}}=0.6666......$in some fractions the division does not stop and obtain a certain block of digits which is repeated over and over again. Such kinds of decimals numbers are called recurring decimals.
 ${\displaystyle \frac{3}{2}}=1.5$ which is the reciprocal