Find the value of 56 ÷ 8 × 3 + 30 - 25 ÷ 5 + 10.
56
Evaluating Expressions Using Order of Operations
The question asks us to find the value of the expression: \(56 \div 8 \times 3 + 30 - 25 \div 5 + 10\).
To solve this expression accurately, we need to follow the correct order of operations. A commonly used rule for the order of operations is BODMAS or PEMDAS.
- Brackets / Parentheses
- Orders / Exponents
- Division / Multiplication (from left to right)
- Addition / Subtraction (from left to right)
Let's apply this rule step-by-step to the given expression:
\(56 \div 8 \times 3 + 30 - 25 \div 5 + 10\)
Step 1: Perform Division and Multiplication (from left to right)
First, we look for division and multiplication operations and perform them as we encounter them from left to right.
- The first operation from the left is \(56 \div 8\).
\(56 \div 8 = 7\)
Now, the expression becomes:
\(7 \times 3 + 30 - 25 \div 5 + 10\)
- Next operation from the left is \(7 \times 3\).
\(7 \times 3 = 21\)
The expression is now:
\(21 + 30 - 25 \div 5 + 10\)
- Moving further left to right, we find another division: \(25 \div 5\).
\(25 \div 5 = 5\)
The expression is now:
\(21 + 30 - 5 + 10\)
Step 2: Perform Addition and Subtraction (from left to right)
Now that all divisions and multiplications are done, we perform addition and subtraction operations from left to right.
- First operation from the left is \(21 + 30\).
\(21 + 30 = 51\)
The expression becomes:
\(51 - 5 + 10\)
- Next operation from the left is \(51 - 5\).
\(51 - 5 = 46\)
The expression is now:
\(46 + 10\)
- The final operation is \(46 + 10\).
\(46 + 10 = 56\)
So, the value of the expression \(56 \div 8 \times 3 + 30 - 25 \div 5 + 10\) is 56.
Let's summarize the steps in a table:
| Step | Operation | Expression |
|---|---|---|
| Original | \(56 \div 8 \times 3 + 30 - 25 \div 5 + 10\) | |
| 1a | \(56 \div 8\) | \(7 \times 3 + 30 - 25 \div 5 + 10\) |
| 1b | \(7 \times 3\) | \(21 + 30 - 25 \div 5 + 10\) |
| 1c | \(25 \div 5\) | \(21 + 30 - 5 + 10\) |
| 2a | \(21 + 30\) | \(51 - 5 + 10\) |
| 2b | \(51 - 5\) | \(46 + 10\) |
| 2c | \(46 + 10\) | \(56\) |
The final value of the expression is 56.
Revision Table: Understanding Order of Operations
| Rule | Meaning | Priority |
|---|---|---|
| B / P | Brackets / Parentheses | Highest |
| O / E | Orders / Exponents | Second Highest |
| D / M | Division / Multiplication | Third (Left to Right) |
| A / S | Addition / Subtraction | Lowest (Left to Right) |
Additional Information: Why Order of Operations Matters
Following the correct order of operations is crucial in mathematics to ensure that everyone arrives at the same unique answer for a given expression. Without a standard order, different people might perform operations in different sequences, leading to varying results. This standardisation is fundamental in algebra, calculus, computer programming, and many other fields that rely on consistent mathematical calculations.
For example, if we didn't follow the order and just calculated from left to right without respecting the rules, the calculation might incorrectly proceed as:
- \(56 \div 8 = 7\)
- \(7 \times 3 = 21\)
- \(21 + 30 = 51\)
- \(51 - 25 = 26\)
- \(26 \div 5 = 5.2\) (This is incorrect, as division has higher priority than subtraction)
- \(5.2 + 10 = 15.2\) (This incorrect result is very different from 56)
This example clearly shows why adhering to the order of operations like BODMAS or PEMDAS is essential for accurate mathematical computations.
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:
