How-To Guides
Step-by-step guides that teach you how to perform calculations manually.
How to Perform Fundamental Algebraic Operations: A Step-by-Step Guide
Master essential algebraic operations: solve equations, factor polynomials, and work with exponents and roots. Learn by hand with formulas and examples.
Read guideHow to Solve Absolute Value Equations Manually
Learn to solve absolute value equations step-by-step using the case split method. Understand the formula, common pitfalls, and verify solutions.
Read guideHow to Calculate the Greatest Integer Function (Floor Function): Step-by-Step Guide
Learn to manually calculate the floor function ⌊x⌋ for any real number. Understand its definition, formula, and common pitfalls with worked examples.
Read guideHow to Convert Number Bases: Step-by-Step Guide
Learn to manually convert numbers between binary, octal, decimal, and hexadecimal bases using step-by-step methods and formulas.
Read guideHow to Calculate the Nth Root: Step-by-Step Guide
Learn to manually calculate the Nth root of any number. This guide covers the formula, prerequisites, a worked example, and common pitfalls.
Read guideHow to Convert Numbers to and From Scientific Notation: Step-by-Step Guide
Learn to manually convert numbers to and from scientific notation. Step-by-step guide with formulas, examples, and common pitfalls.
Read guideHow to Calculate Modulo: Step-by-Step Guide
Learn to manually calculate the modulo (remainder after division) for any integers. Includes formula, examples, and common pitfalls.
Read guideHow to Calculate Cube Roots: Step-by-Step Guide
Learn to calculate cube roots manually using estimation and an iterative refinement method. Understand the formula and avoid common pitfalls.
Read guideHow to Calculate Speed, Distance, or Time: Step-by-Step Guide
Learn to manually calculate speed, distance, or time using d=s×t. This guide covers formula rearrangement, unit conversion, and worked examples.
Read guideHow to Calculate Unit Rate: Step-by-Step Guide
Learn to calculate unit rate manually with this step-by-step guide. Includes formula, a worked example, common pitfalls, and when to use a calculator.
Read guideHow to Calculate Financial Ratios: Step-by-Step Guide
Learn to manually calculate essential financial ratios for operational and strategic analysis. This guide covers formulas, a worked example, and common pitfalls.
Read guideHow to Write Numbers in Expanded Form: Step-by-Step Guide
Learn to write numbers in expanded form by hand. Understand place value, formulas, and work through examples with this detailed guide.
Read guideHow to Manually Check if a Number is Prime: Step-by-Step Guide
Learn to manually check if an integer is prime using the trial division method. Understand the formula, worked examples, and common pitfalls.
Read guideHow to Calculate Place Value: Step-by-Step Guide
Learn to manually identify the place value of each digit in any number, including decimals. Understand the underlying formulas and avoid common pitfalls.
Read guideHow to Round to Significant Figures: Step-by-Step Guide
Learn to round numbers to a specified number of significant figures. This guide covers rules, formulas, examples, and common pitfalls.
Read guideHow to Convert Numbers To and From Scientific Notation: Step-by-Step Guide
Learn to convert numbers to and from scientific notation manually. Understand the A x 10^b format, formulas, worked examples, and common pitfalls.
Read guideHow to Calculate Modulo: Step-by-Step Guide
Learn to calculate the modulo (remainder after division) by hand using the formula a = nq + r. Includes examples and common pitfalls.
Read guideHow to Calculate Factors and Factor Pairs: Step-by-Step Guide
Learn to manually find all factors and factor pairs of any positive integer using trial division. Includes formulas, a worked example, and common pitfalls.
Read guideHow to Perform 2x2 Matrix Operations Manually: A Comprehensive Guide
Learn to manually calculate 2x2 matrix addition, multiplication, determinant, and transpose. Master the formulas with step-by-step examples and common pitfalls.
Read guideHow to Calculate Exponents: Step-by-Step Guide
Learn to manually calculate exponents, including positive, negative, and fractional powers. Understand the formulas with worked examples and common pitfalls.
Read guideHow to Calculate Logarithms Manually: Step-by-Step Guide
Learn to calculate logarithms in any base (common, natural, or custom) using the change-of-base formula. Includes examples and pitfalls.
Read guideHow to Manually Convert Between Binary, Decimal, Octal, and Hexadecimal
Learn step-by-step how to manually convert numbers between binary, decimal, octal, and hexadecimal systems using formulas and worked examples.
Read guideHow to Calculate Prime Factorization: Step-by-Step Guide
Learn to manually perform prime factorization. Break down any composite number into its prime components using trial division with a step-by-step example.
Read guideHow to Perform Long Multiplication: Step-by-Step Guide
Master long multiplication for any two large numbers. Learn the step-by-step process, including partial products, carrying, and summing to find the final result.
Read guideHow to Perform Long Division: Step-by-Step Guide
Learn long division with remainders step-by-step. Master the formula, practice with a worked example, avoid common pitfalls, and understand when to use a calculator.
Read guideHow to Round Numbers: Step-by-Step Guide
Learn to manually round numbers to any specified decimal place. This guide covers the underlying rules, provides a worked example, and highlights common pitfalls.
Read guideHow to Calculate Percentages: Step-by-Step Guide
Learn to calculate percentages, including increases and decreases, manually. Understand the formulas, see worked examples, and avoid common pitfalls.
Read guideHow to Perform Basic Arithmetic Operations Manually: Step-by-Step Guide
Learn to manually perform addition, subtraction, multiplication, and division. Understand formulas, see worked examples, and avoid common pitfalls.
Read guideHow to Perform Core Arithmetic and Number Operations: Step-by-Step Guide
Master core arithmetic and number operations like addition, subtraction, rounding, factors, primes, and sequences with this detailed step-by-step guide.
Read guideHow to Calculate a Continued Fraction Manually: Step-by-Step Guide
Learn to manually calculate continued fractions for real numbers, including partial quotients, convergents, and approximations. Understand the underlying algorithm.
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