Introduction to Algebra

Algebra is a branch of mathematics that uses letters to represent numbers. These letters are called variables because their values can vary (change) depending on the situation.

In everyday maths, we work with specific numbers like 5, 12, or 100. But sometimes we need to talk about numbers in a general way, or we might not know what the number is yet. This is where algebra helps us.

Example:

• Instead of saying "a number plus 3," we can write: x + 3
• Here, x represents any number (it could be 2, 10, or even -5)

You can use any letter as a variable, but some are more common:

• x and y are the most popular
• Other letters like a, b, n, p, q are also used
• Sometimes we use letters that remind us of what they represent (like t for time, d for distance)

When we write mathematics using letters, we follow special rules called algebraic notation. Here's how to write different operations:

These work exactly as you'd expect:

• a + b means "add a and b"
• c - d means "subtract d from c"
• x + 5 means "add 5 to x"

Important: In algebra, we do not write the multiplication sign (×).

Instead:

• ab means a × b
• 5x means 5 × x
• 3xy means 3 × x × y

Why? Because the letter x looks too similar to the multiplication sign ×, so we drop the symbol to avoid confusion.

Example:

• "2 times a" is written as 2a (not 2 × a)
• "a times b times c" is written as abc (not a × b × c)

We write division as a fraction:

• a/b means a ÷ b (a divided by b)
• x/5 means x ÷ 5

Powers work the same way as with numbers:

• a² means a × a (a squared)
• x³ means x × x × x (x cubed)
• b⁴ means b × b × b × b

Important note: When you have a number with a power, the power applies only to the letter, not the number in front:

• 4a² means 4 × a × a (NOT 4 × 4 × a)
• Work out the power first (a²), then multiply by 4

• √a means "the square root of a"
• This works just like with numbers

Brackets work the same way as in regular maths:

• 3(a + b) means 3 × (a + b)
• You must work out what's inside the brackets first, then multiply by 3

You can mix all these operations together:

• ab + c means (a × b) + c
• 2x + 3y means (2 × x) + (3 × y)
• a²/b means (a × a) ÷ b

Remember: Follow the order of operations (BIDMAS/BODMAS):

1. Brackets first
2. Indices (powers and roots)
3. Division and Multiplication (left to right)
4. Addition and Subtraction (left to right)