Question

Find the simplified value of \[24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9\].
(a) \[ - 2\]
(b) 2
(c) 1
(d) 3

Answer 1

Hint: Here, we have to find the simplified value of the given expression. We will use the rule of B.O.D.M.A.S. to simplify the given expression and find its value.

Complete step by step solution:
We will use the rule of B.O.D.M.A.S. to simplify the given expression and find its value.
First, we will simplify the expression in the brackets.
Subtracting the numbers with the overline, we get
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 24 \div 3 - 9 \times 3 + \left( {52 - 4} \right) \div 4 + 9\]
Subtracting the numbers in the parentheses/brackets, we get
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 24 \div 3 - 9 \times 3 + 48 \div 4 + 9\]
Now, we will first apply the division operations in the expression.
Dividing 24 by 3 in the expression, we get
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 8 - 9 \times 3 + 48 \div 4 + 9\]
Dividing 48 by 4 in the expression, we get
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 8 - 9 \times 3 + 12 + 9\]
Now, we will first apply the multiplication operations in the expression.
Multiplying 9 by 3 in the expression, we get
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 8 - 27 + 12 + 9\]
Now, we will perform the addition operations in the expression.
Rewriting the expression, we get
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 8 + 12 + 9 - 27\]
Adding the numbers 8, 12, and 9 in the expression, we get
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 29 - 27\]
Finally, we will perform the subtraction operations in the expression.
\[ \Rightarrow 24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9 = 2\]
\[\therefore \] We get the simplified value of the expression \[24 \div 3 - 9 \times 3 + \left( {52 - \overline {8 - 4} } \right) \div 4 + 9\] as 2.
Thus, the correct option is option (b).

Note: The operation \[\overline {8 - 4} \] is a subtraction operation. However, the overline over \[\overline {8 - 4} \] acts as a bracket. Therefore, we have simplified this term within the brackets first.
The acronym B.O.D.M.A.S. stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. According to B.O.D.M.A.S., the expressions in the brackets are simplified first. Then, the division operations are performed, followed by the multiply operations. Then, the terms of the expression are added. Finally, the subtraction operations are performed to get the simplified value of the expression.