Question

How do you simplify \[2\dfrac{1}{2} + 7\left( {\dfrac{6}{7} - \dfrac{1}{7}} \right)\]?

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 and vice versa.

Complete step-by-step solution:
For solving these types of questions we will first give the preference to the BODMAS which means we will give the preference to the:
B = Bracket
O = Of
D = Division
M = Multiplication
A = Addition
S = subtraction
For solving this question we will first take the L.C.M of the denominators of the bracket as we are preferring to the BODMAS:
So the L.C.M of 7 and 7 will be 7 now we will putting the 7 as the whole denominator and we will dividing this whole denominator to the individual denominator and multiply it by the numerator and we will be putting these two as explained and putting the sign as given in the bracket.
$2\dfrac{1}{2} + 7\left( {\dfrac{{6 - 1}}{7}} \right)$
On further solving this we will get:
$\dfrac{5}{2} + 7\left( {\dfrac{5}{7}} \right)$
Now on cancelling the possible terms and further solving:
$\dfrac{5}{2} + 5$
Since 5 is written so we will consider it’s denominator as 1:
$\dfrac{5}{2} + \dfrac{5}{1}$
Now taking the L.C.M, we will be satisfying that the L.C.M will be 2 so similarly what we have done for the bracket we will get:
$\dfrac{{5 + 10}}{2}$
On further solving this we will be getting:
$\dfrac{{15}}{2}$

Hence the correct answer is $\dfrac{{15}}{2}$

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.