Question

Express \[\dfrac{{168}}{{ - 294}}\]as a rational number with denominator: 1470

Answer 1

Hint: We check if the number required in the denominator is formed by multiplying any value to the given denominator. If so we multiply both numerator and denominator with that same number to form a new fraction. Change the negative sign from denominator to numerator by multiplying -1 to both numerator and denominator.
* A rational number is a number that can be represented in the form of \[\dfrac{p}{q}\] where ‘p’ is the numerator and ‘q’ is the denominator.

Complete step-by-step solution:
We are given a fraction \[\dfrac{{168}}{{ - 294}}\].............… (1)
Since we have to express this given number as a rational number having denominator 1470, we check if 1470 is a multiple of 294
We see that \[294 \times 5 = 1470\]
So, 1470 is a multiple of 294
We multiply the fraction given in equation (1) by 5 both in numerator and denominator.
\[ \Rightarrow \dfrac{{168}}{{ - 294}} = \dfrac{{168}}{{ - 294}} \times \dfrac{5}{5}\]
Calculate the product in numerator and denominator in RHS of the equation
\[ \Rightarrow \dfrac{{168}}{{ - 294}} = \dfrac{{840}}{{ - 1470}}\]
We want the number 1470 in the denominator but we have -1470 in the denominator.
We multiply the fraction by -1 on both numerator and denominator
\[ \Rightarrow \dfrac{{168}}{{ - 294}} = \dfrac{{840}}{{ - 1470}} \times \dfrac{{ - 1}}{{ - 1}}\]
Calculate the product in numerator and denominator in RHS of the equation
\[ \Rightarrow \dfrac{{168}}{{ - 294}} = \dfrac{{ - 840}}{{1470}}\]

\[\therefore \]The fraction \[\dfrac{{168}}{{ - 294}}\] as a rational number with denominator 1470 is \[\dfrac{{ - 840}}{{1470}}\]

Note: For this type of question many cancel the common factors between numerator and denominator in terms of writing the simplest form of fraction. Keep in mind we require the denominator to be a fixed number so we don’t cancel the factors instead we multiply with more required terms so as to make the fraction similar to our requirement.