Question

Convert to standard form:
$a)\,\dfrac{{146}}{{ - 365}}\,\,\,\,\,\,\,\,\,\,\,\,b)\,\dfrac{{ - 81}}{{108}}\,\,\,\,\,\,\,\,\,\,\,\,c)\,\dfrac{{35}}{{ - 14}}$

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 to get the answer

Complete step-by-step answer:
$a)\,\dfrac{{146}}{{ - 365}}\,$
At first we will find the factors of both numerator and denominator
Factors of numerator $146 = 2 \times 73$
Factors of denominator $365 = 5 \times 73$
Now writing it in factors we get
$\dfrac{{146}}{{ - 365}} = \dfrac{{2 \times 73}}{{ - 5 \times 73}}$
As $73$ is common to both numerator and denominator, we will cancel it out
$\dfrac{{146}}{{ - 365}} = \dfrac{2}{{ - 5}}$
Now in the standard form minus sign is supposed to be on the numerator but in this case it is on the denominator. Hence we will multiply numerator and denominator by $ - 1$
Multiplying by $\dfrac{{ - 1}}{{ - 1}}$, we get
$\dfrac{{146}}{{ - 365}} = \dfrac{2}{{ - 5}} = - \dfrac{2}{5}$
$b)\,\dfrac{{ - 81}}{{108}}$
Factors of numerator $81 = 3 \times 3 \times 3 \times 3$
Factors of denominator $108 = 2 \times 2 \times 3 \times 3 \times 3$
Using these factors we get
$ - \dfrac{{81}}{{108}} = \dfrac{{3 \times 3 \times 3 \times 3}}{{2 \times 2 \times 3 \times 3 \times 3}}$
Now $3 \times 3 \times 3$ is common so we will cancel it
$ - \dfrac{{81}}{{108}} = - \dfrac{3}{4}$
As minus is on is the numerator.
Therefore, this is standard form.
$c)\,\dfrac{{35}}{{ - 14}}$
Factors of numerator $35 = 5 \times 7$
Factors of denominator $14 = 2 \times 7$
$\dfrac{{35}}{{ - 14}} = \dfrac{{5 \times 7}}{{ - 2 \times 7}}$
Cancelling out common factor we get and also Multiplying by $\dfrac{{ - 1}}{{ - 1}}$we get,
$\dfrac{{35}}{{ - 14}} = \dfrac{5}{{ - 2}} = - \dfrac{5}{2}$

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 numerator. In this case the numbers were small but for factors for large numbers we can use the factorization method.