Question

How do you simplify \[\dfrac{2}{3} + \dfrac{5}{6}\]?

Answer 1

Hint: Here, we will first find the LCM of the given factions and then convert the unlike fractions into like fractions by using the obtained LCM. Then we will add the fractions with the same denominator by using basic mathematical operations to get the required answer.

Complete Step by Step Solution:
We are given an expression in the form of fractions with unequal denominators.
We will find the sum of two fractions with two unequal denominators by finding the Least common multiple of the denominators and then by equalizing the denominators of the two fractions.
Thus, the unlike fraction is converted into a like fraction.
Now, we will find the LCM of two numbers 3 and 6.
 $\begin{array}{*{35}{l}}
   3 & 3 & 6 \\
   2 & 1 & 2 \\
   1 & 1 & 1 \\
\end{array}$
\[L.C.M\left( {3,6} \right) = 3 \times 2\]
Multiplying the terms, we get
\[ \Rightarrow L.C.M\left( {3,6} \right) = 6\]
Thus, the Least Common Multiple of two numbers is 6.
Now, we will find the sum of two fractions.
\[\dfrac{2}{3} + \dfrac{5}{6} = \dfrac{2}{3} \times \dfrac{2}{2} + \dfrac{5}{6} \times \dfrac{1}{1}\]
Multiplying the terms, we get
\[ \Rightarrow \dfrac{2}{3} + \dfrac{5}{6} = \dfrac{4}{6} + \dfrac{5}{6}\]
Now, by rewriting the equation, we get
\[ \Rightarrow \dfrac{2}{3} + \dfrac{5}{6} = \dfrac{{4 + 5}}{6}\]
Adding the terms, we get
\[ \Rightarrow \dfrac{2}{3} + \dfrac{5}{6} = \dfrac{9}{6}\]
Now, dividing the numerator and denominator by a common factor 3, we get
\[ \Rightarrow \dfrac{2}{3} + \dfrac{5}{6} = \dfrac{3}{2}\]

Therefore, the sum of two fractions \[\dfrac{2}{3} + \dfrac{5}{6}\] is\[\dfrac{3}{2}\].

Note: We know that the fractions with the same denominators are called fractions. The fractions with different denominators are called, unlike fractions. Whenever adding or subtracting the fractions, all the fractions should be like fractions. To convert an unlike fraction into a fraction, it is necessary to find the LCM of two numbers. The Least Common Multiple (L.C.M) of two numbers is defined as the smallest number which is divisible by both the numbers. But it is not necessary to have both the denominators the same while doing multiplication and division.