Basic Calculation: Rules, Tricks and Fast Methods

Basic Calculation covers the rules and methods used to solve arithmetic expressions involving integers, fractions, decimals and percentages. This topic includes BODMAS, sign rules, place value, multiplication shortcuts, square calculations and mental maths methods that reduce calculation time and errors.

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What is Basic Calculation?

Basic calculation is the process of performing arithmetic operations such as addition, subtraction, multiplication and division on numbers. It also includes the correct use of signs, brackets, fractions, decimals and operation order.

Arithmetic expressions are solved using the order of operations: brackets first, followed by orders or powers, division and multiplication from left to right, and addition and subtraction from left to right. For example, 18 + 24 ÷ 6 × 2 − 3 = 18 + 4 × 2 − 3 = 23.

Basic Calculation Formula & Tricks

Important Formulas

Order of Operations
BODMAS: Brackets → Orders → Division/Multiplication → Addition/Subtraction

When operations have equal priority, calculate from left to right. Division and multiplication have the same priority, as do addition and subtraction.

Distributive Property
a(b + c) = ab + ac; a(b − c) = ab − ac

Use this property to break multiplication into simpler parts. For example, 24 × 103 = 24 × (100 + 3) = 2472.

Square of a Sum or Difference
(a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²

These identities help calculate squares of numbers close to a convenient base such as 10, 50 or 100.

Fraction Operations
a/b + c/d = (ad + bc)/bd; a/b × c/d = ac/bd

For addition or subtraction, use a common denominator. For multiplication, multiply numerators and denominators directly, then simplify.

Quick Tricks

Multiply by 5 Quickly

Multiply the number by 10 and divide the result by 2. This works because 5 = 10 ÷ 2.

Example: 68 × 5 = 680 ÷ 2 = 340.
Multiply by 25 Quickly

Multiply by 100 and divide by 4 because 25 = 100 ÷ 4.

Example: 48 × 25 = 4800 ÷ 4 = 1200.
Use a Base Near 100

Express each number as a base plus or minus a small value, then apply the distributive property or square identity.

Example: 97 × 104 = (100 − 3)(100 + 4) = 10000 + 100 − 12 = 10088.
Square a Number Ending in 5

For a number 10a + 5, multiply a by a + 1 and append 25.

Example: 35²: 3 × 4 = 12, so 35² = 1225.

Basic Calculation Concepts

BODMAS and Left-to-Right Calculation

BODMAS determines the order in which operations are performed in an expression.

Solve brackets first, then powers or orders, followed by division and multiplication from left to right. Perform addition and subtraction last, also from left to right. Do not treat multiplication as always coming before division; both have equal priority.

Example: 40 − 12 ÷ 3 × 2 = 40 − 4 × 2 = 40 − 8 = 32.

Rules of Signs

For addition and subtraction, compare signs and magnitudes; for multiplication and division, like signs give a positive result and unlike signs give a negative result.

For addition, numbers with the same sign are added and retain that sign. Numbers with different signs are subtracted, and the sign of the number with greater absolute value is retained. In multiplication or division, (+)(+) and (−)(−) are positive, while (+)(−) and (−)(+) are negative.

Example: −8 + 13 = 5, while (−6) × (−4) = 24 and (−28) ÷ 7 = −4.

Fractions and Decimal Calculations

Fractions are added or subtracted using a common denominator, while fractions are multiplied by multiplying corresponding numerators and denominators.

To divide by a fraction, multiply by its reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c), where c and d are non-zero. Decimal places must be aligned during addition and subtraction. In multiplication, count the total decimal places in the factors.

Example: 3/4 + 5/8 = 6/8 + 5/8 = 11/8. Also, 2.5 × 0.4 = 1.00 = 1.

Distributive and Near-Base Multiplication

Break one factor into convenient parts to replace a difficult multiplication with simpler calculations.

Use a(b + c) = ab + ac or a(b − c) = ab − ac. For numbers close to 10, 100 or 1000, select that number as the base and calculate the small differences separately.

Example: 36 × 98 = 36 × (100 − 2) = 3600 − 72 = 3528.

Squares and Common Arithmetic Identities

Square identities convert difficult square calculations into addition and subtraction of simpler terms.

Use (a + b)² or (a − b)² when the number is close to a known square. Other useful identities include a² − b² = (a − b)(a + b) and (a + b)(a − b) = a² − b².

Example: 49² = (50 − 1)² = 2500 − 100 + 1 = 2401.

Basic Calculation Video Lessons

Watch short topic-wise lessons for quick revision.

13 Lessons
Lesson 1 of 13 Quick Revision

BODMAS with Overline Expressions

Learn how to apply BODMAS rules to simplify expressions containing overlines, following the correct order of operations step by step.

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Practice Basic Calculation Questions

Practise published questions related to this topic.

1Evaluate: (5^(1/4)) × (125^(0.25))→ 2Find the value of: (1/((5-√6))) + (1/((5+√6))) - (10/((25-6)))→ 3(√98 - √147)/(√18 - √27) = ?→ 4The value of (27^(2/3) × 9^(-1/2))/(3⁻¹ × 81^(1/4)) is→ 5Find the value of m which satisfies (23/8)¹² × (8/23)¹⁵ × (23/8)⁹ = (8/23)^(8m+8)→ 6If 3^x - 3^(x-1) = 18 , then the value of (2x-1)/(2x+3) is:→ 7Evaluate: 3⁵ × 7⁵ ÷ 21³→ 8The simplified value of √256 - √169 + (√144 - √25)² is:→ 9Simplify : (81² × 10²)/9→ 10Simplify: ((6⁴ × 4⁵ × 6⁵))/((6² × 4² × 6³))→

Basic Calculation Quick Quiz

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Quick Revision Notes

Basic Calculation Revision Points

Use these rules and methods for quick and accurate arithmetic calculations.

  • Follow BODMAS and evaluate equal-priority operations from left to right.
  • Division and multiplication have equal priority; addition and subtraction also have equal priority.
  • For unlike signs in addition, subtract absolute values and retain the sign of the larger absolute value.
  • Like signs give a positive result and unlike signs give a negative result in multiplication and division.
  • To add or subtract fractions, first take a common denominator.
  • To divide by a fraction, multiply by its reciprocal.
  • Use the distributive property to split multiplication into convenient parts.
  • Use (a ± b)² when a number is close to a known base or square number.

Basic Calculation FAQs

What is the correct order of operations in basic calculation?

Use BODMAS: Brackets, Orders, Division or Multiplication from left to right, and Addition or Subtraction from left to right.

How do you solve 24 ÷ 6 × 2?

Division and multiplication have equal priority, so calculate left to right: 24 ÷ 6 × 2 = 4 × 2 = 8.

How do you add 3/4 and 5/8?

Convert 3/4 to 6/8, then add: 6/8 + 5/8 = 11/8, or 1 3/8.

What is the shortcut for multiplying a number by 25?

Multiply the number by 100 and divide by 4. For example, 72 × 25 = 7200 ÷ 4 = 1800.

How do you multiply two numbers close to 100?

Write each number as 100 plus or minus its difference and expand. For example, 98 × 103 = (100 − 2)(100 + 3) = 10000 + 100 − 6 = 10094.

What is the result of −15 + 9?

Subtract the smaller absolute value from the larger one and retain the sign of 15: −15 + 9 = −6.

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