Basics
Addition and subtraction
Addition and subtraction as the most basic arithmetic operations. Terminology, the column method for adding large numbers, and showing both on a number line.
Multiplication
What multiplication is and how it relates to addition. Notation, a picture of it, multiplying by zero, order of operations and the times tables in one place.
Division
What division is and why it is the opposite of multiplication. Explained with examples and, above all, an answer to the question of why we cannot divide by zero.
Why we cannot divide by zero
Why we cannot divide by zero and why the result is not infinity. Several ways of seeing it, the quotient zero divided by zero, and a false proof that 1 = 2.
Polynomials
What a polynomial is. Adding, subtracting and multiplying polynomials, simplifying expressions and worked examples.
Algebraic fractions
An algebraic fraction is a fraction with a polynomial in the numerator and denominator. Simplifying techniques and three worked examples with detailed comments.
Fractions: adding, subtracting, multiplying and dividing
What a fraction is, how to simplify it and what its simplest form is. Adding, subtracting, multiplying and dividing fractions, plus cross-multiplication, with examples.
Taking out common factors
How to take out a common factor and how to expand brackets. The two operations are opposites of each other, explained through a series of worked examples.
Percentages
What percentages are and how to work with them. A percentage as part of a whole, calculating with the unitary method, the tricky trap of adding percentages in sequence, and per mille.
Rounding
How to round numbers to different places. The rules of rounding from tens up to decimals, and the trap of rounding in stages.
Direct and inverse proportion
How to solve proportion problems when you know three values and need the fourth. Direct and inverse proportion, an algorithm with arrows, formulae and worked examples.
Work problems
Work problems: how long do two people take together to do what each does alone in a different time? The method and worked examples.
Mixed numbers
What a mixed number is, with a whole part and a fraction mixed together. An explanation using pizza, how to write them, and how to convert to an improper fraction and back.
