# Algebraic expressions

Which letters can you use as variables?

## Algebraic expressions

How old is Maria? She's two years older than Leon. Maria's age is equal to Leon's age plus two. If Leon is five we can write Maria's age as five plus two. If Leon is 50, we can write Maria's age as fifty plus two.

Let L be Leon's age. Then we can write Maria's age like this: L plus two. L is a symbol that represents a value in this case Leon's age. Every year Leon becomes older and the value represented by L changes. But Maria is always L+2 years old.

When we use letters to represent numbers, open the door to a new part of mathematics - algebra. Algebra helps us to generalise, to find patterns and to express connections. If you write Maria's age as L plus two, you have an algebraic expression. L+2 is more general than the numerical expression 5+2. Here's another algebraic expression that you will surely recognise: The base times the height.

It's what you do to calculate the area of a rectangle. The algebraic expression B times H applies to all rectangles, not just this one. To calculate the expression's value, we plug in the numerical values for the base and height and get twelve times four, which equals 48. Shall we take another example? Leon wants a new bicycle Okay.

and his father is going to help him. If Leon earns enough money for half the bike's price, his father will pay the other half. Write an algebraic expression that describes how much money Leon needs to save if the bicycle he wants costs C kronor. Leon needs to save C divided by two, kronor. Yes, keep peeling those potatoes a while longer.

Algebra is a way of expanding a mathematical argument from concrete, numerical calculations with numbers onto something more general. When you write an algebraic expression, you let one or more numbers be represented by a symbol, usually a letter, that can take different values. As you will find out later, this is very useful.