The value of (26 - 13 × 2) ÷ 2 + 1 is:
1
Understanding the Order of Operations
To find the value of the expression (26 - 13 × 2) ÷ 2 + 1, we need to follow the correct order of operations. This is often remembered using acronyms like BODMAS or PEMDAS.
- Brackets / Parentheses: Operations inside brackets or parentheses are performed first.
- Orders / Exponents: Powers and square roots are calculated next.
- Division and Multiplication: These are performed from left to right.
- Addition and Subtraction: These are performed from left to right after division and multiplication.
Solving the Expression Step-by-Step
Let's apply the BODMAS rule to the given expression: (26 - 13 × 2) ÷ 2 + 1.
Step 1: Solve the expression inside the Brackets (Parentheses).
The expression inside the brackets is (26 - 13 × 2). Within these brackets, we have both multiplication and subtraction. According to BODMAS, Multiplication comes before Subtraction.
Step 2: Perform Multiplication inside the Brackets.
Calculate 13 × 2.
\(13 \times 2 = 26\)
Now substitute this back into the expression inside the brackets:
\((26 - 26)\)
Step 3: Perform Subtraction inside the Brackets.
Calculate 26 - 26.
\(26 - 26 = 0\)
So, the expression inside the brackets simplifies to 0. The original expression now becomes:
\(0 \div 2 + 1\)
Step 4: Perform Division.
Next, we perform the division: 0 ÷ 2.
\(0 \div 2 = 0\)
The expression is now:
\(0 + 1\)
Step 5: Perform Addition.
Finally, we perform the addition: 0 + 1.
\(0 + 1 = 1\)
The value of the expression (26 - 13 × 2) ÷ 2 + 1 is 1.
Let's summarise the steps in a table:
| Step | Operation | Expression | Result |
|---|---|---|---|
| 1 | Inside Brackets (Multiplication) | \(13 \times 2\) | \(26\) |
| 2 | Inside Brackets (Subtraction) | \(26 - 26\) | \(0\) |
| 3 | Division | \(0 \div 2\) | \(0\) |
| 4 | Addition | \(0 + 1\) | \(1\) |
Final Result
The calculated value of the expression (26 - 13 × 2) ÷ 2 + 1 is 1.
Revision Table: Key Order of Operations Concepts
| Rule | Explanation | Example |
|---|---|---|
| Brackets/Parentheses | Evaluate expressions inside grouping symbols first. | \((5 + 3) \times 2 \rightarrow 8 \times 2\) |
| Orders/Exponents | Evaluate powers and roots. | \(4^2 - 10 \rightarrow 16 - 10\) |
| Division and Multiplication | Perform from left to right. | \(12 \div 4 \times 3 \rightarrow 3 \times 3\) |
| Addition and Subtraction | Perform from left to right. | \(10 - 5 + 2 \rightarrow 5 + 2\) |
Additional Information on Mathematical Expressions
Understanding the order of operations is fundamental in mathematics to ensure that expressions are evaluated consistently and correctly. Without a standard order, an expression could have multiple possible values, leading to confusion.
Parentheses are used to override the standard order, forcing the calculation within them to be performed first. If there are nested parentheses (parentheses within parentheses), you work from the innermost set outwards.
Division and multiplication have equal priority, as do addition and subtraction. When these operations appear together in an expression without parentheses, you perform them in the order they appear from left to right.
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