Question

How do you add and subtract fractions with unlike denominators?

Answer 1

Hint: We are given that when fractions with unlike denominators are given then how is the addition and the subtraction operation is carried out. When denominators are not the same, then in that case we make it similar by using the Least Common Multiple (LCM), else we can’t even begin solving them. And once the denominators of both the fractions are similar then we carry out the addition and the subtraction operations easily.

Complete step by step answer:
According to the question given to us, we are given fractions with unlike denominators. And we have to make these fractions undergo addition and subtraction operations.
So, in order to get these fractions undergo addition and subtraction operations, we will first have to make the denominator the same. And for making the denominators the same, we will be using the Least Common Multiple(LCM).
For example – if we have the fractions \[\dfrac{1}{2}\] and \[\dfrac{2}{3}\], then addition of these fractions would be,
\[\dfrac{1}{2}+\dfrac{2}{3}\]
\[LCM(2,3)=6\]
So, we have the LCM as,
\[\Rightarrow \dfrac{3+4}{6}\]
Simplifying the above expression further,
\[\Rightarrow \dfrac{7}{6}\]
Similarly, the subtraction of the fraction is as follows,
\[\dfrac{1}{2}-\dfrac{2}{3}\]
\[LCM(2,3)=6\]
So, we have the LCM as,
\[\Rightarrow \dfrac{3-4}{6}\]
Simplifying the above expression further,
\[\Rightarrow \dfrac{-1}{6}\]

Note: The LCM of two numbers is found by taking the least factor that is common between two numbers. For example – LCM of 6 and 9
\[6=2\times 3\]
\[9=3\times 3\]
So, the LCM will be \[2\times 3\times 3=18\]. Here, from 6 we have taken 2 and from 9 we have taken 3 and since an additional 3 is present in both 6 and 9, we will write 3 again.