ALGEBRA

Algebra involves the use of letters (a, b, c, X, Q, P) or symbols (*, # etc)

to represent numbers

Where is algebra used?

• You would have seen algebra used in ‘formulae’ to work out things;

• The area of a triangle A = ½ BH

• Converting different currencies (money)

• $ AUS = 1.03 $US

Some formulae involving algebra

• Volume of a prism V = L x W x H

• Area of a square A = L X L

• Conversion of Km to miles K = 1.6M

• Conversion of pound weight to Kg K = 2.2P

Why not use numbers?

• Algebra is used where numbers can and will change.

• In the previous example, the area of a triangle will change simply because triangles can have different heights and base measurements.

Algebra Rules (numbers and letters?)

• What does 7h mean?

• It means 7 ‘lots’ of h or more accurately 7 X h

• (h + h + h + h + h + h + h)

• When using algebra we assume that the operation of X is between numbers and letters

We don’t bother using ‘X’

• So 7h means 7 X h

• 6hy means 6 X h X y

• 34hjk means 34 X h X j X k

When using x as a letter

• To avoid confusion between using the letter x

and multiplication X it is best to use x.

• For example 5 xy means 5 x x x y and not

confused with 5 x y

No need to use a single ‘1’

• We don’t bother writing 1g , 1w, 1p etc.

Simply write g, w or p

• fgh means f x g x h

What we can add or subtract.

• To add or subtract algebraic terms the letters must be the same.

• 6i + 7i = 13i

• 6ui + 7i cannot be added!

Algebra (adding & subtracting terms)

• We can add or subtract ‘terms’ as long as they contain the same letter or letters.

(it is like collecting different fruits in separate bowls)

• 6j - 5j = j

• 8w + 4w = 12w

• 5r - 2e (we cannot subtract because they have different letters)

Adding and subtracting algebra terms

• 6t + 5a + 7t + 2a =

• First look at the terms with ‘t’ we have 6t + 7t (that adds up to 13t)• Next look at the terms with ‘a’ we have 5a + 2a (that adds up to 7a)

So the answer is 13t + 7a (we cannot add these together)

What about 7w - 7w = ?

• 7w - 7w = 0w

(anything multiplied by zero is zero)

So answer is 0!

What about 4r - 5r = ?

• Using our knowledge of directed numbers we know that 4 - 5 = - 1

• So 4r - 5r = -1r

• Remember we don’t use ‘1’ so the answer can be written as - r

What about multiplication & divisionof algebraic terms?

That’s a story for next time!

Have a go at these questions.

(a) a + a + a = (e) 4t + 5r + 2t + 5r =

(b) 3b + 2b = (f) 5f - 4f + 3g =

(c) 3b + 2b + b = (g) 9j - 9j =

(d) 5k - 2k - k = (h) 3e + 7r + 2r – 4e =

Practice questions(i) 6e + 6ei + 8e =(j) 10p -12p + 6p =(k) 100q -10q +12x =(l) 3a + 2b – a + 3b – b =(m) a – a + a – a + a + a =(n) 12y + 2x + 0 + 4y =(o) w - 10w + 2x – w =(p) 12xy+ 4x + 4y + 2xy =(q) a + b + a + b – 2a – b =(r) 7t + 7x + 7y + 7t + 2y =(s) p + q + r =(t) 12x– 2x– 7y – 9y =