Question

Simplify: \[63 - ( - 3)[\{ - 2 - \overline {8 - 3} \} + 3\{ 5 + ( - 2)( - 1)\} ]\]

Answer 1

Hint: The given question requires us to solve brackets. The first priority of the bracket is (), followed by {} and last []. We also have to apply the BODMAS rule to solve the given question according to the priority of the mathematical operators.

Complete step-by-step answer:
Mathematical operations such as addition, subtraction, multiplication, and division are included in arithmetic operations. In order to arrive at the correct answer, arithmetic operations must be solved in a specific order. For solving according to specific priority, we use the BODMAS rule.
BODMAS stands for Brackets, Order, Division, Multiplication, Addition and Subtraction. This means that:
First, the expressions within the brackets (), {}, [] are to be solved irrespective of the operators inside the brackets.
Next, the square roots and numbers with powers are to be solved. The O in BODMAS stands for Of or Order.
Then, we must solve the division operation, followed by multiplication, addition, and lastly, subtraction.
Now we can proceed to solve the question as follows:
First, the round brackets () will be solved
\[ = 63 + 3[\{ - 2 - \overline {8 - 3} \} + 3\{ 5 + 2\} ]\]
Next, we will solve the curly brackets {}. Inside the {}, we will first solve addition and then subtraction.
\[ = 63 + 3[\{ - 2 - \overline {8 - 3} \} + 3\{ 7\} ]\]
\[ = 63 + 3[\{ - 2 - 5\} + 3\{ 7\} ]\]
\[ = 63 + 3[\{ - 7\} + 3\{ 7\} ]\]
Now we will multiply the number adjacent to {}
\[ = 63 + 3[ - 7 + 21]\]
Solving the final bracket [], we get,
\[ = 63 + 3[14]\]
Multiplication will take precedence over addition. Hence, we will get,
\[ = 63 + 42\]
\[ = 105\]
Hence \[63 - ( - 3)[\{ - 2 - \overline {8 - 3} \} + 3\{ 5 + ( - 2)( - 1)\} ] = 105\].
So, the correct answer is “105”.

Note: Notice the line above \[\overline {8 - 3} \]. In mathematical terminology, it is known as Vinculum. A vinculum is a horizontal line used for a particular purpose in mathematical notation. It can be used as an over line over a mathematical expression to show that it should be regarded as a category/grouped item.