Question

How do you $\dfrac{{12}}{{18}}$ to its lowest term?

Answer 1

In this question we need to determine the lowest term of $\dfrac{{12}}{{18}}$. We will determine the greatest common factor of both the numbers and then divide the numbers with the GCF obtained, by which we will get the required answer.

Complete step-by-step solution:
We need to determine $\dfrac{{12}}{{18}}$ to its lowest term.

Now, let us determine the greatest common factor of $12$ and $18$.

First, we are going to determine the prime factorization of both the given numbers.

Prime factorization is a method of finding prime numbers which multiply to make the original number.

Now, let us determine the prime factorization of $12$,
$12 = 2 \times 2 \times 3$

Now, let us determine the prime factorization of $18$,
$18 = 2 \times 3 \times 3$

So, from the prime factorization of both the numbers, we can say that the common factors of both the numbers are $2$ and $3$.

Therefore, to determine the GCF of both the given numbers, we need to multiply the common factors of $12$ and $18$.

Thus, GCF$= 2 \times 3$ $= 6$

Hence, the GCF of $12$ and $18$ is $6$.

Now to determine the lowest term let us divide both the numerator and denominator of
$\dfrac{{12}}{{18}}$ by the GCF of the two numbers which is $6$.

$\dfrac{{\dfrac{{12}}{6}}}{{\dfrac{{18}}{6}}} = \dfrac{2}{3}$

Therefore, the lowest term of $\dfrac{{12}}{{18}}$ is $\dfrac{2}{3}$.

Note: In this question it is important to note that the Greatest Common Factor (GCF) is the greatest number that will divide both $12$ and $18$. In other words, it is the number that contains all the factors common to both numbers. The Greatest Common Factor (GCF) is also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF).

We have another method for finding the GCF, which is called ‘listing’. In that method we will list the multiples of both the given numbers until we find the first duplicate. But, this method is awful for the greatest numbers.

To reduce the fraction to its lowest term, divide the numerator and the denominator by the greatest common factor (GCF). This is called simplifying the fraction.