What is $\frac{11}{45}$ multiplied by its reciprocal

Full solution

Q. What is

\frac{11}{45}

multiplied by its reciprocal

Understand Reciprocal Concept: Understand the concept of a reciprocal. The reciprocal of a number is a number which, when multiplied by the original number, gives a product of $1$ . For a fraction, the reciprocal is obtained by swapping the numerator and the denominator.
Identify Reciprocal of $\frac{11}{45}$ : Identify the reciprocal of $\frac{11}{45}$ . The reciprocal of $\frac{11}{45}$ is $\frac{45}{11}$ because we swap the numerator and the denominator.
Multiply by Reciprocal: Multiply the original fraction by its reciprocal. $\newline$ Now we multiply $\frac{11}{45}$ by its reciprocal, which is $\frac{45}{11}$ . $\newline$ $(\frac{11}{45}) \times (\frac{45}{11}) = (\frac{11\times45}{45\times11})$
Simplify Multiplication: Simplify the multiplication. $\newline$ Since the numerator and the denominator have common factors, they can be simplified. $\newline$ $(11\times45) / (45\times11) = 1/1$ $\newline$ This is because $11/11$ is $1$ and $45/45$ is also $1$ .
Conclude Result: Conclude the result. $\newline$ The result of multiplying a number by its reciprocal is always $1$ .