Question

Evaluate $2\left[ {\left\{ {\left( { - 36} \right) \div \left( { - 18} \right)} \right\} + \left( { - 13} \right) + \left( { - 18} \right) \times \left( { - 2} \right)} \right].$

Answer 1

Hint: Use the BODMAS rule to evaluate 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 $2\left[ {\left\{ {\left( { - 36} \right) \div \left( { - 18} \right)} \right\} + \left( { - 13} \right) + \left( { - 18} \right) \times \left( { - 2} \right)} \right].$
Expression contains one division, two multiplications and one addition.
In subtraction of two numbers, the sign of the result will be the sign of the largest of two numbers.
Solve the value in the square brackets first.
By BODMAS rule, we have to solve the division first.
$\left( { - 36} \right) \div \left( { - 18} \right)$ is the only division in the expression.
Solve the division and then replace the division with its result in the expression.
$
  \left( { - 36} \right) \div \left( { - 18} \right) = 2 \\
  2\left[ {\left\{ {\left( { - 36} \right) \div \left( { - 18} \right)} \right\} + \left( { - 13} \right) + \left( { - 18} \right) \times \left( { - 2} \right)} \right] = 2\left[ {2 + \left( { - 13} \right) + \left( { - 18} \right) \times \left( { - 2} \right)} \right] \\
 $
The next one is multiplication according to the BODMAS rule.
$\left( { - 18} \right) \times \left( { - 2} \right)$ is the multiplication. Solve the multiplication and replace the multiplication with its result in the expression.
$
  \left( { - 18} \right) \times \left( { - 2} \right) = 36 \\
  2\left[ {2 + \left( { - 13} \right) + \left( { - 18} \right) \times \left( { - 2} \right)} \right] = 2\left[ {2 + \left( { - 13} \right) + 36} \right] \\
 $
The next one is addition according to the BODMAS rule.
2+36 is the addition. Solve the addition and replace the addition with its result.
$
  2 + 36 = 38 \\
  2\left[ {2 + \left( { - 13} \right) + 36} \right] = 2\left[ {2 + 36 + \left( { - 13} \right)} \right] = 2\left[ {38 - 13} \right] \\
 $
The next one is subtraction.
38-13 is the subtraction. Solve the subtraction and replace the subtraction with its result.
$2\left[ {38 - 13} \right] = 2\left[ {25} \right] = 2 \times 25 = 50$
Therefore, the value of $2\left[ {\left\{ {\left( { - 36} \right) \div \left( { - 18} \right)} \right\} + \left( { - 13} \right) + \left( { - 18} \right) \times \left( { - 2} \right)} \right]$ is 50.

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.