Question

How do you write $\dfrac{14}{35}$ in simplest form?

Answer 1

Hint: Prime factorises the value given in numerator and denominator of the fraction given in the question, then divides both numerator and denominator of the fraction by that particular number which are common in both numerator and denominator.
Like,
\[\dfrac{4}{6}\], here, if we prime factorise 4 and 6 we will get,
\[4=2\times 2\]
\[6=2\times 3\]
As, 2 is common in both numerator and denominator, so dividing numerator and denominator of fraction by 2,
Hence, \[\dfrac{4}{6}\] in its simplest form will be \[\dfrac{2}{3}\], applying this concept to write the given fraction in its simplest form.

Complete step-by-step solution:
As per question,
As, we have to write, $\dfrac{14}{35}$ in its simplest form.
As, we know that,
Simplest form is that particular form of fraction in which we cannot further divide the numerator and denominator of fraction both by any common number.
So,
For writing $\dfrac{14}{35},$ we need to factorise both numerator and denominator of fraction.
As, we know that,
Prime factorisation of,
$14=2\times 7$
$35=5\times 7$
From above we can clearly conclude that $7$ is common in prime factorisation of both numerator and denominator.
So, for converting $\dfrac{14}{35}$ to simplest form, divide both numerator and denominator by $7.$
Hence,
$\dfrac{14}{35}=\dfrac{\dfrac{14}{7}}{\dfrac{35}{7}}$
$\Rightarrow \dfrac{2}{5}$

We can write $\dfrac{14}{35}$ into simplest form as $\dfrac{2}{5}$

Note: (1) The unit of fraction or any fractional value is unit less, means when we represent any term in form of fraction then doesn’t contain any specific unit.
(2) Fraction means part, like $\dfrac{2}{5}$ means, $2$ part out total $5$ part.
(3) Simplest form of fraction cannot be further divided by any of the common number except $1.$