How to Solve: CUET Quant – Simplification and Approximation (BODMAS, Bar, Decimals)

How to Solve: CUET Quant – Simplification and Approximation (BODMAS, Bar, Decimals)

Introduction

"If you can simplify 3.8 × 2.5 + 12 ÷ 0.4 in under 30 seconds, you’ll save minutes on CUET Quant—minutes you can use to crush the rest of the paper."

What You Need To Know First

1. Basic arithmetic operations: Addition, subtraction, multiplication, division.
2. Place value of decimals: Tenths, hundredths, thousandths.
3. Fraction-decimal conversion: e.g., ½ = 0.5, ¾ = 0.75.

Key Vocabulary

Formulas To Know

1. BODMAS Rule (MEMORISE THIS)

2. Brackets → Orders (powers/roots) → Division/Multiplication (left to right) → Addition/Subtraction (left to right).

3. Recurring Decimal to Fraction (MEMORISE THIS)

4. For a single repeating digit: ( 0.\overline{a} = \frac{a}{9} )
   Example: ( 0.\overline{3} = \frac{3}{9} = \frac{1}{3} )

5. For two repeating digits: ( 0.\overline{ab} = \frac{ab}{99} )
   Example: ( 0.\overline{12} = \frac{12}{99} = \frac{4}{33} )

6. Approximation Shortcut (MEMORISE THIS)

7. If ( a ) and ( b ) are close to ( x ), then ( a \times b \approx x^2 + (a + b - 2x)x ).
   Example: ( 4.9 \times 5.1 \approx 5^2 + (4.9 + 5.1 - 10) \times 5 = 25 + 0 = 25 ).

Step-by-Step Method

Step 1: Scan the Expression

• Identify brackets, bars, and operations.
• Underline recurring decimals (e.g., ( 0.\overline{6} )) and convert them to fractions.

Step 2: Apply BODMAS

• Brackets first: Solve innermost brackets, then outer ones.
• Orders (powers/roots): Next, solve exponents (e.g., ( 2^3 = 8 )).
• Division/Multiplication: Left to right.
• Addition/Subtraction: Left to right.

Step 3: Handle Decimals

• Convert decimals to fractions if easier (e.g., 0.5 = ½).
• For approximation, round to 1-2 decimal places.

Step 4: Simplify Step-by-Step

• Break the problem into smaller parts.
• Write intermediate steps to avoid mistakes.

Step 5: Verify

• Recheck BODMAS order.
• For approximation, ensure rounding doesn’t change the answer too much.

Worked Example (Using Steps Above)

Problem: Simplify ( 3.6 \div 0.9 + (2.5 \times 1.2) - 1.\overline{3} )

Step 1: Scan - No brackets (except implied in ( 1.\overline{3} )). - Convert ( 1.\overline{3} ) to fraction: ( 1.\overline{3} = 1 + \frac{1}{3} = \frac{4}{3} ).

Step 2: BODMAS - Division: ( 3.6 \div 0.9 = 4 ) - Multiplication: ( 2.5 \times 1.2 = 3 ) - Addition: ( 4 + 3 = 7 ) - Subtraction: ( 7 - \frac{4}{3} = \frac{21}{3} - \frac{4}{3} = \frac{17}{3} )

Step 3: Decimals - Already handled in Step 1.

Step 4: Simplify - Final answer: ( \frac{17}{3} ) or ( 5.\overline{6} ).

Step 5: Verify - Recheck calculations: ( 3.6 \div 0.9 = 4 ) ✔️, ( 2.5 \times 1.2 = 3 ) ✔️, ( 7 - 1.333... = 5.666... ) ✔️.

Worked Examples

Example 1 - Basic

Problem: Simplify ( 8 + 2 \times 3 \div 0.5 )

Solution: 1. BODMAS: Multiplication/Division first (left to right).
- ( 2 \times 3 = 6 )
- ( 6 \div 0.5 = 12 ) 2. Addition: ( 8 + 12 = 20 )

What we did and why: - Followed BODMAS to avoid ( 8 + 2 = 10 ), then ( 10 \times 3 = 30 ) (wrong!).

Example 2 - Medium

Problem: Simplify ( (1.2 + 0.8) \times 2.\overline{3} - 5 \div 0.25 )

Solution: 1. Brackets: ( 1.2 + 0.8 = 2 ) 2. Convert ( 2.\overline{3} ) to fraction: ( 2 + \frac{1}{3} = \frac{7}{3} ) 3. Multiplication: ( 2 \times \frac{7}{3} = \frac{14}{3} ) 4. Division: ( 5 \div 0.25 = 20 ) 5. Subtraction: ( \frac{14}{3} - 20 = \frac{14}{3} - \frac{60}{3} = -\frac{46}{3} )

What we did and why: - Converted recurring decimals early to avoid errors. - Handled division last in BODMAS order.

Example 3 - Exam Style

Problem: Approximate ( \frac{3.98 \times 1.02}{0.51} ) to 2 decimal places.

Solution: 1. Round numbers:
- ( 3.98 \approx 4 )
- ( 1.02 \approx 1 )
- ( 0.51 \approx 0.5 ) 2. Simplify: ( \frac{4 \times 1}{0.5} = \frac{4}{0.5} = 8 ) 3. Refine approximation:
- ( 3.98 \times 1.02 \approx 4 \times 1 + (3.98 + 1.02 - 5) \times 1 = 4 + 0 = 4 )
- ( \frac{4}{0.51} \approx \frac{4}{0.5} = 8 ) 4. Final answer: 8.00

What we did and why: - Used approximation shortcuts to save time. - Verified by refining the estimate.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, CUET warriors—here’s your last-minute cheat sheet for Simplification and Approximation:

1. BODMAS is king: Brackets first, then powers, then division/multiplication (left to right), then addition/subtraction (left to right). Write it on your rough sheet if you forget!
2. Recurring decimals? Convert them to fractions fast. ( 0.\overline{3} = \frac{1}{3} ), ( 0.\overline{142857} = \frac{1}{7} ).
3. Approximation? Round numbers to 1 decimal place, solve, then check if the answer makes sense. If options are close, refine your estimate.
4. Watch for traps: Examiners love hiding brackets and recurring decimals. Scan the question twice before solving.
5. Practice 5 problems tonight: Pick one from each type—basic, medium, and approximation. Time yourself. You’ve got this!

Final Tip: "On exam day, underline BODMAS steps in your rough work. It keeps you from panicking and making silly mistakes. Good luck!