Question

How do you write the fraction $\dfrac{9}{{21}}$ in simplest form?

Answer 1

Hint: First we will reduce the term by forming factors of each term. Then we will factorise the other term. Form such two sets of the factors of the given terms. Then take the intersection of these two sets. Also, define the factorisation method.

Complete step-by-step solution:
We will start off by factoring each of the terms and then evaluating the common factors.
We will first evaluate the factors of $9$.
$\Rightarrow 9:\{ 1,3,9\} $
Now we will evaluate the factors of $21$.
$\Rightarrow 21:\{ 1,3,7,21\} $
Now we will evaluate the common factors among them and then substitute in the main fraction.
$
\Rightarrow \dfrac{{3 \times 3}}{{3 \times 7}} \\
\Rightarrow \dfrac{3}{7} \\
 $

Hence, the simplest form of fraction $\dfrac{9}{{21}}$ is $\dfrac{3}{7}$.

Additional information:Factorisation consists of writing a number or another mathematical object as a product of several objects of the same kind. In particular, a univariate polynomial with complex coefficients admits a unique factorisation into linear polynomials; this is a version of the fundamental theorem of algebra.by the fundamental theorem of arithmetic, every integer greater than $1$ has unique factorisation into prime numbers, which are those integers which cannot be further factored into the product of integers greater than one.

Note: The above solution can be done using another method.
Take the given expression: ${x^2} = 49$
Take the square root on both the sides of the equation.
$\sqrt {{x^2}} = \sqrt {{{( \pm 7)}^2}} $
Square and square root cancel each other.
$ \Rightarrow x = \pm 7$
Also, remember the square of positive and the negative term gives a result always as positive and square root of the positive term can give negative or positive terms.