1. The document discusses algebraic operations such as simplifying fractions, adding and subtracting fractions, and multiplying and dividing fractions. It provides examples of how to perform these operations on both simple and algebraic fractions. 2. Methods for changing the subject of a formula are described. The "change side, change sign" rule is introduced for solving equations and changing the subject of formulas. Examples demonstrate using this rule to make different variables the subject of given formulas. 3. Harder examples of changing the subject of a formula are presented, including formulas involving square and square root terms. Readers are instructed on applying the same methods to these more difficult formulas.

1. Algebraic Operations
Simplest Form
Adding / Sub Fractions
Multiple / Divide Fractions
Subject of Formula
Harder Subject of Formula

2. Starter Questions
1. Simplify the following fractions :
9 10
(a) (b)
27 35
2. Find the lowest multiple of 2 and3
1 1 3 5
3. Calculate (a) (b)
2 4 4 6
3
4. Calculate 8

3. Learning Intention Success Criteria
1. To explain how to simplify
algebraic fractions.
1. Understand term
Highest Common Factor.
Algebraic Operations
2. Simplify algebraic fractions
by identifying HCF.

4. Fraction in
Simplest form
We can sometimes reduce fractions to a simpler form if
the numerator and denominator have a number or letter
in common.
Examples
12
15
3 4
3 5
4
5
HCF = 3
2
y
y
y y
y 1
y
y
HCF = Y

5. Fraction in
Simplest form
Examples
2
2
6
b
b
2
6
b
b b
1
3b
3
2
a
a
a a a
a a 1
a
a
3
1
1
1
1
1
1
1

6. Fraction in
Simplest form
Examples
2
3
( 1)
( 1)
y
y
( 1)( 1)
( 1)( 1)( 1)
y y
y y y
1
( 1)y
1
1
1
1

7. Starter Questions
1. Simplify the following fractions :
3
4
3g 5e
(a) (b)
9g 2e
2. Find the lowest multiple of 4 and 9
1 1 3 5
3. Calculate (a) (b)
2 5 10 6
3
4. Calculate 27

8. Learning Intention Success Criteria
1. To explain how to add and
subtract algebraic
fractions.
1. Know how to add and sub
simple fractions
Algebraic Operations
2. Apply same knowledge to add
and sub algebraic fractions.

9. Adding Algebraic Fractions
3 1
5 5
3 1
5
4
5
LCM = 5
Example 1a
3 1
d d
3 1
d
4
d
LCM = d
Example 1b

10. Subtract Algebraic Fractions
3 2
4 5
15 8
20 20
7
20
LCM = 20
Example 2a
3 2
p q
3 2q p
pq
LCM = pq
Example 2b
23 pq
pq qp
23 pq
p q q p
3 5 2 4
4 5 5 4

11. Adding Algebraic Fractions
3 1
4 6
9 2
12 12
11
12
LCM = 12
Example 3a
2
3 1
2x x
2
3 2
2
x
x
LCM = 2x2
Example 3b
2 2
3 2
2 2
x
x x
2
3 1 2
2 2
x
x x x
3 3 1 2
4 3 6 2

12. 3 4
3. -
2a 3a
Starter Questions
Calculate the following :
1 1
1. +
2 3
2 5
2. +
h h
2
4 3
4. -
y y

13. Learning Intention Success Criteria
1. To explain how to multiply
and divide by algebraic
fractions.
1. Know rules for multiplication
and division of simple
fractions.
Algebraic Operations
2. Apply knowledge to algebraic
fractions.
Multiplication and division

14. 3 4
8 5
3
10
Example 1a
2
5 3
6
a
a
5
2a
Example 1b
Algebraic Fractions
Multiplication and division
3 4
8 5
2
1
2
5 3
6
a
a2
11
a

15. 4 5
9 6
8
15
Example 2a
2 5
3
xy x
y
2
2
15
y
Example 2b
Algebraic Fractions
Multiplication and division
4 6
9 5
3
2 2
3 5
xy y
x
1
1

16. 3 a
3.
2a 4
Starter Questions
Calculate the following :
1 1
1.
2 3
2 5
2.
h h
2
4 3
4.
y y

17. Learning Intention Success Criteria
1. To explain how to change
the subject of a formula
using
“change side change sign”
method.
1. Know change sign change sign
for solving equations.
Algebraic Operations
2. Apply knowledge to change
subject of a formula.
The Subject of a Formula

18. Algebraic Fractions
The Subject of a Formula
The formula below is used to work out
the circumference of a circle
C D
Since the formula works out C , then C is called
the subject of the formula.

19. Algebraic Fractions
The Subject of a Formula
We can make D the subject of the formula
by using the rule
“ opposite side opposite side “
C D
C
D
C
D

20. What Goes In The Box ?
1
y = x - 1
4
Make y the subject of the formulae below :
x + y = 8
x = y - 9
-x + 2y = 2
x = 4( y + 1 )
y = 8- x
y = x + 9
1
y = x + 1
2

21. 3 a
3.
2a 4
Starter Questions
Calculate the following :
1 1
1.
2 3
2 5
2.
h h
2
4 3
4.
y y

22. Learning Intention Success Criteria
1. To explain how to change
the subject of a formula
containing square and
square root terms.
1. Know change sign change sign
for solving equations.
Algebraic Operations
2. Apply knowledge to change
subject of harder formulae
including square and square
root terms.
The Subject of a Formula

23. Algebraic Fractions
The Subject of a Formula
Example : The force of the air against a train is
given by the formula below.
Make the speed (S) the subject of the formula.
2 F
S
k
F
S
k

24. Algebraic Fractions
The Subject of a Formula
Example : The thickness of a rope T cm to lift a
weight W tonnes can be worked out
by the formula below.
Make W the subject of the formula.
4
9
W
T
9
4
T
W
2
9
4
T
W
2
9
4
T
W