Question

How do you simplify $\dfrac{3}{4} - \dfrac{2}{3}$?

Answer 1

Hint: This problem deals with simplifying the given expression through the process of L.C.M. Given the expression in terms of fractions but not integers. So we have to proceed in the simplification of the given expression by applying the process of L.C.M to the denominators of the given two fractions in the expression.

Complete step-by-step solution:
Here consider the given expression as given below:
$ \Rightarrow \dfrac{3}{4} - \dfrac{2}{3}$
Now take the L.C.M of the both the denominators of $\dfrac{3}{4}$ and $\dfrac{2}{3}$.
Here the denominators are 4 and 3.
L.C.M is the least common multiple.
So now we have to find the least common multiple of 4 and 3, here as we know that the number 3 being a prime number. So the L.C.M of 4 and 3 would be the product of these numbers which is equal to 12.
As $4 \times 3 = 12$.
Now simplifying the given expression as shown below:
$ \Rightarrow \dfrac{3}{4} - \dfrac{2}{3}$
Here the common denominator will be the L.C.M. of the denominators 3 and 4, which is equal to 12.
$ \Rightarrow \dfrac{{3\left( 3 \right) - 2\left( 4 \right)}}{{12}}$
Now as the common denominator is formed, now while multiplying the numerator with the factor when split the denominators separately, which gives the same expression as given before.
Now simplifying the numerator as shown below:
$ \Rightarrow \dfrac{{9 - 8}}{{12}} = \dfrac{1}{{12}}$
$\therefore \dfrac{3}{4} - \dfrac{2}{3} = \dfrac{1}{{12}}$

The simplification of $\dfrac{3}{4} - \dfrac{2}{3}$ is $\dfrac{1}{{12}}$.

Note: Please note that while solving the above given problem, here the L.C.M of any two prime numbers will always be equal to their product, but whereas for two composite numbers, the L.C.M may or may not be equal to their product.