Simplification BODMAS Fast Calculation Questions for UP POLICE CONSTABLE

BODMAS Rule - The Foundation

BODMAS is the sequence in which you must solve any mathematical expression. Think of it as a traffic rule for numbers — if you break the order, you crash. B = Bracket (parentheses first), O = Order (powers, roots), D = Division, M = Multiplication, A = Addition, S = Subtraction. Division and Multiplication have equal priority — solve left to right. Same for Addition and Subtraction. Most mistakes happen when students multiply before dividing, or add before subtracting, just because they see the operation first.

• Always solve Brackets first, even if they contain simple operations
• Powers and roots (Order) come before basic arithmetic
• Division and Multiplication are equal priority — go left to right, not by which you see first
• Addition and Subtraction are equal priority — go left to right
• Nested brackets: solve innermost bracket first, then work outward
• BODMAS applies even in word problems disguised as equations

Common Bracket Types & Removal

UP Police exams use three bracket types: () round, {} curly, [] square. Solve innermost first. When removing brackets, watch the sign before them — if negative sign precedes a bracket, flip all signs inside. This is where 40% of simplification errors happen. Example: 10 - (5 + 3) = 10 - 8 = 2, NOT 10 - 5 + 3 = 8.

• Innermost bracket always solved first
• Negative sign before bracket flips all signs inside: -(a + b) = -a - b
• Positive sign before bracket keeps all signs: +(a + b) = a + b
• Remove one bracket level at a time — don't rush
• After removing brackets, reapply BODMAS to the simplified expression

Fast Calculation Tricks for Speed

UP Police gives 90-120 seconds for 3 simplification questions. You cannot afford long division or slow mental math. Use these tricks: (1) Factorization — spot common factors and cancel before multiplying. (2) Fraction shortcuts — convert decimals to fractions early. (3) Grouping — rearrange terms (addition/multiplication are commutative) to make mental math easier. (4) Approximation — if answer choices are far apart, round and estimate. (5) Vedic shortcuts — cross-multiplication for fractions, digit-sum checks.

• Factorize before multiplying: 24 × 5 = (20 + 4) × 5 = 100 + 20 = 120, faster than direct
• Cancel common factors in fractions immediately: (12 × 15) / (18 × 10) = (2 × 3) / (3 × 2) = 1
• Rearrange for easier mental math: 7 + 23 + 13 = 7 + 13 + 23 = 20 + 23 = 43
• Convert decimals to fractions early: 0.5 = 1/2, 0.25 = 1/4, saves time in division
• Use digit-sum rule to verify: sum of digits of answer should match sum of digits of correct result (mod 9)

Handling Fractions & Decimals in Simplification

Fractions and decimals mixed in one expression slow you down. Convert all to one form early. If expression has mostly fractions, keep fractions. If mostly decimals, convert to decimals. Division of fractions is a common trap: a/b ÷ c/d = a/b × d/c (flip and multiply). Decimal division: 12 ÷ 0.5 = 12 × 2 = 24 (multiply by reciprocal).

• Convert all decimals to fractions or all fractions to decimals — don't mix
• Division of fractions: flip the second fraction and multiply
• Decimal division: multiply by reciprocal (12 ÷ 0.4 = 12 × 2.5 = 30)
• Simplify fractions before operations: 6/9 = 2/3 first, then multiply
• Common decimal-to-fraction: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.2 = 1/5

Exponents & Order Operations

Order (powers, roots) comes before multiplication and division. This trips up many. 2 + 3^2 = 2 + 9 = 11, NOT (2 + 3)^2 = 25. Negative exponents: 2^-1 = 1/2. Fractional exponents: 4^(1/2) = 2 (square root). In UP Police, exponents are usually small (2, 3, or 1/2) — no complex powers.

• Exponents apply only to the number they're attached to: 2 × 3^2 = 2 × 9 = 18, not (2 × 3)^2
• Negative exponent means reciprocal: 5^-1 = 1/5
• Fractional exponent: a^(1/n) = nth root of a; a^(m/n) = (nth root of a)^m
• Order of operations: solve exponents before multiplying/dividing
• Square roots and cube roots are common in UP Police — memorize 1-15 squares and 1-10 cubes

• Ignoring BODMAS and solving left to right: 10 - 5 + 3 solved as (10 - 5) + 3 = 8 is correct, but 10 - (5 + 3) = 2 is different. Many students auto-solve left to right without checking brackets.
• Flipping signs incorrectly when removing negative brackets: -(5 - 3) should be -5 + 3 = -2, but students write -5 - 3 = -8. Remember: negative sign flips ALL signs inside.
• Multiplying before dividing just because multiplication is 'higher': 12 ÷ 3 × 2 = (12 ÷ 3) × 2 = 8, NOT 12 ÷ (3 × 2) = 2. Division and multiplication are equal — go left to right.
• Forgetting to simplify fractions before operations: Multiplying 6/9 × 3/4 directly gives 18/36, then simplify to 1/2. Better: simplify first (2/3 × 3/4 = 6/12 = 1/2) — fewer arithmetic errors.
• Mishandling decimals in division: 10 ÷ 0.5 should be 10 × 2 = 20, but students divide 10 by 0.5 as 10 / 5 = 2 (wrong). Always flip and multiply for decimals.

• BODMAS = Bracket, Order, Division-Multiplication, Addition-Subtraction. Mnemonic: 'Buy One, Do Multiplication And Subtraction' (silly but sticks).
• Negative Bracket Flip: Think of a minus sign as a 'mirror' — it flips all signs inside. -(a + b) becomes -a - b, like a mirror image.
• Division-Multiplication Equal: They're 'twins' — always go left to right, never skip ahead. Same for Addition-Subtraction.
• Fraction Division Flip: 'Flip the second, multiply the first' — a/b ÷ c/d → a/b × d/c. Rhyme it to remember.

• UP Police Constable typically gives 1-2 pure BODMAS simplification questions (no word problem wrapper) in the Numerical Ability section. Expect 30-45 seconds per question if you're fast.
• Recent papers show increasing use of nested brackets and mixed fractions/decimals. Single-bracket questions are now rare. Practice 2-3 bracket levels.
• Negative brackets appear in 60% of recent papers. Drill the sign-flip rule until it's automatic — this is your speed multiplier.
• Decimal-to-fraction conversion is a hidden time-saver. If you see 0.5, 0.25, 0.2 in an expression, convert immediately. Saves 10-15 seconds per question.
• Answer choices are usually far apart (e.g., 5, 12, 18, 24). If you're unsure, estimate/round and pick the closest. Full precision is rarely needed — speed beats perfection here.