SlideShare a Scribd company logo
4048 2EM Algebra – Change Subject (1) Math Academy®
All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, or
stored in any retrieval system of any nature without prior permission.
Math Academy® 1
Knowing is not enough; we must apply. Willing is not enough; we must do.
Johann Wolfgang von Goethe
Notes: Changing Subject of a Formula
Example 1: Make the letter in the brackets the subject of the given formula.
Example 2:
Example 3:
(3 )
2
w
x y c+ = ( )x
z
yx
m
=
-
( )y
1x y
m z
-
=
m
x y
z
- =
m
x y
z
- =
2
a
b c
x
= + ( )x
2 1
a b c
x
+
=
2 1x
a b c
=
+
2
a
x
b c
=
+
2( )
a
x
b c
=
+
Common mistake
m m
z
x y
- =
FLIP EACH side
Multiply on both sidesm
ALONEy
LHS and RHS one term each
FLIP EACH side (not flip individually)
Multiply on both sidesa
Common mistake
1 1
2
x
a b c
= +
LHS: ALONEx
Technique:
Flip
4048 2EM Algebra – Change Subject (1) Math Academy®
All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, or
stored in any retrieval system of any nature without prior permission.
Math Academy® 2
Example 4:
Example 5:
Example 6:
3 2x y k
k y
-
= ( )x
2
R r
T
r
+
=
-
( )r
1
11
=+
ba
( )b
1 1
1
b a
= -
1 1a
b a a
= -
1 1a
b a
-
=
1 1
b a
a
=
-
1
a
b
a
=
-
appears oncex Do not Cross-multiply
appears twicer Cross-multiply
Group terms with r
Cross- Multiply
Factorise r
Make the term containing
on one side.b
Make Same Denominator
Flip
Do not make same denominator
at this stage (else appear
everywhere --- Tedious !!)
b

More Related Content

What's hot

factoring perfect square trinomial
factoring perfect square trinomialfactoring perfect square trinomial
factoring perfect square trinomial
JessebelBautista
 
1.1 ss factoring the difference of two squares
1.1 ss factoring the difference of two squares1.1 ss factoring the difference of two squares
1.1 ss factoring the difference of two squares
JessebelBautista
 
Factoring difference of two squares
Factoring difference of two squaresFactoring difference of two squares
Factoring difference of two squares
laila_barrera
 
Factoring the difference of two squares
Factoring the difference of two squaresFactoring the difference of two squares
Factoring the difference of two squares
Lorie Jane Letada
 
Power point for theorem
Power point for theoremPower point for theorem
Power point for theorem
41695870
 
Math academy-partial-fractions-notes
Math academy-partial-fractions-notesMath academy-partial-fractions-notes
Math academy-partial-fractions-notes
Math Academy Singapore
 
05 perfect square, difference of two squares
05   perfect square, difference of two squares05   perfect square, difference of two squares
05 perfect square, difference of two squares
majapamaya
 
Factoring the difference of two squares
Factoring the difference of two squaresFactoring the difference of two squares
Factoring the difference of two squares
Lorie Jane Letada
 
Section 1.5 distributive property (algebra)
Section 1.5 distributive property (algebra)Section 1.5 distributive property (algebra)
Section 1.5 distributive property (algebra)
Algebra / Mathematics
 
Algebra 7 Point 6
Algebra 7 Point 6Algebra 7 Point 6
Algebra 7 Point 6
herbison
 
5.3 Solving Quadratics by Finding Square Roots
5.3 Solving Quadratics by Finding Square Roots5.3 Solving Quadratics by Finding Square Roots
5.3 Solving Quadratics by Finding Square Roots
hisema01
 
common monomial factor
 common monomial factor common monomial factor
common monomial factor
JessebelBautista
 
Factoring Perfect Square Trinomial
Factoring Perfect Square TrinomialFactoring Perfect Square Trinomial
Factoring Perfect Square Trinomial
Majesty Ortiz
 
Lecture 10
Lecture 10Lecture 10
Lecture 10
FahadYaqoob5
 
Factoring difference of squares
Factoring difference of squaresFactoring difference of squares
Factoring difference of squares
brittanyhurley1
 
Polynomials Test Answers
Polynomials Test AnswersPolynomials Test Answers
Polynomials Test Answers
ste ve
 
Markov number
Markov numberMarkov number
Markov number
Kabuto Yakushi
 
Project in Mathematics. Functions
Project in Mathematics. FunctionsProject in Mathematics. Functions
Project in Mathematics. Functions
NikkaVerone
 
Determinants
DeterminantsDeterminants
Determinants
scnbmitchell
 
Distributive property
Distributive propertyDistributive property
Distributive property
marniekrentz
 

What's hot (20)

factoring perfect square trinomial
factoring perfect square trinomialfactoring perfect square trinomial
factoring perfect square trinomial
 
1.1 ss factoring the difference of two squares
1.1 ss factoring the difference of two squares1.1 ss factoring the difference of two squares
1.1 ss factoring the difference of two squares
 
Factoring difference of two squares
Factoring difference of two squaresFactoring difference of two squares
Factoring difference of two squares
 
Factoring the difference of two squares
Factoring the difference of two squaresFactoring the difference of two squares
Factoring the difference of two squares
 
