Question

Solve
 \[16 + 20 \times 40 \div 20 \times 40 - 20 = ? \]

Answer 1

Hint: Use BODMAS rule to solve the given expression in the problem, which is given as:
B- Bracket
O- of
D- Division
M- Multiplication
A- Addition
S- Subtraction
Follow the above priority orders from left to right of the given expression. Don't solve the expression from any side without using the BODMAS rule.

Complete step-by-step answer:
As, we need to find the value if the expression: -
 \[16 + 20 \times 40 \div 20 \times 40 - 20 = ? \] . . . . . . . . . (i)
Now, we know the rule of BODMAS is given as:
B- Bracket first
O- Orders (i.e. Powers, of, square roots)
D- Division (left to right)
M- Multiplication (left to right)
A- Addition (left to right)
S- Subtraction (left to right)
The above rule suggests that we need to follow the priority of the above mentioned order with any given expression with involvement of algebraic signs \[ + , - , \times , \div ,(\,\,\,),\,of \] etc.
Now, coming to the question, given expression in the question is:
 \[16 + 20 \times 40 \div 20 \times 40 - 20 = ? \]
Now, as the given expression has not any involvement of bracket and of/square/power etc., so, we need to solve \[' \div ' \] part between two numbers 40 and 20 as follows:
 \[16 + 20 \times 40 \div 20 \times 40 - 20 \]
So, we know \[40 \div 20 = 2 \] , hence, the above expression will become
 \[16 + 20 \times 2 \times 40 - 20 \] . . . . . . . . . (ii)
Now, as there is no investment of \[' \div ' \] sign more in the above expression, so, we need to solve the multiplication \[\left( \times \right) \] between numbers 20 and 2 because we have to solve the expression from left to right as per the rules of BODMAS.
Hence, as we know:
 \[20 \times 2 = 40 \]

So, we can write the expression (ii) as
 \[16 + 40 \times 40 - 20 \] . . . . . . . . . (iii)
Now, we need to solve \[40 \times 40 \] in the above expression as per the BODMAS rule.
So, we know
 \[40 \times 40 = 1600 \]
Hence, equation (iii) can be re-written as:
 \[16 + 1600 - 20 \] . . . . . . . . . (iv)
Now, as we can observe that there is no further involvement of \[\left( \times \right) \] sign in the above expression. So, we need to solve \[16 + 1600 \] first as per the priority of \[' + ' \] and \[' - ' \] in the BODMAS rule. So, we know:
 \[16 + 1600 = 1616 \]

Hence, equation (iv) can be written as:
 \[1616 - 20 \] . . . . . . . . . (v)

Now, we can subtract 20 from 1616 simply to solve the above expression. Hence, we get the above equation as:
 \[1616 - 20 = 1596 \]

Hence, we get the value of the given expression in the problem as:
 \[16 + 20 \times 40 \div 20 \times 40 - 20 = 1596 \]


Note: One may solve the given expression from the left side and proceed to right without using the BODMAS rule, which is the wrong approach and will not give the same answer as given in the solution. There may be the same problem which can give the same answer by solving the expression from left to right but do not think that we can solve all the problems of this kind without using the BODMAS rule. So, be careful with this concept. This is the blunder mistake done by the students with these types of problems.

Always apply BODMAS rule from left to right side i.e. solve \[' \div '\,or\,' \times '\,or\,' - '\,or\,' + ' \] from left side (which is coming first from left).