Finding the Value of the Expression

The question asks us to find the value of the expression \(122 + 345 – 1 \times 1011 \div 337\). To solve this type of problem, we need to follow the correct order of operations. The commonly used rule for the order of operations is BODMAS or PEMDAS.

Understanding the Order of Operations (BODMAS/PEMDAS)

The BODMAS/PEMDAS rule dictates the sequence in which operations should be performed in a mathematical expression:

• B/P: Brackets or Parentheses first
• O/E: Orders or Exponents (powers, square roots, etc.) next
• D/M: Division and Multiplication (from left to right)
• A/S: Addition and Subtraction (from left to right)

Step-by-Step Calculation

Let's apply the BODMAS/PEMDAS rule to the given expression: \(122 + 345 – 1 \times 1011 \div 337\)

Step 1: Division

According to BODMAS/PEMDAS, we perform Division and Multiplication before Addition and Subtraction. Looking from left to right, we have multiplication and division. Let's perform the division first:

Calculate \(1011 \div 337\).

\(1011 \div 337 = 3\)

The expression now becomes:

\(122 + 345 – 1 \times 3\)

Step 2: Multiplication

Next, we perform the multiplication:

Calculate \(1 \times 3\).

\(1 \times 3 = 3\)

The expression now becomes:

\(122 + 345 – 3\)

Step 3: Addition and Subtraction

Now we only have addition and subtraction left. We perform these operations from left to right.

First, perform the addition:

Calculate \(122 + 345\).

\(122 + 345 = 467\)

The expression now becomes:

\(467 – 3\)

Finally, perform the subtraction:

Calculate \(467 – 3\).

\(467 – 3 = 464\)

Final Result

The value of the expression \(122 + 345 – 1 \times 1011 \div 337\) is \(464\).

Revision Table: Key Concepts

Additional Information: BODMAS/PEMDAS Explained

The BODMAS (or PEMDAS) rule is fundamental in arithmetic and algebra. Without a standard order, expressions could have multiple possible values, leading to ambiguity. The rule establishes a hierarchy: operations within brackets or parentheses are always done first, followed by powers or roots. Then, multiplication and division are performed from left to right as they have equal priority. Finally, addition and subtraction are performed from left to right, also having equal priority.

In our problem, we had both multiplication and division (\(1 \times 1011 \div 337\)). Conventionally, when operations of the same priority level (like multiplication and division, or addition and subtraction) appear in the same expression, they are evaluated from left to right. So, \(1 \times 1011 \div 337\) is calculated as \((1 \times 1011) \div 337\) if multiplication comes first, or \(1 \times (1011 \div 337)\) if division comes first. In the given expression \(1 \times 1011 \div 337\), the structure implies \(1 \times (1011 \div 337)\) is often clearer, especially written this way, or \(1 \times (1011/337)\). Both interpretations \( (1 \times 1011) / 337 \) and \( 1 \times (1011 / 337) \) yield the same result here because multiplication and division are associative in this way, but following the left-to-right rule strictly after priority levels, one would evaluate \(1 \times 1011\) first IF it appeared before the division. However, \(1011 \div 337\) is a simple division that results in an integer (3), which makes the calculation easier and follows the standard interpretation where division/multiplication are done left-to-right. In this specific case, \(1 \times 1011 \div 337\) means \(1 \times (1011/337)\) which is \(1 \times 3 = 3\). If it were \(1011 \div 337 \times 1\), following left-to-right within the same priority level, we'd do \(1011 \div 337 = 3\), then \(3 \times 1 = 3\). The result is the same here.

The key takeaway is to systematically apply the order of operations to avoid errors in calculation.