Calculating the Value Using the BODMAS Rule

The question asks us to find the value of a mathematical expression involving several operations: division, 'of', multiplication, addition, subtraction, and parentheses. To correctly solve such an expression, we must follow the standard order of operations, commonly known as BODMAS or PEMDAS.

Understanding the BODMAS Rule

The BODMAS rule provides a specific sequence for performing operations in an expression:

• B: Brackets (Parentheses) - Solve the operations inside brackets first.
• O: Of (Orders or Exponents) - Next, solve powers, roots, or the 'of' operation.
• D: Division
• M: Multiplication
• A: Addition
• S: Subtraction

Division and Multiplication have the same priority and should be performed from left to right. Similarly, Addition and Subtraction have the same priority and should be performed from left to right.

Step-by-Step Calculation

The given expression is:

\(5 \div 10 \text{ of } 10 \times 4 + 4 \div 4 \text{ of } 4 \times 10 + (10 - 4) \div 16 \times 4\)

Step 1: Solve the Brackets

First, we evaluate the expression inside the brackets:

\((10 - 4) = 6\)

Substitute this value back into the expression:

\(5 \div 10 \text{ of } 10 \times 4 + 4 \div 4 \text{ of } 4 \times 10 + 6 \div 16 \times 4\)

Step 2: Solve the 'Of' operations

Next, we perform the 'of' operations, which are equivalent to multiplication:

• \(10 \text{ of } 10 = 10 \times 10 = 100\)
• \(4 \text{ of } 4 = 4 \times 4 = 16\)

Substitute these values into the expression:

\(5 \div 100 \times 4 + 4 \div 16 \times 10 + 6 \div 16 \times 4\)

Step 3: Perform Division and Multiplication (from left to right)

Now, we perform all division and multiplication operations from left to right, treating the expression as three separate terms joined by addition:

Term 1: \(5 \div 100 \times 4\)

\(5 \div 100 = \frac{5}{100} = \frac{1}{20}\)

So, Term 1 is \(\frac{1}{20} \times 4 = \frac{4}{20} = \frac{1}{5}\)

Term 2: \(4 \div 16 \times 10\)

\(4 \div 16 = \frac{4}{16} = \frac{1}{4}\)

So, Term 2 is \(\frac{1}{4} \times 10 = \frac{10}{4} = \frac{5}{2}\)

Term 3: \(6 \div 16 \times 4\)

\(6 \div 16 = \frac{6}{16} = \frac{3}{8}\)

So, Term 3 is \(\frac{3}{8} \times 4 = \frac{12}{8} = \frac{3}{2}\)

Substitute these simplified terms back into the expression:

\(\frac{1}{5} + \frac{5}{2} + \frac{3}{2}\)

Step 4: Perform Addition (from left to right)

Finally, we perform the addition:

\(\frac{1}{5} + \frac{5}{2} + \frac{3}{2}\)

First, add the fractions with the same denominator:

\(\frac{5}{2} + \frac{3}{2} = \frac{5 + 3}{2} = \frac{8}{2} = 4\)

Now, add this result to the remaining term:

\(\frac{1}{5} + 4\)

To add a fraction and a whole number, convert the whole number into a fraction with the same denominator:

\(4 = \frac{4 \times 5}{5} = \frac{20}{5}\)

So, the expression becomes:

\(\frac{1}{5} + \frac{20}{5} = \frac{1 + 20}{5} = \frac{21}{5}\)

The final value of the expression is \(\frac{21}{5}\).

Summary of Steps

The calculated value matches option 4.

Revision Table: BODMAS Order of Operations

Additional Information on Order of Operations

The order of operations is crucial in mathematics to ensure that everyone arrives at the same result for a given expression. Without a standard order, an expression like \(2 + 3 \times 4\) could be interpreted differently: either as \((2 + 3) \times 4 = 5 \times 4 = 20\) or as \(2 + (3 \times 4) = 2 + 12 = 14\). The BODMAS/PEMDAS rule resolves this ambiguity, stipulating that multiplication is performed before addition, leading to the correct result of 14.

PEMDAS is another acronym used in some regions, standing for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It represents the same order of operations as BODMAS.