Simplification: Rules, Formulas, Tricks and Shortcuts
Simplification involves reducing a numerical expression to its simplest value by applying BODMAS, arithmetic operations, fractions, decimals, percentages, powers and roots in the correct order. This page covers simplification formulas, calculation rules, useful shortcuts and solved examples for expressions commonly asked in quantitative aptitude.
What is Simplification?
The usual order is Brackets, Orders or powers, Division, Multiplication, Addition and Subtraction, written as BODMAS. Operations at the same level are performed from left to right. For example, 18 + 6 ÷ 3 × 2 = 18 + 2 × 2 = 22.
Simplification Formula & Tricks
Important Formulas
Use a common denominator for addition and subtraction. For division, multiply the first fraction by the reciprocal of the second.
Convert a percentage into a fraction or decimal before applying it to a number.
These rules apply when the base is the same. The zero-power rule applies to every non-zero base.
Use these identities to expand or simplify expressions containing squares and conjugate factors.
Quick Tricks
In a product of fractions, cancel common factors across the numerator and denominator before multiplication. This reduces the numbers and prevents unnecessary calculation.
Use familiar equivalents such as 50% = 1/2, 25% = 1/4, 20% = 1/5 and 12.5% = 1/8.
Rewrite numbers with the same base before applying exponent laws.
For approximation questions, round numbers to convenient nearby values and check whether the exact option is consistent with the estimate.
Simplification Concepts
BODMAS Order of Operations
First solve brackets, then powers or roots. Next perform division and multiplication from left to right, followed by addition and subtraction from left to right. Division does not always come before multiplication; both have equal priority.
Simplification of Fractions
For addition or subtraction, convert fractions to a common denominator. For multiplication, multiply corresponding numerators and denominators. To divide by a fraction, multiply by its reciprocal. The denominator cannot be zero.
Decimals and Percentages
For decimal addition or subtraction, align decimal points. For multiplication by 10, 100 or 1000, shift the decimal point right by 1, 2 or 3 places. For division by these values, shift it left by the same number of places.
Powers and Square Roots
For positive numbers, √(ab) = √a × √b. Perfect-square factors can be taken outside a root. For example, √72 = √(36 × 2) = 6√2. Also, 5² = 25 and √25 = 5.
Approximation in Simplification
Round numbers according to the required accuracy. Keep more precision when subtracting close values or when the answer options are close. Approximation is different from exact simplification because the rounded result may not equal the original expression.
Simplification Video Lessons
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Fraction Operations: Add, Subtract, Multiply, Divide
Learn how to add, subtract, multiply, and divide fractions, including the core steps needed to simplify and solve fraction-based quantitative aptitude problems.
Practice Simplification Questions
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Simplification Revision Points
Recall the calculation order, fraction rules, conversions and exponent properties before solving an expression.
- Apply brackets first, followed by powers or roots.
- Perform division and multiplication from left to right.
- Perform addition and subtraction from left to right.
- For fraction addition or subtraction, use a common denominator.
- To divide by a fraction, multiply by its reciprocal.
- x% of y = xy/100.
- aᵐ × aⁿ = aᵐ⁺ⁿ and aᵐ ÷ aⁿ = aᵐ⁻ⁿ for the same non-zero base.
- Cancel common factors before multiplying fractions or ratios.
Simplification FAQs
What is the correct order in BODMAS?
Solve Brackets first, then Orders or powers, followed by Division and Multiplication from left to right, and finally Addition and Subtraction from left to right.
Should multiplication always be done before division?
No. Division and multiplication have equal priority, so they are performed from left to right. For example, 24 ÷ 6 × 2 = 4 × 2 = 8.
How do you simplify 2/3 + 5/9?
Convert 2/3 to 6/9, then add: 6/9 + 5/9 = 11/9.
How do you calculate a percentage of a number?
Use x% of y = xy/100. For example, 15% of 240 = 15 × 240 ÷ 100 = 36.
What is the value of 0.04 × 0.5?
0.04 × 0.5 = 0.020 = 0.02.
How can √180 be simplified?
√180 = √(36 × 5) = 6√5, because 36 is the largest perfect-square factor of 180.