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What is algebra?
1000 years ago, Islamic scholars developed algebra, a way of solving problems in mathematics. The word "algebra" comes from the Arabic al-jabr, meaning "rejoining of broken parts". Algebra uses kinds of sums called formulae, in which some of the numbers are replaced by letters, such as x + 5 = 8.
What is algebra for?
Medieval scholars developed algebra to help them work out more advanced mathematical problems. But their work on algebra soon became useful for solving problems in everyday life, such as how much money people owed to one another, or the best ways to build roads and canals. Today, algebra is essential in many industries including business, banking and construction.
Variables
Algebra is useful when we need to do a calculation where there are one or more values (numbers) that we don't know, or could change. In algebra, these unknown values are replaced by letters, such as x, y or z. They are known as variables.
Algebraic formulae
A sum in algebra is called a formula. A formula is like a recipe. It tells us what we need to put in to get a certain result. Algebraic formulae always contain at least one unknown value, represented by a letter.
In algebra, letters written next to one another are meant to be multiplied. For example:
area = hw
tells us that area = height x width.
This is to avoid confusing the multiplication symbol x with the commonly used variable x.
Equations
An equation is a statement that two values are equal. This is indicated by the equals sign =.
This means that if part of the equation is unknown, we can use algebra to work out what it is. This is called "solving an equation".
When solving an equation, we have to perform the same operation—for example subtraction or addition—on both sides of the equals sign, to keep it balanced.
To solve the equation in this example, we need to find the value of x. First we need to do some rearranging to get x on one side of the equals sign and the rest of the formula on the other.
Let's say we have the equation x + 8 = 10
To get x on its own, we need to take away, or subtract, the 8. Whatever we do on one side, we also have to do to the other. Subtracting 8 from 10 is 2.
Subtracting 8 from both sides leaves us with x = 2
Consultant: Adam Larking
Key words
equation a formula that uses the equals sign, such as x + 8 = 10
formulae types of sums in which some of the numbers are replaced by letters
values numbers or letters (often x, y, and z) in an algebraic formula
variable an unknown or changeable value in an algebraic formula which is represented by a letter such as x, y or z
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