Question

How do you write $\dfrac{{45}}{{60}}$ in the simplest form$?$

Answer 1

Hint: In this question we are going to write the above fraction in the simplest form by using the Greatest Common Factor method.
First we are going to find the Greatest Common Factor of the numerator and the denominator.
Next divide both the numerator and the denominator by the Greatest Common Factor.
Hence we can get the required solution.

Complete step-by-step solution:
In this question we are going to write the above fraction in the simplest form.
First write the given fraction and mark it as $\left( 1 \right)$
The given fraction is $\dfrac{{45}}{{60}}$
Now we are going to find the Greatest Common Factor for both the numerator and the denominator
List the prime factors of each number.
$ \Rightarrow 45 = 5 \times 3 \times 3$
And $60 = 5 \times 2 \times 2 \times 3$
Both the numbers have $5$ and $3$ in common.
Multiplying those two numbers we get the GCF,
$ \Rightarrow 5 \times 3 = 15$
That is, GCF $\left( {45,60} \right)$ is $15$
Next divide both the numerator and the denominator by the Greatest Common Factor $15$ and rewrite the fraction.
$ \Rightarrow \dfrac{{\dfrac{{45}}{{15}}}}{{\dfrac{{60}}{{15}}}}$
$ \Rightarrow \dfrac{{45}}{{15}} \times \dfrac{{15}}{{60}}$
Simplifying the above step we can get the result,
$ \Rightarrow \dfrac{3}{4}$

Thus $\dfrac{3}{4}$ is the simplified fraction for $\dfrac{{45}}{{60}}$ by using the Greatest Common Factor method.

Note: We can also solve this problem by using another method as follows:
We are going to simplify the problem using the prime factorization method.
The given fraction is $\dfrac{{45}}{{60}}$
Now we are going to find the prime factors for both the numerator and the denominator and rewrite the fraction in the form of prime factors.
Prime factors for $45 = 5 \times 3 \times 3$
Prime factors for $60 = 5 \times 2 \times 2 \times 3$
$ \Rightarrow \dfrac{{45}}{{60}} = \dfrac{{5 \times 3 \times 3}}{{5 \times 2 \times 2 \times 3}}$
Solve and rewrite the fraction as
$ \Rightarrow \dfrac{{45}}{{60}} = \dfrac{3}{{2 \times 2}}$
$ \Rightarrow \dfrac{{45}}{{60}} = \dfrac{3}{4}$
Thus $\dfrac{3}{4}$ is the simplified fraction for $\dfrac{{45}}{{60}}$ by using the prime factorization method.