Explanation
For “Simplify: 324 / 18 x 3”, retain the exact signs, brackets, powers and numerical conditions before beginning the calculation. The question-specific working recorded with the item is: Applying BODMAS to 324 / 18 x 3 gives 54..
Improve calculation speed with BODMAS, fractions, decimals, surds, indices, approximation and mixed arithmetic questions.
FAQ
Common questions and clear answers for this topic.
Simplification involves solving mathematical expressions using BODMAS rule. BODMAS stands for: Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. The rule determines the order in which operations are performed. Simplification is a major topic in SSC CGL Tier 1, IBPS Clerk, SBI Clerk, Railway Group D, and all competitive exams.
Important properties for Simplification: Squares up to 30, Cubes up to 15, Square roots of perfect squares up to 400, Multiplication tables up to 20. Also remember: a squared - b squared = (a+b)(a-b), (a+b) squared = a squared + 2ab + b squared, (a-b) squared = a squared - 2ab + b squared, a cubed + b cubed = (a+b)(a squared - ab + b squared). Memorizing these speeds up simplification in exams.
Approximation means finding a value close to the exact answer. In simplification and DI questions, when options are far apart, use rounding to save time. Techniques: Round to nearest 10 or 100, use percentage fractions (25% = 1/4, 33% = 1/3), estimate square roots. In competitive exams, approximation questions require finding the value closest to the actual answer.
Fraction simplification shortcuts: When adding fractions a/b + c/d, use cross multiplication: (ad+bc)/bd. Simplify by finding GCD first. Useful fraction equivalents: 1/7 = 0.142, 1/6 = 0.167, 1/3 = 0.333, 2/3 = 0.667. For mixed numbers: 3 and 2/5 = 17/5. When dividing fractions: multiply by reciprocal. Practice minimum 20 simplification questions daily for exam preparation.
Surds are irrational numbers expressed with square roots or other roots. Simplification rules: root(a) x root(b) = root(ab), root(a)/root(b) = root(a/b), (root(a)) squared = a. Rationalization: Multiply top and bottom by conjugate to remove surd from denominator. Example: 1/(2+root 3) = (2-root 3)/((2+root 3)(2-root 3)) = (2-root 3)/(4-3) = 2-root 3. Surds appear in SSC CGL and IBPS exams.
Convert mixed values where needed, use a common denominator, and apply division as multiplication by the reciprocal.
54, option A.
Changing operation order, losing a sign, or simplifying a factor where cancellation is invalid.
Substitute it back, estimate its magnitude, or recompute using an equivalent form.
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