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Math Articles and Guides

Browse all math topics covered on shtools. From basic algebra to fraction conversions, find clear explanations and worked examples for every concept.

Algebra

Algebra Formulas

Core algebra formulas every student needs, from linear equations to quadratic expressions.

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Algebra

Algebraic Expressions

Learn how to read, write, and simplify algebraic expressions with variables and constants.

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Algebra

Polynomials Explained

What polynomials are, how to identify them, and how to work with them step by step.

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Algebra

Factoring Polynomials

Techniques for factoring polynomial expressions including GCF, grouping, and special patterns.

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Fractions

Fractions to Decimals

Convert any fraction to a decimal quickly using division, with worked examples.

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Fractions

Equivalent Fractions

Understand what equivalent fractions are and how to find them by multiplying or dividing.

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Algebra

Algebra Topics

Browse all algebra guides covering expressions, equations, polynomials, and more.

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Fractions

Fractions Topics

All fraction guides in one place - equivalent fractions, conversions, and operations.

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Algebra

Algebraic Fractions

How to simplify, add, subtract, multiply, and divide algebraic fractions.

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Algebra

The Remainder Theorem

Use the remainder theorem to find remainders when dividing polynomials.

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Algebra

Dividing Polynomials

Step-by-step guide to polynomial long division and synthetic division.

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Fractions

Fractions Equivalent to 1/2

List of fractions that are equal to one half, with visual examples.

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Fractions

Fractions Equivalent to 2/3

All fractions equivalent to two thirds explained with simple multiplication.

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Fractions

Fractions Equivalent to 1/4

Fractions equal to one quarter with full worked examples.

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Fractions

1/3 as a Percent

How to convert one third to a percentage, approximately 33.33%.

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Fractions

2/3 as a Percent

Two thirds as a percentage equals approximately 66.67%.

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Fractions

3/5 as a Percent

Three fifths as a percentage is exactly 60%.

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Math Basics

Order of Operations (PEMDAS)

PEMDAS and BODMAS explained with worked examples, a priority table, and common mistakes to avoid.

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Percentages

How to Calculate Percentage

Four types of percentage problems explained: finding a percent, percent change, reverse percentage, and more.

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Number Theory

GCF and LCM

How to find the greatest common factor and least common multiple using listing, prime factorization, and the shortcut formula.

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Statistics

Mean, Median and Mode

How to calculate each type of average and when to use which — with a real-world dataset comparison.

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Number Theory

Prime Numbers

What prime numbers are, how to test any number for primality, a full list to 229, and why they matter.

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Math Basics

Ratios and Proportions

How to simplify ratios, solve proportions using cross-multiplication, and apply them to real-world problems.

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Number Systems

Roman Numerals

Full guide to reading and writing Roman numerals — symbol chart, rules, the six subtractive pairs, and common examples.

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Number Systems

Binary, Decimal, Octal & Hex

How binary, hexadecimal, octal, and decimal number systems work, with conversion examples and a quick reference chart.

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Multiplication

Times Tables 1 to 12

The complete 12×12 multiplication table with patterns, memory tricks, and a focused list of the hardest facts.

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Geometry

Types of Triangles

All triangle types by sides and angles, with area and perimeter formulas, Pythagorean theorem, and worked examples.

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Algebra

Exponents and Powers

All seven exponent rules explained with examples — product, quotient, power, zero, negative, and fractional exponents.

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Math Basics

Negative Numbers

Adding, subtracting, multiplying, and dividing negative numbers — with clear explanations of why the rules work.

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