Why use letters?
Sometimes in algebra you will use the initial letter of a word to stand in for that word.
For example, the area of a square can be found by multiplying the length by the length.
You could write this as l x l
Or you could write it as l2
Even if you are working with different squares, with different length of side, you can use l x l or l2 to find the answer every time.
Using more than one letter
Sometimes you might have more than one unknown value. For example, the area of a rectangle can be found by multiplying the length by the breadth. If you wrote this with just question marks or empty boxes it would look like this:
? + ? or +
Which is which? It’s confusing.
You could use l for length and b for breadth instead:
l x b
The letters make it clearer which is which.
Again, the values can change so that you can use this for lots of different rectangles.
Question
Can you come up with algebraic expressions to show the following:
- The area of a triangle is half times the base times the height.
- The perimeter of a pentagon is five times the length of each side.
- The speed of an object is the distance travelled divided by the time it took
- The weight of an object is its mass mutliplied by the force of gravity
You might have picked different letters (that's fine!) but your answers should look a bit like this:
- A = ½ b x h or A = ½ bh (where A is the area, b is the base and h is the height)
- p = 5 x s or 5s (where p is the perimeter and s is the length of a side)
- s = d ÷ t or s=d/t (where s is the speed, d is the distance and t is the time)
- w = m x g or 2=mg (where w is the weight, m is the mass and g is gravity)