Tools in This Collection
Fraction Calculator
Add, subtract, multiply, and divide fractions with automatic simplification
Scientific Notation Converter
Convert between standard and scientific notation for large and small numbers
Prime Factorization Calculator
Decompose any integer into prime factors with a complete factor tree
GCF and LCM Calculator
Find greatest common factor and least common multiple using the Euclidean algorithm
Logarithm Calculator
Calculate logarithms in any base including natural log and log base 10
Exponent Calculator
Compute powers including fractional, negative, and decimal exponents
Mean Median Mode Calculator
Find the mean, median, and mode of any data set
Long Division Calculator
Perform long division with step-by-step remainder tracking
Arithmetic and Number Theory Workflow
Arithmetic operations form the foundation of all higher mathematics. Whether you're solving fraction problems for a math class, performing number theory calculations for computer science, or verifying engineering computations, these tools handle the arithmetic with step-by-step explanations.
Fraction arithmetic requires finding common denominators before adding or subtracting. To add 3/4 + 1/6, find the LCM of 4 and 6: LCM(4,6) = 12. Convert to 9/12 + 2/12 = 11/12. For multiplication: 3/4 × 1/6 = 3/24 = 1/8 (simplify by dividing by GCF(3,24) = 3). The Fraction Calculator handles all four operations with automatic simplification and step-by-step working, showing each intermediate step.
For number theory, prime factorization decomposes any integer into its prime building blocks. 360 = 2³ × 3² × 5. Knowing the prime factorization makes GCF and LCM trivial: GCF(360, 84) = 2² × 3 = 12. The Prime Factorization Calculator displays the complete factor tree. The GCF and LCM Calculator uses the efficient Euclidean algorithm — GCF(48, 18) = GCF(18, 12) = GCF(12, 6) = 6.
Scientific notation is essential for very large or very small numbers. Avogadro's number 602,200,000,000,000,000,000,000 = 6.022 × 10²³. An electron's mass 0.000000000000000000000000000000911 kg = 9.11 × 10⁻³¹ kg. The Scientific Notation Converter handles both directions and performs arithmetic in scientific notation. For exponents and logarithms, log₁₀(1000) = 3 and log₂(256) = 8. The Logarithm Calculator handles any base, and the Exponent Calculator computes powers including fractional and negative exponents.
The Mean Median Mode Calculator and Long Division Calculator round out the arithmetic toolkit — the latter is particularly useful for showing polynomial division steps that come up in algebra.
Frequently Asked Questions
How do I add fractions with different denominators?
Find the least common multiple (LCM) of both denominators, convert each fraction to an equivalent fraction with that LCM as the denominator, then add the numerators. For 3/4 + 1/6: LCM(4,6) = 12. Convert to 9/12 + 2/12 = 11/12. The Fraction Calculator shows each step automatically for any operation.
What is scientific notation and when should I use it?
Scientific notation writes numbers as a decimal between 1 and 10 multiplied by a power of 10. Avogadro's number 6.022 × 10²³ is easier to read and compute with than 602,200,000,000,000,000,000,000. Use it for very large numbers (astronomical distances, molecular counts) or very small numbers (atomic scales, engineering tolerances). Scientific notation also makes multiplication and division simpler: multiply the decimals and add the exponents.
What is the difference between GCF and LCM?
GCF (Greatest Common Factor) is the largest number that divides both values evenly — GCF(12, 8) = 4. LCM (Least Common Multiple) is the smallest number divisible by both values — LCM(12, 8) = 24. GCF is used to simplify fractions. LCM is used to find common denominators. They're related: LCM(a,b) = (a × b) / GCF(a,b).
How do I calculate a logarithm?
Logarithm log_b(x) = y means b^y = x. So log₁₀(1000) = 3 because 10³ = 1000. Natural log (ln) uses base e ≈ 2.718: ln(7.389) ≈ 2 because e² ≈ 7.389. For any other base, use the change of base formula: log_b(x) = log(x) / log(b). The Logarithm Calculator handles all bases and shows the conversion.