Introduction
Mixed operations combine fractions, percentages, roots, exponents, and the BODMAS rule in a single problem. These are common in competitive exams and test both your calculation speed and clarity in applying rules step by step. The key is to simplify one part at a time without skipping.
Pattern: Mixed Operations (Combined)
Pattern
Key idea: Follow BODMAS strictly and apply simplification rules (fractions, roots, exponents, percentages) in order, step by step.
Step-by-Step Example
Question
Simplify: (50% of 240 + √81) ÷ (2/3 of 18)
Options:
- A) 10.75
- B) 11
- C) 9.5
- D) 12
Solution
-
Step 1: Compute percentage
Find 50% of 240 → (50/100) × 240 = 120. -
Step 2: Evaluate the root
Simplify √81 = 9. -
Step 3: Form numerator
Numerator = 120 + 9 = 129. -
Step 4: Compute fraction operation
Denominator: 2/3 of 18 = (2/3) × 18 = 12. -
Step 5: Perform final division
129 ÷ 12 = 10.75. -
Final Answer:
10.75 → Option A. -
Quick Check:
Numerator 129, Denominator 12 → 129/12 = 10.75 ✅
Quick Variations
1. Problems may include percentages + roots + fractions.
2. Some include exponents and surds in one expression.
3. Can also test addition/subtraction with mixed forms like decimals and fractions.
Trick to Always Use
- Step 1 → Always handle percentages and fractions first.
- Step 2 → Simplify roots and exponents next.
- Step 3 → Apply BODMAS order (brackets → division/multiplication → addition/subtraction).
- Step 4 → Reduce to simplest form step by step, never jump directly.
Summary
Summary
In mixed operation problems:
- Break the problem into smaller parts.
- Use BODMAS strictly for order of operations.
- Handle fractions, percentages, and roots carefully before final addition/subtraction.
- Always check with a quick recomputation to avoid small calculation mistakes.
Hint: Convert percentages to fraction (x/100) and simple fractions to decimals (1/2 = 0.5) for quick calculation.
Common Mistakes: Forgetting to convert % to fraction or mis-evaluating the square root.