Maths Made Simple
Past papers, memos, worksheets and video lessons — all free, all in one place.
Free Maths Lessons
Plain-language lessons for Grades 8–12, written by a South African maths teacher. Every lesson explains a topic, works through exam-style examples step by step, and ends with a worksheet you can try — answers included. Tap a grade to jump straight to it.
Properties of Whole Numbers
The commutative, associative and distributive properties, the identity roles of 0 and 1, and why dividing by 0 is undefined — the rules that let you rearrange any calculation, with a diagram, worked examples and an exam-style worksheet with memo.
Read the lessonFactors, Multiples & Prime Factorisation
What factors and multiples really are (and how never to mix them up), what makes a number prime, and how to break any number into its prime factors with a factor tree — worked examples, a clear diagram and an exam-style worksheet with memo.
Read the lessonHCF and LCM (Highest Common Factor & Lowest Common Multiple)
Highest Common Factor and Lowest Common Multiple made simple by reading them straight off the prime factors — with a Venn-diagram picture, exam-style worked examples and word problems, plus a worksheet with memo.
Read the lessonAdding and Subtracting Integers
Ordering integers on a number line, then the two adding rules and the 'add the opposite' trick for subtracting — with a number-line diagram, exam-style worked examples, a worksheet with memo and a quick quiz.
Read the lessonMultiplying and Dividing Integers
The one sign rule that covers both × and ÷ — same signs give a positive, different signs give a negative — shown as a grid, with exam-style worked examples, a worksheet with memo and a quick quiz.
Read the lessonIntegers: Squares, Cubes, Roots & Mixed Operations
Squares, cubes, square roots and cube roots of integers, the crucial difference between (−3)2 and −32, and how to run BODMAS through a calculation containing negatives — worked examples, worksheet with memo and a quiz.
Read the lessonProperties of Integers & Inverses
The commutative, associative and distributive properties applied to integers, plus additive and multiplicative inverses — what they are, how exams ask for them, with worked examples, a worksheet with memo and a quiz.
Read the lessonOrder of Operations: Getting BODMAS Right
Do calculations in the wrong order and you get the wrong answer, even with perfect arithmetic. BODMAS is the rule that fixes that.
Read the lessonEquivalent Fractions & Simplifying
What the top and bottom of a fraction actually mean, how to build equivalent fractions, and how to simplify to lowest terms using the HCF — with a bar diagram, worked examples, a worksheet with memo and a quiz.
Read the lessonAdding & Subtracting Fractions
Adding and subtracting fractions with the same denominator, with different denominators using the LCD, and with mixed numbers — shown with a bar diagram, exam-style worked examples, a worksheet with memo and a quiz.
Read the lessonMultiplying & Dividing Fractions
Multiplying straight across, the reciprocal, and why dividing by a fraction means multiplying by its flip — including mixed numbers and dividing whole numbers by fractions, with worked examples, a worksheet with memo and a quiz.
Read the lessonSquares, Cubes & Roots of Fractions
Squaring and cubing fractions, and finding square roots and cube roots of fractions — the rule is simply 'do it to the top and to the bottom', with worked examples, a worksheet with memo and a quiz.
Read the lessonFractions of Quantities, Grouping & Sharing
Finding a fraction of an amount, working backwards from a fraction to the whole, and the grouping and sharing word problems that carry the marks in exams — worked examples, a worksheet with memo and a quiz.
Read the lessonDecimals: Place Value, Ordering & Rounding
What each digit after the decimal point is worth, how to compare and order decimals correctly, and how to round off to a given number of decimal places — with a place-value chart, worked examples, a worksheet with memo and a quiz.
Read the lessonAdding & Subtracting Decimals
The one rule that makes decimal addition and subtraction reliable — line up the decimal points — plus filling gaps with zeros and money problems, with worked examples, a worksheet with memo and a quiz.
Read the lessonMultiplying & Dividing Decimals
Counting decimal places when multiplying, the shift trick for dividing by a decimal, multiplying and dividing by 10, 100 and 1000, and estimating the answer first — worked examples, a worksheet with memo and a quiz.
Read the lessonSquares, Cubes & Roots of Decimals
Squaring and cubing decimals, and finding square and cube roots of decimals, using the decimal-place count or by converting to fractions — with worked examples, a worksheet with memo and a quiz.
Read the lessonExtending Numeric & Geometric Patterns
Spotting what a pattern is doing — a constant difference, a constant ratio, or something else entirely — and extending it, including patterns given as diagrams or tables, with worked examples, a worksheet with memo and a quiz.
Read the lessonPattern Rules: In Words and in Algebra
Turning a pattern into a general rule — first described in words, then written algebraically as Tₙ = dn + c — and using that rule to find far-off terms or to work backwards, with worked examples, a worksheet with memo and a quiz.
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Danemathics: Rise to Legend
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