Question

How do you solve \[x - \dfrac{2}{3} = \dfrac{4}{5}\] ?

Answer 1

Hint: We need to find the value of ‘x’. The given problem we need to rearrange the given equation by adding \[\dfrac{2}{3}\] on both sides of the equation. Afterwards we will have a sum of two fractions. We can solve this using the LCM method and on further simplifying we will get the required result.

Complete step-by-step answer:
We have
 \[x - \dfrac{2}{3} = \dfrac{4}{5}\] .
Now adding \[\dfrac{2}{3}\] on both sides of the equation, we have:
 \[x = \dfrac{4}{5} + \dfrac{2}{3}\]
Now we need to find the LCM of 5 and 3.
Since ‘3’ as factors 1 and 3.
‘5’ as factors 1 and 5.
We can see that the least common factor is \[3 \times 5 = 15\] .
Now multiplying and dividing the whole right hand side of the equation by 15. We get,
 \[ \Rightarrow x = \dfrac{{\left( {\dfrac{4}{5} + \dfrac{2}{3}} \right) \times 15}}{{15}}\]
 \[ = \dfrac{{\left( {\dfrac{4}{5} \times 15 + \dfrac{2}{3} \times 15} \right)}}{{15}}\]
On cancelling on the numerator we get,
 \[ = \dfrac{{\left( {(4 \times 3) + (2 \times 5)} \right)}}{{15}}\]
 \[ = \dfrac{{12 + 10}}{{15}}\]
 \[ = \dfrac{{22}}{{15}}\] .
Thus we have \[ \Rightarrow x = \dfrac{{22}}{{15}}\]
So, the correct answer is “$x = \dfrac{{22}}{{15}}$”.

Note: Fractions are a big part of our daily life and the mathematical world, so we must understand how to perform mathematical operations on two different fractions. In the given question, we have to add the two given fractions. The fractions having the same denominator can be added easily but when the denominators are different, then we first find the LCM of the terms in the denominator and then add the fractions. Using this approach, we can find out the correct answer. Here we can see in the above problem that ‘3’ and ‘5’ are prime numbers. The LCM of prime numbers is equal to the product of the numbers.