Question

Find the value of $25of\left[ {62 - \left\{ {6 \times 4 \times \left( {19 - 2} \right)of8} \right\}} \right]$

Answer 1

Hint: ‘of’ means multiplication. So multiply the terms when there is an ‘of’ between them. Use the BODMAS rule to solve the given expression. First solve the division part, next solve the multiplication, after this addition and finally subtraction. If any of the operations in the expression is missing then just jump to the next operation following the BODMAS rule.

Complete step-by-step answer:
We are given to evaluate the expression $25of\left[ {62 - \left\{ {6 \times 4 \times \left( {19 - 2} \right)of8} \right\}} \right]$
Replace ‘of’ with a multiplication symbol.
$25of\left[ {62 - \left\{ {6 \times 4 \times \left( {19 - 2} \right)of8} \right\}} \right] = 25 \times \left[ {62 - \left\{ {6 \times 4 \times \left( {19 - 2} \right) \times 8} \right\}} \right]$
Expression contains four multiplications and two subtractions.
In subtraction of two numbers, the sign of the result will be the sign of the larger of two numbers.
By BODMAS rule, we have to solve the division first. But there is no division so multiply.
$6 \times 4$ is the plain multiplication, so solve it first.
$
  6 \times 4 = 24 \\
   \to 25 \times \left[ {62 - \left\{ {6 \times 4 \times \left( {19 - 2} \right) \times 8} \right\}} \right] = 25 \times \left[ {62 - \left\{ {24 \times \left( {19 - 2} \right) \times 8} \right\}} \right] \\
 $
To multiply 24 with (19-2) first solve the subtraction. The sign of the larger number is positive so the result will have the positive sign.
$
  19 - 2 = 17 \\
  25 \times \left[ {62 - \left\{ {24 \times \left( {19 - 2} \right) \times 8} \right\}} \right] = 25 \times \left[ {62 - \left\{ {24 \times 17 \times 8} \right\}} \right] \\
 $
Now find the product of 24, 17 and 8.
$
  24 \times 17 \times 8 = 3264 \\
  25 \times \left[ {62 - \left\{ {24 \times 17 \times 8} \right\}} \right] = 25 \times \left[ {62 - 3264} \right] \\
 $
Now solve the expression in the square brackets, subtraction. The sign of the larger number is negative so the result will have the negative sign.
$
  62 - 3264 = - 3202 \\
  25 \times \left[ {62 - 3264} \right] = 25 \times \left( { - 3202} \right) \\
 $
Now solve the final multiplication.
$25 \times \left( { - 3202} \right) = - 80050$
Therefore, the value of $25of\left[ {62 - \left\{ {6 \times 4 \times \left( {19 - 2} \right)of8} \right\}} \right]$ is -80050.

Note: BODMAS stands for Brackets Orders Division Multiplication Addition Subtraction. This rule states that if an expression contains brackets ((), {}, []) we have to solve the bracket first followed by orders which means powers and roots, then division, multiplication, addition and subtraction from left to right. So be careful with the order while solving arithmetic expressions.