Transcript Algebraic Fractions and Change the Subject - Mr

Algebraic Operations
Simplest Form
Adding / Sub Fractions
Multiple / Divide Fractions
Subject of Formula
Harder Subject of Formula
Starter Questions
1.
Simplify the following fractions :
9
(a)
27
10
(b)
35
2.
Find the lowest multiple of 2 and 3
3.
1 1
Calculate (a) 
2 4
4.
Calculate
3
8
3 5
(b) 
4 6
Algebraic Operations
Learning Intention
1. To explain how to simplify
algebraic fractions.
Success Criteria
1. Understand term
Highest Common Factor.
2. Simplify algebraic fractions
by identifying HCF.
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
HCF = 3
12 3  4 4


15 3  5 5
HCF = Y
y2 y  y  y  y

1
y
y
Fraction in
Simplest form
Examples
1
1
2b
2b
1


2
6b
6  b  b 3b
3
1
1
1
a
aaa
a


a

1
aa
a2
3
1
1
Fraction in
Simplest form
Examples
1
1
1
( y  1)( y  1)
( y  1)


( y  1)
( y  1)( y  1)( y  1)
( y  1)3
2
1
1
Exercise 1 Page 186
Starter Questions
1.
Simplify the following fractions :
3g
(a)
4
9g
5e3
(b)
2e
2.
Find the lowest multiple of 4 and 9
3.
1 1
Calculate (a) 
2 5
4.
Calculate
3
27
3 5
(b)

10 6
Algebraic Operations
Learning Intention
1. To explain how to add and
subtract algebraic
fractions.
Success Criteria
1. Know how to add and sub
simple fractions
2. Apply same knowledge to add
and sub algebraic fractions.
Adding Algebraic Fractions
Example 1a
Example 1b
3 1

5 5
3 1

d d
LCM = 5
LCM = d
31

5
4

5

31
d
4

d
Subtract Algebraic Fractions
Example 2a
Example 2b
3 2

4 5
3 2

p q
LCM = 20
LCM = pq
35 2 4


45 5 4
15 8


20 20
7

20
3q 2 p


p q q  p
3q 2 p


pq qp
3q  2 p

pq
Adding Algebraic Fractions
Example 3a
3 1

4 6
Example 3b
LCM = 12
LCM = 2x2
33 12


43 62
9 2


12 12
11

12
3
1
 2
2x x
3 x
12

 2
2x  x x  2
3x
2


2
2x
2x 2
3x  2

2x 2
Adding / Subtracting
Algebraic Fractions
Exercise 2 Page 200
Starter Questions
Calculate the following :
1.
1 1
+
2 3
3.
3
4
2a 3a
2.
2 5
+
h h
4.
4
3
2
y
y
Algebraic Operations
Multiplication and division
Learning Intention
1. To explain how to multiply
and divide by algebraic
fractions.
Success Criteria
1. Know rules for multiplication
and division of simple
fractions.
2. Apply knowledge to algebraic
fractions.
Algebraic Fractions
Multiplication and division
Example 1a
Example 1b
3 4

8 5
5a 3
 2
6 a
1
5a 3 1

 2
26 a a
3 41
 
8 5
2
3

10
5

2a
Algebraic Fractions
Multiplication and division
Example 2a
Example 2b
4 5

9 6
2xy 5x

3
y
1
2xy
y


3
5x 1
4 62
 
9 5
3
8

15
2y 2

15
Algebraic Fractions
Multiplication and division
Exercise 3 Page 200
Starter Questions
Calculate the following :
1.
1 1

2 3
3.
3
a

2a
4
2.
2 5

h h
4.
4
3

2
y
y
Algebraic Operations
The Subject of a Formula
Learning Intention
1. To explain how to change
the subject of a formula
using
“change side change sign”
method.
Success Criteria
1. Know change sign change sign
for solving equations.
2. Apply knowledge to change
subject of a formula.
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.
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
D
C

What Goes In The Box ?
Make y the subject of the formulae below :
-x + 2y = 2
x+y=8
y = 8- x
1
y= x+1
2
x=y-9
x = 4( y + 1 )
y=x+9
1
y= x-1
4
Exercise 4 Page 202
Starter Questions
Calculate the following :
1.
1 1

2 3
3.
3
a

2a
4
2.
2 5

h h
4.
4
3

2
y
y
Algebraic Operations
The Subject of a Formula
Learning Intention
1. To explain how to change
the subject of a formula
containing square and
square root terms.
Success Criteria
1. Know change sign change sign
for solving equations.
2. Apply knowledge to change
subject of harder formulae
including square and square
root terms.
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.
F
S 
k
2
F
S 
k
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 W
T 
9
9T
 W
4
2
 9T 

 W
 4 
2
 9T 
W 

 4 
Algebraic Fractions
The Subject of a Formula
Exercise 6 Page 204