Evaluating the Mathematical Expression

To find the value of the given mathematical expression, we need to follow the order of operations. A common rule for the order of operations is BODMAS or PEMDAS.

BODMAS stands for:

• Brackets (or Parentheses)
• Orders (powers, square roots, etc.)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

The given expression is:

$\small 11 \times 2 + (45 \div 9) + (72 \div 8) - 5 + 4$

Step-by-Step Calculation using BODMAS

Step 1: Evaluate the expressions inside the Brackets.

We have two sets of brackets: $(45 \div 9)$ and $(72 \div 8)$.

• $\small 45 \div 9 = 5$
• $\small 72 \div 8 = 9$

Substitute these values back into the expression:

$\small 11 \times 2 + 5 + 9 - 5 + 4$

Step 2: Perform Multiplication and Division from left to right.

In the current expression, we have one multiplication:

• $\small 11 \times 2 = 22$

Substitute this value back into the expression:

$\small 22 + 5 + 9 - 5 + 4$

Step 3: Perform Addition and Subtraction from left to right.

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

• $\small 22 + 5 = 27$
• $\small 27 + 9 = 36$
• $\small 36 - 5 = 31$
• $\small 31 + 4 = 35$

So, the final value of the expression $\small 11 \times 2 + (45 \div 9) + (72 \div 8) - 5 + 4$ is 35.

Revision Table: BODMAS Order

Additional Information on Order of Operations

Understanding the correct order of operations is crucial in mathematics to ensure calculations are performed consistently, leading to a single correct answer for any given expression. Without a standard order, different people might interpret the same expression differently.

BODMAS and PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) are just different acronyms for the same set of rules. The operations are grouped by priority:

• Highest priority: Brackets/Parentheses
• Next priority: Orders/Exponents (powers, roots, etc.)
• Third priority: Division and Multiplication (at the same level, done from left to right)
• Lowest priority: Addition and Subtraction (at the same level, done from left to right)

When operations are at the same level (like division and multiplication, or addition and subtraction), you simply work from the left side of the expression to the right.