Question

Solve \[3\dfrac{1}{2} + 4\dfrac{2}{3}\]

Answer 1

Hint:
To solve this problem, first convert the mixed fraction into fraction. To do that, if we considered the first term \[3\dfrac{1}{2}\], to convert this into fraction we need to multiply $3$ and $2$ we get $6$, add this with the number $1$ and the answer will be $7$, this is our numerator of our required fraction and the denominator will be $2$. The required fraction will be $\dfrac{7}{2}$. And repeat the same for the second term too and simplify further more you will get the required answer.

Complete step by step solution:
Let us consider the given question,
\[3\dfrac{1}{2} + 4\dfrac{2}{3}\]
To convert this into fraction, first we need to know what is mixed fraction. Mixed fraction is nothing, but the combination of a whole number and the fraction. Let us consider the first term which is \[3\dfrac{1}{2}\]. Here, $3$ is the whole number and $\dfrac{1}{2}$ is the fraction. To convert this into fraction follow the three steps given below,
Step: -1 Multiply the whole number and the denominator of the fraction, which is,
$3 \times 2 = 6$
Step: -2 Add $6$ and $1$, which is in the numerator of the fraction. We get
$6 + 1 = 7$
Step: -3 $7$ is the numerator of the required fraction. And the denominator is the denominator of
the given fraction which is $2$. And the required fraction is,
\[3\dfrac{1}{2} = \dfrac{7}{2}\] … (1)
Repeat the step for the second term we get,
\[4\dfrac{2}{3} = \dfrac{{14}}{3}\] … (2)
Add (1) and (2), we get
\[3\dfrac{1}{2} + 4\dfrac{2}{3} = \dfrac{7}{2} + \dfrac{{14}}{3}{\text{ }}\]
Taking L.C.M we get,
\[3\dfrac{1}{2} + 4\dfrac{2}{3} = \dfrac{{21 + 28}}{6}3\dfrac{1}{2} + 4\dfrac{2}{3} = \dfrac{{49}}{6}\]
This is our required answer.

Note: To take L.C.M for any two fractions, let’s say \[\dfrac{7}{2} + \dfrac{{14}}{3}\], consider the denominator of the two fractions which is $2$ and $3$, now find the least common multiple of both the number which is $6$. The LCM is $6$.
\[\dfrac{7}{2} + \dfrac{{14}}{3} = \dfrac{{7 \times 3}}{{2 \times 3}} + \dfrac{{14 \times 2}}{{3 \times 2}} = \dfrac{{21 + 28}}{6} = \dfrac{{49}}{6}\]
This is our required answer.