Question

Write each of the following rational numbers in standard form:
\[\dfrac{{299}}{{ - 161}}\]

Answer 1

Hint: Here we are given a rational number which is not in standard form. We are asked to convert this number into standard form. To do this first of all we divide them with their common factors till we reach a point where we cannot divide it further and the only common factor left between them is \[1\]. Then we make sure that there is no negative sign on the denominator. Thus we will reach the standard form of a given number.

Complete step-by-step solution:
We are given a rational number \[\dfrac{{299}}{{ - 161}}\] and are required to write it in standard form.
We know that if a rational number is such that both the numerator and denominator have \[1\] as only common factors and there is no negative sign on the denominator, the rational number is said to be in standard form.
Using this we will divide them with their common factors. We know that \[23\] is their only common factor other than \[1\]. So we move ahead as,
\[ \Rightarrow \dfrac{{299}}{{ - 161}} = \dfrac{{13}}{{ - 7}}\]
We know that there is no negative sign on denominator in standard form, so,
\[ \Rightarrow \dfrac{{299}}{{ - 161}} = \dfrac{{ - 13}}{7}\]
Thus we get the standard form of \[\dfrac{{299}}{{ - 161}}\] as \[\dfrac{{ - 13}}{7}\].

Note: We can also say that in standard form both the numerator and denominator are co-prime to each other. We should always try to write any rational number in its standard form as it is the simplest form of that number. Always try to divide the numerator and denominator with the Greater Common Factor as it can lead to the faster simplifications of the fraction.