Question

How do you simplify $\left( {2\dfrac{1}{3} + 1\dfrac{2}{5}} \right) + 3\dfrac{2}{3}$

Answer 1

Hint: In order to solve this question we will first take the lowest common multiple (L.C.M) of the denominators and then we will put it as denominator and will divide the denominators individually the quotient coming will be multiplied by the consecutive numerator and the product coming will be added as it is “+” sign in between fraction and do same then add it.

Complete step-by-step solution:
For solving these types of question we will first solve the bracket then we will further solve the whole equation it is because we are applying the BODMAS which means:
B = Bracket
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
Before we apply this BODMAS we will first simplify this bracket so converting this mixed equation to fraction form:
$\left( {\dfrac{7}{3} + \dfrac{7}{5}} \right) + \dfrac{{11}}{3}$
Now on solving the bracket we will be getting the L.C.M of denominator as 15 and we will be solving it by dividing the whole denominator by individual denominator and multiplying it by the numerator and solving it:
$\left( {\dfrac{{35 + 21}}{{15}}} \right) + \dfrac{{11}}{3}$
Now we will be finalizing the bracket:
$\dfrac{{56}}{{15}} + \dfrac{{11}}{3}$
Now similarly we will applying the same process for solving these two fraction we will getting the L.C.M as 15 now we will diving the whole denominator to the individual denominator and multiplying it by numerator:
$\dfrac{{56 + 55}}{{15}}$
Now on further solving this we will be getting:
$\dfrac{{111}}{{15}}$

Hence the correct answer is $\dfrac{{111}}{{15}}$

Note: While solving these types of we should keep in mind that the solution may be done will the preference of the BODMAS if it not done in such a way the answer we will obtain will be wrong, in case we obtain correct answer the method we are applying will be wrong.