Advanced Arithmetic Calculator | Complete Math Operations

Complete Arithmetic Operations Calculator

Our advanced arithmetic calculator handles everything from basic operations to complex expressions. Enter your expression below and get instant results with detailed step-by-step solutions. Perfect for students, teachers, and anyone needing quick and accurate calculations.

M+

M-

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x^y

√

Step-by-Step Solution

Calculation History

Specialized Arithmetic Calculators

Explore our comprehensive suite of specialized arithmetic calculators designed to handle specific mathematical operations with precision and clarity. Each calculator provides detailed step-by-step solutions to help you understand the concepts better.

Addition & Subtraction

Perform addition and subtraction operations with multiple numbers. Get step-by-step solutions and see the properties of these operations.

Add numbers:

Add multiple numbers:

Subtract numbers:

Combine addition and subtraction:

Generate addition table:

Multiplication & Division

Perform multiplication and division operations with multiple numbers. Get step-by-step solutions and see the properties of these operations.

Multiply numbers:

Multiply multiple numbers:

Divide numbers:

Find quotient and remainder:

Generate multiplication table:

Powers & Roots

Calculate powers, square roots, and nth roots of numbers. Get step-by-step solutions and see the properties of these operations.

Calculate power:

Calculate square root:

Calculate nth root:

Properties of Powers

Powers have several important properties that are useful in simplifying expressions:

Product of Powers with Same Base

When multiplying powers with the same base, add the exponents.

$$x^a \times x^b = x^{a+b}$$

Example: $$2^3 \times 2^4 = 2^7 = 128$$

Quotient of Powers with Same Base

When dividing powers with the same base, subtract the exponents.

$$x^a \div x^b = x^{a-b}$$

Example: $$2^7 \div 2^3 = 2^4 = 16$$

Power of a Power

When raising a power to another power, multiply the exponents.

$$(x^a)^b = x^{a \times b}$$

Example: $$(2^3)^2 = 2^6 = 64$$

Multiple Operations (PEMDAS/BODMAS)

Evaluate expressions with multiple operations following the correct order of operations. Get step-by-step solutions and see how the order of operations works.

Evaluate expression:

Evaluate complex expression:

Order of Operations (PEMDAS/BODMAS)

When evaluating expressions with multiple operations, follow the order of operations to get the correct result:

PEMDAS (USA)

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

BODMAS (UK, India, and other countries)

Brackets
Orders (powers and roots)
Division and Multiplication (from left to right)
Addition and Subtraction (from left to right)

Example: 2 + 3 × 4

Step 1: Multiplication takes precedence over addition.

3 × 4 = 12

Step 2: Perform addition.

2 + 12 = 14

Result: 2 + 3 × 4 = 14

Arithmetic Properties and Applications

Arithmetic is the foundation of mathematics and has countless applications in everyday life. Understanding the properties and applications of arithmetic operations can help you solve problems more efficiently.

Properties of Addition

Commutative Property: $$a + b = b + a$$
Example: $$5 + 3 = 3 + 5 = 8$$
Associative Property: $$(a + b) + c = a + (b + c)$$
Example: $$(2 + 3) + 4 = 2 + (3 + 4) = 9$$
Identity Property: $$a + 0 = a$$
Example: $$7 + 0 = 7$$
Inverse Property: $$a + (-a) = 0$$
Example: $$5 + (-5) = 0$$

Properties of Multiplication

Commutative Property: $$a \times b = b \times a$$
Example: $$5 \times 3 = 3 \times 5 = 15$$
Associative Property: $$(a \times b) \times c = a \times (b \times c)$$
Example: $$(2 \times 3) \times 4 = 2 \times (3 \times 4) = 24$$
Identity Property: $$a \times 1 = a$$
Example: $$7 \times 1 = 7$$
Distributive Property: $$a \times (b + c) = (a \times b) + (a \times c)$$
Example: $$3 \times (4 + 5) = (3 \times 4) + (3 \times 5) = 12 + 15 = 27$$
Zero Property: $$a \times 0 = 0$$
Example: $$7 \times 0 = 0$$

Real-Life Applications

Financial: Budgeting, shopping, banking, investing
Everyday: Cooking, time management, travel, home improvement
Educational: Grade calculation, science, statistics, computer science
Professional: Business, engineering, healthcare, construction

Mental Math Tricks

Multiplying by 5: Divide by 2, then multiply by 10
Example: $$36 \times 5 = (36 \div 2) \times 10 = 18 \times 10 = 180$$
Multiplying by 9: Multiply by 10, then subtract the original number
Example: $$7 \times 9 = (7 \times 10) - 7 = 70 - 7 = 63$$
Multiplying by 11: For two-digit numbers, add the digits and place between them
Example: $$42 \times 11 = 4(4+2)2 = 462$$
Squaring numbers ending in 5: Take the tens digit, multiply by next integer, append 25
Example: $$35^2 = 3 \times 4 = 12, append 25 = 1225$$

Ultimate Arithmetic Calculator Suite