Simplify 1¼ ÷ (2 ÷ ¼ of 28)

To solve this expression, we must follow the BODMAS rule, which dictates the order of operations: Brackets, Of, Division, Multiplication, Addition, and Subtraction.

1. Analyze the Expression

The expression is: $1\frac{1}{4} \div (2 \div \frac{1}{4} \text{ of } 28)$

First, convert the mixed fraction to an improper fraction: $1\frac{1}{4} = \frac{5}{4}$

2. Solve inside the bracket

According to BODMAS, we handle "Of" before "Division" inside the bracket.

• Step A: Solve "Of" $\frac{1}{4} \text{ of } 28 = \frac{1}{4} \times 28 = 7$

• Step B: Solve the Division inside the bracket Now the bracket becomes: $(2 \div 7)$ $2 \div 7 = \frac{2}{7}$

3. Complete the final division

Now substitute the result back into the main expression: $\frac{5}{4} \div \frac{2}{7}$

To divide by a fraction, we multiply by its reciprocal: $\frac{5}{4} \times \frac{7}{2} = \frac{5 \times 7}{4 \times 2} = \frac{35}{8}$

4. Convert to a mixed fraction

Divide 35 by 8: $35 \div 8 = 4$ remainder $3$ So, $\frac{35}{8} = 4\frac{3}{8}$

Conclusion

Comparing our result to the options provided: A. $1\frac{3}{8}$ B. $2\frac{3}{4}$ C. $4\frac{3}{8}$ D. $3\frac{1}{5}$

The calculated value matches option C.

Exam Tip: Always remember that in BODMAS, "Of" acts like multiplication but takes precedence over standard division. If you had divided 2 by 1/4 first, you would have gotten the wrong answer. Always look for the "Of" and solve it immediately!