Give feedback
Chapter overview
Learning goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Algebra uses letters called 'variables' to represent unknown quantities. The basic rules for algebraic notation help write terms in a concise way. These terms can then be used in expressions, formulae or equations.
The letter 'a' could represent an apple. Two apples could be described by $\underline{2a}$.
RULE | DESCRIPTION | EXAMPLE |
---|---|---|
Add equal variables | Add the numbers and copy the variable. If there is no number with the variable, it means $1$. For example, $x$ means $1x$ | $x+x=2x$ |
Subtract equal variables | Subtract the numbers and copy the variable. | $7x-5x=2x$ |
Multiply same variables | Multiplying the same variables changes the power. When multiplying add powers, if there is no number with the variable, it means $1$. | $x \times x = x^2$ |
Multiply different variables | Write the letters without the multiplication sign. Multiplying different variables will not change their powers. | $x \times y = xy$ |
Note: terms made of different variables cannot be added or subtracted.
Formulae help find quantities.
$F=ma$ | Calculate the force on an obejct from its mass and acceleration. |
$P = 2(l+w)$ | Calculate the perimeter of a rectangle from its length and width. |
$A=\frac{1}{2} bh$ | Calculate the area of a triangle from its base and its height. |
An equation is formed when two expressions equal each other.
$\frac x 2 =5$ |
$2x-3=7$ |
$x^2 -2x-8=0$ |
Algebra uses letters called 'variables' to represent unknown quantities. The basic rules for algebraic notation help write terms in a concise way. These terms can then be used in expressions, formulae or equations.
The letter 'a' could represent an apple. Two apples could be described by $\underline{2a}$.
RULE | DESCRIPTION | EXAMPLE |
---|---|---|
Add equal variables | Add the numbers and copy the variable. If there is no number with the variable, it means $1$. For example, $x$ means $1x$ | $x+x=2x$ |
Subtract equal variables | Subtract the numbers and copy the variable. | $7x-5x=2x$ |
Multiply same variables | Multiplying the same variables changes the power. When multiplying add powers, if there is no number with the variable, it means $1$. | $x \times x = x^2$ |
Multiply different variables | Write the letters without the multiplication sign. Multiplying different variables will not change their powers. | $x \times y = xy$ |
Note: terms made of different variables cannot be added or subtracted.
Formulae help find quantities.
$F=ma$ | Calculate the force on an obejct from its mass and acceleration. |
$P = 2(l+w)$ | Calculate the perimeter of a rectangle from its length and width. |
$A=\frac{1}{2} bh$ | Calculate the area of a triangle from its base and its height. |
An equation is formed when two expressions equal each other.
$\frac x 2 =5$ |
$2x-3=7$ |
$x^2 -2x-8=0$ |
FAQs
Question: What is algebraic notation?
Answer: Algebraic notation involves writing algebraic terms, with a combination of numbers and letters. These terms can then be used further in expressions and equations.
Question: What are variables?
Answer: Variables are a short hand way to name a quantity. The letter variable can then be used in an expression.
Question: What is algebra?
Answer: Algebra uses letters called variables to represent unknown quantities.
Theory
Exercises
© 2020 – 2023 evulpo AG
Your data protection
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners who may combine it with other information that you’ve provided them or that they’ve collected from your use of their services. By clicking on either "Accept cookies" or "Necessary cookies only", you agree to this (read more in our Privacy Policy). Privacy Policy