Solving Mathematical Expressions using BODMAS/PEDMAS

To find the value of the given expression, we need to follow the order of operations. The standard order is BODMAS or PEDMAS.

• B/P: Brackets / Parentheses
• O/E: Orders / Exponents (powers, square roots, etc.)
• DM: Division and Multiplication (from left to right)
• AS: Addition and Subtraction (from left to right)

The given expression is:

$\qquad 9 + 9 \div 18 \times 27 + 36 \div 9 \times 18 + 54 \div 9 \times 18$

Let's break down the calculation step-by-step according to the order of operations.

Step 1: Perform Division and Multiplication from left to right

We have three parts involving division and multiplication:

1. $9 \div 18 \times 27$
2. $36 \div 9 \times 18$
3. $54 \div 9 \times 18$

Calculation for the first part: $9 \div 18 \times 27$

• First, perform the division: $9 \div 18 = \frac{9}{18} = \frac{1}{2}$
• Next, perform the multiplication: $\frac{1}{2} \times 27 = \frac{27}{2}$

So, $9 \div 18 \times 27 = \frac{27}{2}$.

Calculation for the second part: $36 \div 9 \times 18$

• First, perform the division: $36 \div 9 = 4$
• Next, perform the multiplication: $4 \times 18 = 72$

So, $36 \div 9 \times 18 = 72$.

Calculation for the third part: $54 \div 9 \times 18$

• First, perform the division: $54 \div 9 = 6$
• Next, perform the multiplication: $6 \times 18 = 108$

So, $54 \div 9 \times 18 = 108$.

Step 2: Substitute the calculated values back into the expression

The original expression now becomes:

$\qquad 9 + \frac{27}{2} + 72 + 108$

Step 3: Perform Addition from left to right

Combine the whole numbers first:

$\qquad 9 + 72 + 108 + \frac{27}{2}$

$\qquad (9 + 72) + 108 + \frac{27}{2}$

$\qquad 81 + 108 + \frac{27}{2}$

$\qquad (81 + 108) + \frac{27}{2}$

$\qquad 189 + \frac{27}{2}$

Step 4: Add the whole number and the fraction

To add 189 and $\frac{27}{2}$, we need a common denominator, which is 2. We can write 189 as $\frac{189 \times 2}{2} = \frac{378}{2}$.

$\qquad \frac{378}{2} + \frac{27}{2}$

Now, add the numerators:

$\qquad \frac{378 + 27}{2} = \frac{405}{2}$

The final value of the expression is $\frac{405}{2}$.

Revision Table: Order of Operations (BODMAS/PEDMAS)

Additional Information: Arithmetic Expression Evaluation

Evaluating arithmetic expressions accurately requires strict adherence to the order of operations. This ensures that everyone gets the same result for a given expression. If the order is not followed, the result will likely be incorrect.

In the expression $9 + 9 \div 18 \times 27 + 36 \div 9 \times 18 + 54 \div 9 \times 18$, notice how Division and Multiplication have the same priority. When they appear together, you must work from left to right.

• $9 \div 18 \times 27$: Calculate $9 \div 18$ first, then multiply by 27.
• $36 \div 9 \times 18$: Calculate $36 \div 9$ first, then multiply by 18.
• $54 \div 9 \times 18$: Calculate $54 \div 9$ first, then multiply by 18.

Only after all divisions and multiplications are done can you proceed with additions (and subtractions, if any, also from left to right).