algebraic operations simplest form adding / sub fractions multiple / divide fractions subject of...
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Algebraic OperationsAlgebraic Operations
Simplest Form
Adding / Sub Fractions
Multiple / Divide Fractions
Subject of Formula
Harder Subject of Formula
Starter QuestionsStarter Questions
1. Simplify the following fractions :
9 10 (a) (b)
27 352. Find the lowest multiple of 2 and 3
1 1 3 53. Calculate (a) (b)
2 4 4 6
34. Calculate 8
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. To explain how to simplify algebraic fractions.
1.1. Understand term Understand term Highest Common Factor.Highest Common Factor.
Algebraic Operations
2.2. Simplify algebraic Simplify algebraic fractions by identifying fractions by identifying HCF.HCF.
Fraction in Fraction in Simplest formSimplest form
We can sometimes reduce fractions to a simpler form if the numerator and denominator have a
number or letter in common.Examples
1215
3 43 5
45
HCF = 3
2yy
y yy
1y
y
HCF = Y
Fraction in Fraction in Simplest formSimplest form
Examples
2
26bb
26
bb b
13b
3
2
aa
a a aa a 1
aa
3
1
1
1
1
1
1
1
Fraction in Fraction in Simplest formSimplest form
Examples
2
3
( 1)( 1)yy
( 1)( 1)( 1)( 1)( 1)
y yy y y
1( 1)y
1
1
1
1
Exercise 1 Page 186
Starter QuestionsStarter Questions
1. Simplify the following fractions : 3
4
3g 5e (a) (b)
9g 2e2. Find the lowest multiple of 4 and 9
1 1 3 53. Calculate (a) (b)
2 5 10 6
34. Calculate 27
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. To explain how to add and subtract algebraic fractions.
1.1. Know how to add and sub Know how to add and sub simple fractionssimple fractions
Algebraic Operations
2.2. Apply same knowledge to Apply same knowledge to add and sub algebraic add and sub algebraic fractions.fractions.
Adding Algebraic Adding Algebraic FractionsFractions
3 15 5
3 15
45
LCM = 5
Example 1a
3 1
d d
3 1
d
4d
LCM = d
Example 1b
Subtract Algebraic Subtract Algebraic FractionsFractions
3 24 5
15 820 20
720
LCM = 20
Example 2a
3 2
p q
3 2
q ppq
LCM = pq
Example 2b
23
pqpq qp
23
pq
p q q p
3 5 2 44 5 5 4
Adding Algebraic Adding Algebraic FractionsFractions
3 14 6
9 212 12
1112
LCM = 12
Example 3a
2
3 12
x x
2
3 22
xx
LCM = 2x2
Example 3b
2 2
3 22 2
xx x
2
3 1 22 2
x
x x x
3 3 1 24 3 6 2
Adding / SubtractingAdding / Subtracting Algebraic Fractions Algebraic Fractions
Exercise 2 Page 200
3 43. -
2a 3a
Starter QuestionsStarter Questions
Calculate the following :
1 11. +
2 32 5
2. +h h
2
4 34. -
y y
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. To explain how to multiply and divide by algebraic fractions.
1.1. Know rules for Know rules for multiplication and division multiplication and division of simple fractions.of simple fractions.
Algebraic Operations
2.2. Apply knowledge to Apply knowledge to algebraic fractions.algebraic fractions.
Multiplication and division
3 48 5
310
Example 1a
2
5 36
a
a
52
a
Example 1b
Algebraic FractionsMultiplication and division
3 48 5
2
12
5 36
a
a2
11
a
4 59 6
815
Example 2a
2 53
xy x
y
2215
y
Example 2b
Algebraic FractionsMultiplication and division
4 69 5
3
2 23 5
xy y
x
1
1
Algebraic FractionsMultiplication and division
Exercise 3 Page 200
3 a3.
2a 4
Starter QuestionsStarter Questions
Calculate the following :
1 11.
2 3 2 5
2. h h
2
4 34.
y y
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. To explain how to change the subject of a formula using
“change side change sign”
method.
1.1. Know change sign change Know change sign change sign for solving equations.sign for solving equations.
Algebraic Operations
2.2. Apply knowledge to Apply knowledge to change subject of a change subject of a formula.formula.
The Subject of a Formula
Algebraic FractionsThe 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 FractionsThe 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
What Goes In The Box ?
1y = 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
1y = x + 1
2
Exercise 4 Page 202
3 a3.
2a 4
Starter QuestionsStarter Questions
Calculate the following :
1 11.
2 3 2 5
2. h h
2
4 34.
y y
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. To explain how to change the subject of a formula containing square and square root terms.
1.1. Know change sign change Know change sign change sign for solving equations.sign for solving equations.
Algebraic Operations
2.2. Apply knowledge to Apply knowledge to change subject of harder change subject of harder formulae including square formulae including square and square root terms.and square root terms.
The Subject of a Formula
Algebraic FractionsThe 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
Sk
F
Sk
Algebraic FractionsThe 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.
49
W
T
94
T
W
294
T
W
294
T
W
Exercise 6 Page 204
Algebraic FractionsThe Subject of a Formula