Solve : 2 × 6 - 12 ÷ 4 + 2 = ?
11
Solving Mathematical Expressions Using Order of Operations
To solve mathematical expressions that involve multiple operations like multiplication, division, addition, and subtraction, we need to follow a specific order. This order is commonly known as BODMAS or PEMDAS.
- Brackets (or Parentheses)
- Orders (or Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's apply this rule to the given expression:
\(2 \times 6 - 12 \div 4 + 2\)
Step-by-Step Solution for the Expression
Following the BODMAS/PEMDAS rule:
Step 1: Perform Division and Multiplication
First, we look for division and multiplication operations from left to right.
- There is a multiplication: \(2 \times 6\). Calculate this first.
- There is a division: \(12 \div 4\). Calculate this next.
Calculating the multiplication:
\(2 \times 6 = 12\)
Calculating the division:
\(12 \div 4 = 3\)
Now, substitute these values back into the original expression:
The expression becomes: \(12 - 3 + 2\)
Step 2: Perform Addition and Subtraction
Next, we perform addition and subtraction operations from left to right.
- Start with the subtraction: \(12 - 3\).
- Then, perform the addition: Add \(2\) to the result.
Calculating the subtraction:
\(12 - 3 = 9\)
Now, add the remaining number:
\(9 + 2 = 11\)
Final Result of the Calculation
After following the order of operations, the final result of the expression \(2 \times 6 - 12 \div 4 + 2\) is \(11\).
| Operation | Step | Expression | Result |
|---|---|---|---|
| Original | - | \(2 \times 6 - 12 \div 4 + 2\) | - |
| Multiplication | 1 | \(12 - 12 \div 4 + 2\) | \(2 \times 6 = 12\) |
| Division | 2 | \(12 - 3 + 2\) | \(12 \div 4 = 3\) |
| Subtraction | 3 | \(9 + 2\) | \(12 - 3 = 9\) |
| Addition | 4 | \(11\) | \(9 + 2 = 11\) |
Revision Table: Key Math Concepts
| Concept | Description | Importance |
|---|---|---|
| Order of Operations | A rule that dictates the sequence in which mathematical operations should be performed. | Ensures a unique and correct answer for any mathematical expression. |
| BODMAS/PEMDAS | Acronyms representing the order: Brackets/Parentheses, Orders/Exponents, Division/Multiplication, Addition/Subtraction. | Helps remember the correct sequence of operations. |
| Mathematical Expression | A combination of numbers, variables, and operation symbols. | Represents a mathematical relationship or quantity. |
Additional Information on Order of Operations
The order of operations is fundamental in mathematics. Without it, expressions could have multiple different answers depending on the order in which operations are performed. For example, in the expression \(10 - 2 \times 3\), if you did subtraction first (\(10 - 2 = 8\)), then multiplied (\(8 \times 3 = 24\)), you'd get 24. However, following BODMAS/PEMDAS, multiplication comes before subtraction. So, you calculate \(2 \times 3 = 6\) first, then subtract (\(10 - 6 = 4\)), getting the correct answer, 4. This illustrates why following the prescribed order is crucial.
Remember that Division and Multiplication have the same priority, and you perform them from left to right as they appear in the expression. Similarly, Addition and Subtraction have the same priority and are performed from left to right.
Important Questions from Logical Puzzle
Which two numbers should be interchanged to make the given equation correct?
9 + 7 × 5 – 18 ÷ 2 = 3 × 4 – 10 + 45 ÷ 5Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the equation.
60 * 2 * 3 * 6 * 5 * 43
Which of the following interchange of numbers and mathematical signs would make the given equation correct?
30 ÷ 6 × 4 + 15 - 35 = 25
Which two signs need to be interchanged to make the following equation correct?
23 + 84 ÷ 14 × 8 − 3 = 5
Select the correct combination of mathematical signs that can sequentially replace the * signs and make the equation correct.
68 * 138* 23 * 54 * 20
