Solve: 11 × 3 + (45 ÷ 9) + (72 ÷ 8) - 5 + 4
46
Understanding the Mathematical Expression
We are asked to solve the mathematical expression: \(11 \times 3 + (45 \div 9) + (72 \div 8) - 5 + 4\). To solve this, we need to follow the correct order of operations. A common mnemonic for the order of operations is BODMAS or PEMDAS.
- Brackets (or Parentheses) first
- Orders (or Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Step-by-Step Solution using Order of Operations
Let's break down the expression step by step following the BODMAS/PEMDAS rule.
Step 1: Solve the expressions inside the Brackets (Parentheses).
The expression has two sets of brackets:
- \(45 \div 9\)
- \(72 \div 8\)
Calculating these:
- \(45 \div 9 = 5\)
- \(72 \div 8 = 9\)
Now, substitute these values back into the original expression:
\(11 \times 3 + 5 + 9 - 5 + 4\)
Step 2: Perform Multiplication and Division (from left to right).
In the current expression, we have one multiplication:
- \(11 \times 3\)
Calculating this:
- \(11 \times 3 = 33\)
Substitute this value back into the expression:
\(33 + 5 + 9 - 5 + 4\)
Step 3: Perform Addition and Subtraction (from left to right).
Now, we perform the additions and subtractions from left to right:
- \(33 + 5 = 38\)
- \(38 + 9 = 47\)
- \(47 - 5 = 42\)
- \(42 + 4 = 46\)
The final result of the expression is 46.
Final Result of the Expression
Following the order of operations, the value of the expression \(11 \times 3 + (45 \div 9) + (72 \div 8) - 5 + 4\) is 46.
The calculation steps can be summarized as:
\(11 \times 3 + (45 \div 9) + (72 \div 8) - 5 + 4\)
\(11 \times 3 + 5 + 9 - 5 + 4\) (Solved Brackets)
\(33 + 5 + 9 - 5 + 4\) (Solved Multiplication)
\(38 + 9 - 5 + 4\) (Addition)
\(47 - 5 + 4\) (Addition)
\(42 + 4\) (Subtraction)
\(46\) (Addition)
Revision Table: Order of Operations (BODMAS/PEMDAS)
| Order | Operation Type | Mnemonic (BODMAS) | Mnemonic (PEMDAS) |
|---|---|---|---|
| 1 | Brackets / Parentheses | B | P |
| 2 | Orders / Exponents | O | E |
| 3 | Division and Multiplication (Left to Right) | DM | MD |
| 4 | Addition and Subtraction (Left to Right) | AS | AS |
Additional Information: Why Order of Operations Matters
The order of operations is crucial in mathematics to ensure that everyone arrives at the same answer for a given expression. Without a standard order, expressions could be interpreted in multiple ways, leading to different results. For example, if we performed addition before multiplication in this problem, we would get a completely different answer. The BODMAS/PEMDAS rule provides a clear set of instructions to follow, making mathematical expressions unambiguous.
Remember to always work from left to right when you have operations of the same priority (like multiplication and division, or addition and subtraction).
Important Questions from Simplification
Simplify the following expression.
\(\left(\frac{7}{16} \div \frac{1}{2}\:of\: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}\)
The value of \(\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)\) is:
The value of \(\left[ {\frac{4}{7}\rm \;of\;2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left( {3\frac{1}{5} \div 4\frac{1}{2}\;\rm of\;\;5\frac{1}{3}} \right)\) is:
The value of \(\frac{{0.0203 \times 2.92}}{{0.7 \times 0.0365 \times 2.9}} \div \frac{{{{\left( {12.12} \right)}^2} - {{\left( {8.12} \right)}^2}}}{{{{\left( {0.25} \right)}^2} + \left( {0.25} \right)\left( {19.99} \right)}}\) is:
The value of 4 ÷ 12 of [3 ÷ 4 of {(4 - 2) × 6 ÷ 2}] - 2 × 6 ÷ 8 + 3 is:
