Question

Write the following rational numbers in the standard form: $\dfrac{{68}}{{ - 119}}$.

Answer 1

Hint: In order to solve this question, we need to find the factors of the numerator and denominator at first. Then we need to cancel out the common factors from both the numerator and denominator. After that multiply numerator and denominator by -1 to get the answer.

Complete step-by-step answer:
Given: - The number is $\dfrac{{68}}{{ - 119}}$.
At first, we will find the factors of both numerator and denominator.
The factors of the numerator are,
$ \Rightarrow 68 = 2 \times 2 \times 17$
The factors of denominator are,
$ \Rightarrow 119 = 7 \times 17$
Now writing it in factors we get,
$ \Rightarrow \dfrac{{68}}{{ - 119}} = \dfrac{{2 \times 2 \times 17}}{{ - 7 \times 17}}$
As 17 is common to both numerator and denominator, we will cancel it out,
$ \Rightarrow \dfrac{{68}}{{ - 119}} = \dfrac{4}{{ - 7}}$
Now in the standard form minus sign is supposed to be on the numerator but in this case, it is on the denominator. So, we will multiply numerator and denominator by -1,
Multiplying by -1, we get
$ \Rightarrow \dfrac{{68}}{{ - 119}} = \dfrac{4}{{ - 7}} \times \dfrac{{ - 1}}{{ - 1}}$
Simplify the terms,
$\therefore \dfrac{{68}}{{ - 119}} = \dfrac{{ - 4}}{7}$

Hence the number $\dfrac{{68}}{{ - 119}}$ in the standard form is $\dfrac{{ - 4}}{7}$.

Note: Standard form in the above question means that the numerator and denominator should have no number in common i.e. they are co-prime numbers and if there is a negative sign, it should be on the numerator. In this case, the numbers were small but for factors for large numbers, we can use the factorization method.
In mathematics, rational numbers are the numbers that can be represented as $\dfrac{p}{q}$, where p and q are integers and q must not be equal to 0. If q is equal to 1 then the given rational number will become an integer, that means, every integer is a rational number.