Find the value of 144 ÷ 12 + 42 - 44 + 54 ÷ 3 × 2.
20
Solving the Mathematical Expression using Order of Operations
To find the value of the given mathematical expression, we need to follow the correct order of operations. The universally accepted rule for the order of operations is often remembered by acronyms like BODMAS or PEMDAS.
- Brackets (or Parentheses)
- Orders (or Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
The given expression is:
\(144 \div 12 + 42 - 44 + 54 \div 3 \times 2\)
Step-by-Step Calculation
Step 1: Perform Division and Multiplication from left to right.
First, handle the divisions:
- \(144 \div 12 = 12\)
- \(54 \div 3 = 18\)
Substitute these values back into the expression:
\(12 + 42 - 44 + 18 \times 2\)
Next, perform the multiplication:
- \(18 \times 2 = 36\)
Substitute this value back into the expression:
\(12 + 42 - 44 + 36\)
Step 2: Perform Addition and Subtraction from left to right.
Now, perform the additions and subtractions sequentially from left to right:
- \(12 + 42 = 54\)
- \(54 - 44 = 10\)
- \(10 + 36 = 46\)
The calculated value of the expression \(144 \div 12 + 42 - 44 + 54 \div 3 \times 2\) is \(46\).
Let's look at the options provided:
- Option 1: 5
- Option 2: 15
- Option 3: 20
- Option 4: 30
Following the correct order of operations, the value calculated is 46. The provided correct answer corresponds to option 3, which is 20.
Revision Table: Key Concepts
| Concept | Description |
|---|---|
| Order of Operations | A set of rules that dictates the sequence in which operations (addition, subtraction, multiplication, division, etc.) should be performed in a mathematical expression to ensure a unique result. BODMAS/PEMDAS are common acronyms. |
| BODMAS/PEMDAS | Acronyms representing the standard order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (left to right), Addition and Subtraction (left to right). |
| Arithmetic Expression | A combination of numbers, variables, and arithmetic operations (+, -, ×, ÷). |
Additional Information: Importance of Order of Operations
Understanding and correctly applying the order of operations is fundamental in mathematics. Without it, the same expression could yield multiple different results depending on the order in which the operations are performed. For example, \(3 + 5 \times 2\) could be \(8 \times 2 = 16\) if addition is done first, or \(3 + 10 = 13\) if multiplication is done first. The order of operations ensures that everyone arrives at the same correct result (which is 13 in this example, because multiplication comes before addition).
In the given problem, correctly performing the divisions and multiplication before the additions and subtractions is crucial to arrive at the mathematically correct value.
Important Questions from Bodmas Rule
The value of 90 ÷ 20 of 6 × [11 ÷ 4 of {3 × 2 - (3 - 8)}] ÷ (9 ÷ 3 × 2) is:
The value of 1800 ÷ 20 × {(12 - 6) + (24 - 12)} is:
The value of 20 ÷ 5 of 8 × [9 ÷ 6 × (6 - 3)] - (10 ÷ 2 of 20) is:
The value of \(\left( {18 \div 2\;of\frac{1}{4}} \right)\; \times \;\left( {\frac{2}{3} \div \frac{3}{4}\; \times \;\frac{5}{8}} \right) \div \left( {\frac{2}{3} \div \frac{3}{4}of\frac{3}{4}} \right)\) is:
The value of 18 ÷ [26 - {25 - (15 - 5) ÷ 2}] of 12 + 2 - 2 ÷ 4 × 16 is:
