Question

Solve $ \dfrac{{13}}{7} \div \dfrac{2}{5} - \dfrac{1}{2} + 2\dfrac{2}{3} \times \dfrac{6}{7} $

Answer 1

Hint: In order to answer this question, to solve the given expression, we will go through the BODMAS rule, and we will perform the various operations as per the BODMAS rule step by step to get the required value.

Complete step by step solution:
As we can see, the given expression will be solved by the BODMAS rule.
The given expression is:
 $ \dfrac{{13}}{7} \div \dfrac{2}{5} - \dfrac{1}{2} + 2\dfrac{2}{3} \times \dfrac{6}{7} $
As we know, in BODMAS rule- there are various operations that will be done to get the final value. In this rule, we will do operations in a manner.
Step-1: We will first check whether the bracket is in the expression or not, if the bracket is there then we will do it on the bracket first, or if the bracket is not there then we will do the next operation according to the BODMAS rule. So, in the given operation we will do division operation first as bracket is not in the given expression:
 $
  \therefore \dfrac{{13}}{7} \div \dfrac{2}{5} - \dfrac{1}{2} + 2\dfrac{2}{3} \times \dfrac{6}{7} \\
   = \dfrac{{13}}{7} \times \dfrac{5}{2} - \dfrac{1}{2} + \dfrac{8}{3} \times \dfrac{6}{7} \\
   = \dfrac{{65}}{{14}} - \dfrac{1}{2} + \dfrac{{16}}{7} \;
  $
Step-2: Now, according to the BODMAS rule, we will do the addition operation-
 $
   = \dfrac{{65 + 32}}{{14}} - \dfrac{1}{2} \\
   = \dfrac{{97}}{{14}} - \dfrac{1}{2} \;
  $
Step-3: Now, only one operation is left i.e.. subtraction:-
 $
   = \dfrac{{97 - 7}}{{14}} \\
   = \dfrac{{90}}{{14}} \\
   = \dfrac{{45}}{7} \;
  $
Hence, the required value of the given expression is $ \dfrac{{45}}{7} $ .
So, the correct answer is “ $ \dfrac{{45}}{7} $ ”.

Note: BODMAS is an acronym and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS