1. Basic Linear Algebra Objectives
Manipulating algebraic Terms and Expressions
Collecting like Terms
Removing brackets
Factorising
Multiplication of Algebraic Terms
Simplifying Algebraic Fractions
Dividing Fractions
Manipulating algebraic equations
Solving a single linear equations
24 October, 2019
INTO Foundation L3 MH

2. Starter - add adjacent expressions to make a new expression in the cell above

3. 17t +7
9t +8
7t -1
3t-8
5t +1
4t +7
2t +3
3t -2
t +9
2t -17

4. … Starter eggs …? … I went to the market with a basket of eggs…
I sold half my eggs plus half an egg to Alan
I sold half of my remaining eggs plus half an egg to Barry
I sold half of my remaining eggs plus half an egg to Charlie
I sold half of my remaining eggs plus half an egg to Denise
I sold half of my remaining eggs plus half an egg to Ellen
I was left with just one egg.
Are the above transactions possible without breaking eggs?
How many eggs did I start with?

5. Basic Algebra In Algebra we Use symbols to represent unknown numbers
We solve equations to find the values of these unknown quantities
An algebraic EXPRESSION consists of one or more TERMS separated by +/- operators
TERMS
EXPRESSION
24 October, 2019
INTO Foundation L3 MH

6. Collecting Terms
We should always reduce algebraic expressions to their simplest form as an answer
We can only collect like Terms
Simplifies to
24 October, 2019
INTO Foundation L3 MH

7. Brackets Example 4t+ 16ty can be written as 4t(1+4y)
We can use brackets to factorise an expression
Take out a common factor
Example
4t+ 16ty can be written as 4t(1+4y)
Brackets can also be thought of as simplifying an expression
Brackets can also be used to explicitly define the order of operations
Find the value of 2x+4xy and 2(x+4xy); when x=2,y=3
24 October, 2019
INTO Foundation L3 MH

8. Removing Brackets a(b+c) ≡ ab + ac
This is the opposite to factorisation
The factor outside the bracket multiplies each Term inside.
a(b+c) ≡ ab + ac
-a(b-c) ≡ -ab +ac (Same as arithmetic )
We do not explicitly write the multiplication term in algebra because it looks too much like an “ “
Use the curly “ “ , although on the slides I sometimes use the “x” for convenience
24 October, 2019
INTO Foundation L3 MH

9. Removing Brackets Simplify expand brackets collect terms
24 October, 2019
INTO Foundation L3 MH

10. Multiplication of Terms
This is where our knowledge of the laws of indices comes in handy
Division similar
Example
24 October, 2019
INTO Foundation L3 MH

11. Division of Terms Example : Simplify
We normally write an expression like this as a fraction
Then we cancel variables
24 October, 2019
INTO Foundation L3 MH

12. Simplifying Algebraic Fractions
We do this in exactly the same way as with numerical fractions
Example
24 October, 2019
INTO Foundation L3 MH

13. Fractions
Example Example
24 October, 2019
INTO Foundation L3 MH

14. Dividing Fractions Simply Invert the divisor and multiply
24 October, 2019
INTO Foundation L3 MH

15. Summary so far
Looked at handling simple algebraic expressions, terms and fractions
Do exercise ->Section 1 Basic Algebraic Manipulation and solving equations Q1-Q6
Next solving simple Algebraic equations
24 October, 2019
INTO Foundation L3 MH

16. Single linear equations
-This is generally very straight forward
-Essentially all you need to do is rearrange the equation in terms of the unknown variable
-As long as you do the same thing to both sides an equation will still be valid
Lets make up some examples!!
24 October, 2019
INTO Foundation L3 MH

17. 2 quick Examples 3(x+2)=24 4(x+2)=9(x+2)
Now Do: Section 1 Basic Algebraic Manipulation and solving equations Q7- onwards
24 October, 2019
INTO Foundation L3 MH