Although maths may seem hard to some people, the point of maths is to make hard things easy!

Algebra helps a lot with this by reducing complicated sentences into simple algebraic statements.

The first part of an algebraic statement we will look at is algebraic expressions.

Algebraic expressions use letters and symbols instead of words. So instead of saying “three times the height of the wall” we can just write 3x, with x meaning the height of the wall.

Worked Example

• Write in a shorter way: “The length of a piece of string with 3cm cut off it”
• Write in a shorter way: “The total number of cakes baked if I bake two cakes for each of my friends and 5 spare cakes”
• What English phrase could be represented by 4h.

Exercise 1

Geometric problems

Sometimes we have geometrical problems where some of the lengths or angles are unknown. We can use algebra to help us in these cases, finding an answer which we can later substitute the values into when they are known.

Worked Example

Calculate the area of this rectangle:

Exercise 2

Units

Algebra can be helpful when changing units. For instance, if we use x to represent a number of years, but we want to represent a number of days, we can replace x with 365x

Similarly, if we use y to represent a number of horses and we are interested in how many horses legs there are, we can replace y with 4y (assuming none of the horses have lost legs).

To do this though we need to know many facts, like how many days there are in a year.

Worked Example

• How many days are there in:
  • 4 weeks
  • 9 weeks
  • x weeks
  • 5x weeks

Exercise 3

Answers to all 3 Exercises