Question

By what number should $ - \dfrac{{33}}{{60}}$ be divided to get $ - \dfrac{{22}}{8}$ ?

Answer 1

Hint: In this question, we have to deal with rational numbers. A number is called rational when it can be expressed in the form $\dfrac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$; otherwise the number would become infinity. Some examples of rational numbers are: $\dfrac{1}{2},{\text{ }}\dfrac{4}{3},{\text{ }}\dfrac{5}{7},{\text{ }}1$ etc. Similarly, we have irrational numbers and they can not be expressed in the form $\dfrac{p}{q}$. Examples of irrational numbers are:$\sqrt 2 ,\sqrt 3,{\text{ }}\pi $ etc. All rational and irrational numbers together make the collection of real numbers , which is denoted by the letter $R$.

Complete step by step answer:
Let the required number is $x$ , then according to the given question;
$ \left( { - \dfrac{{33}}{{60}}} \right) \div x = \left( { - \dfrac{{22}}{8}} \right)$
We know that, if $a \div b = a \times \dfrac{1}{b}$
Using the above logic, our equation reduces to;
$ \left( { - \dfrac{{33}}{{60}}} \right) \times \dfrac{1}{x} = \left( { - \dfrac{{22}}{8}} \right)$
On further simplification;
$ \dfrac{{33}}{{60}} \times \dfrac{1}{x} = \dfrac{{22}}{8}$
$ \Rightarrow \dfrac{{11}}{{20}} \times \dfrac{1}{x} = \dfrac{{11}}{4}$
We have to find the value of $x$ , therefore taking all the other values to the other side;
$ \Rightarrow \dfrac{1}{{20}} \times \dfrac{1}{x} = \dfrac{1}{4}$
Further solving the above equation, we get the value of $x$ as;
$ \Rightarrow x = \dfrac{1}{5}$
Therefore , $\left( { - \dfrac{{33}}{{60}}} \right)$ should be divided by $\dfrac{1}{5}$ to get the value equals to $\left( { - \dfrac{{22}}{8}} \right)$.

Note: There are some special characteristics of rational numbers. Every rational number can be either expressed as terminating decimal or repeating decimal. $\left( 1 \right)$ Every number with a terminating decimal point is a rational number. For example: $2.5$ . $\left( 2 \right)$ Every number with repeating decimal is also a rational number. For example: $3.333333$ . So, either a rational number will be a terminating decimal
or a repeating decimal. An irrational number on the other hand will neither be a terminating nor a
repeating decimal . For example: $2.4897623$ and the value goes on like this . So, non-terminating and
non-repeating decimals are properties of irrational numbers.