Solving the Mathematical Expression using BODMAS

To solve the given mathematical expression, we need to follow the order of operations, commonly known by the acronym BODMAS or PEMDAS. This rule dictates the sequence in which operations should be performed:

• Brackets (Parentheses)
• Of (Orders, e.g., powers, square roots, and 'of')
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

The given expression is:

\((5 + 3 \div 5 \times 5) \div (3 \div 3 \text{ of } 6) \text{ of } (4 \times 4 \div 4 \text{ of } 4 + 4 \div 4 \times 4)\)

Let's solve each part of the expression following the BODMAS rule.

Evaluating the First Bracket: (5 + 3 ÷ 5 × 5)

Inside the first bracket, we have addition, division, and multiplication. According to BODMAS, we perform division and multiplication before addition.

First, perform the division:

\(3 \div 5 = \frac{3}{5}\)

Next, perform the multiplication:

\(\frac{3}{5} \times 5 = 3\)

Finally, perform the addition:

\(5 + 3 = 8\)

So, the value of the first bracket is 8.

Evaluating the Second Part: (3 ÷ 3 of 6)

Inside the second part, we have division and 'of'. According to BODMAS, 'of' is treated before division.

First, evaluate the 'of' part:

\(3 \text{ of } 6 = 3 \times 6 = 18\)

Next, perform the division:

\(3 \div 18 = \frac{3}{18} = \frac{1}{6}\)

So, the value of the second part is \(\frac{1}{6}\).

Evaluating the Third Bracket: (4 × 4 ÷ 4 of 4 + 4 ÷ 4 × 4)

Inside the third bracket, we have multiplication, division, 'of', and addition. First, evaluate 'of'.

Evaluate the 'of' part:

\(4 \text{ of } 4 = 4 \times 4 = 16\)

Now the expression inside the bracket becomes:

\((4 \times 4 \div 16 + 4 \div 4 \times 4)\)

Next, perform multiplication and division from left to right.

\(4 \times 4 = 16\)

\(16 \div 16 = 1\)

\(4 \div 4 = 1\)

\(1 \times 4 = 4\)

Now the expression inside the bracket is:

\((1 + 4)\)

Finally, perform the addition:

\(1 + 4 = 5\)

So, the value of the third bracket is 5.

Combining the Evaluated Parts

Now substitute the values back into the original expression:

\(8 \div (\frac{1}{6}) \text{ of } 5\)

According to BODMAS, 'of' comes before division.

Evaluate the 'of' part:

\((\frac{1}{6}) \text{ of } 5 = \frac{1}{6} \times 5 = \frac{5}{6}\)

Now the expression is:

\(8 \div \frac{5}{6}\)

Finally, perform the division. Dividing by a fraction is the same as multiplying by its reciprocal.

\(8 \div \frac{5}{6} = 8 \times \frac{6}{5}\)

\(8 \times \frac{6}{5} = \frac{48}{5}\)

To express this as a mixed number, divide 48 by 5:

\(48 \div 5 = 9\) with a remainder of \(3\).

So, \(\frac{48}{5} = 9\frac{3}{5}\).

The value of the expression is \(9\frac{3}{5}\).

Revision Table: BODMAS Order of Operations

Additional Information: Understanding 'Of' in BODMAS

The term 'of' in mathematical expressions, especially in the context of fractions or percentages, signifies multiplication. For example, 'half of 10' means \( \frac{1}{2} \times 10 \). In BODMAS, the 'Of' operation is typically performed after simplifying brackets but before division and multiplication. This is a common point of confusion, as 'of' is essentially multiplication but is often given higher priority than standard multiplication/division from left to right.