Power point for theorem
Power point for theoremPower point for theorem
Power point for theorem
 
Math academy-partial-fractions-notes
Math academy-partial-fractions-notesMath academy-partial-fractions-notes
Math academy-partial-fractions-notes
 
05 perfect square, difference of two squares
05   perfect square, difference of two squares05   perfect square, difference of two squares
05 perfect square, difference of two squares
 
Factoring the difference of two squares
Factoring the difference of two squaresFactoring the difference of two squares
Factoring the difference of two squares
 
Section 1.5 distributive property (algebra)
Section 1.5 distributive property (algebra)Section 1.5 distributive property (algebra)
Section 1.5 distributive property (algebra)
 
Algebra 7 Point 6
Algebra 7 Point 6Algebra 7 Point 6
Algebra 7 Point 6
 
5.3 Solving Quadratics by Finding Square Roots
5.3 Solving Quadratics by Finding Square Roots5.3 Solving Quadratics by Finding Square Roots
5.3 Solving Quadratics by Finding Square Roots
 
common monomial factor
 common monomial factor common monomial factor
common monomial factor
 
Factoring Perfect Square Trinomial
Factoring Perfect Square TrinomialFactoring Perfect Square Trinomial
Factoring Perfect Square Trinomial
 
Lecture 10
Lecture 10Lecture 10
Lecture 10
 
Factoring difference of squares
Factoring difference of squaresFactoring difference of squares
Factoring difference of squares
 
Polynomials Test Answers
Polynomials Test AnswersPolynomials Test Answers
Polynomials Test Answers
 
Markov number
Markov numberMarkov number
Markov number
 
Project in Mathematics. Functions
Project in Mathematics. FunctionsProject in Mathematics. Functions
Project in Mathematics. Functions
 
Determinants
DeterminantsDeterminants
Determinants
 
Distributive property
Distributive propertyDistributive property
Distributive property
 

More from Math Academy Singapore

Sec 3 A Maths Notes Indices
Sec 3 A Maths Notes IndicesSec 3 A Maths Notes Indices
Sec 3 A Maths Notes Indices
Math Academy Singapore
 
JC Vectors summary
JC Vectors summaryJC Vectors summary
JC Vectors summary
Math Academy Singapore
 
Functions JC H2 Maths
Functions JC H2 MathsFunctions JC H2 Maths
Functions JC H2 Maths
Math Academy Singapore
 
Vectors2
Vectors2Vectors2
Complex Numbers 1 - Math Academy - JC H2 maths A levels
Complex Numbers 1 - Math Academy - JC H2 maths A levelsComplex Numbers 1 - Math Academy - JC H2 maths A levels
Complex Numbers 1 - Math Academy - JC H2 maths A levels
Math Academy Singapore
 
Recurrence
RecurrenceRecurrence
Functions 1 - Math Academy - JC H2 maths A levels
Functions 1 - Math Academy - JC H2 maths A levelsFunctions 1 - Math Academy - JC H2 maths A levels
Functions 1 - Math Academy - JC H2 maths A levels
Math Academy Singapore
 
Probability 2 - Math Academy - JC H2 maths A levels
Probability 2 - Math Academy - JC H2 maths A levelsProbability 2 - Math Academy - JC H2 maths A levels
Probability 2 - Math Academy - JC H2 maths A levels
Math Academy Singapore
 
Probability 1 - Math Academy - JC H2 maths A levels
Probability 1 - Math Academy - JC H2 maths A levelsProbability 1 - Math Academy - JC H2 maths A levels
Probability 1 - Math Academy - JC H2 maths A levels
Math Academy Singapore
 

More from Math Academy Singapore (9)

Sec 3 A Maths Notes Indices
Sec 3 A Maths Notes IndicesSec 3 A Maths Notes Indices
Sec 3 A Maths Notes Indices
 
JC Vectors summary
JC Vectors summaryJC Vectors summary
JC Vectors summary
 
Functions JC H2 Maths
Functions JC H2 MathsFunctions JC H2 Maths
Functions JC H2 Maths
 
Vectors2
Vectors2Vectors2
Vectors2
 
Complex Numbers 1 - Math Academy - JC H2 maths A levels
Complex Numbers 1 - Math Academy - JC H2 maths A levelsComplex Numbers 1 - Math Academy - JC H2 maths A levels
Complex Numbers 1 - Math Academy - JC H2 maths A levels
 
Recurrence
RecurrenceRecurrence
Recurrence
 
Functions 1 - Math Academy - JC H2 maths A levels
Functions 1 - Math Academy - JC H2 maths A levelsFunctions 1 - Math Academy - JC H2 maths A levels
Functions 1 - Math Academy - JC H2 maths A levels
 
Probability 2 - Math Academy - JC H2 maths A levels
Probability 2 - Math Academy - JC H2 maths A levelsProbability 2 - Math Academy - JC H2 maths A levels
Probability 2 - Math Academy - JC H2 maths A levels
 
Probability 1 - Math Academy - JC H2 maths A levels
Probability 1 - Math Academy - JC H2 maths A levelsProbability 1 - Math Academy - JC H2 maths A levels
Probability 1 - Math Academy - JC H2 maths A levels
 

Recently uploaded

Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityNatural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Akanksha trivedi rama nursing college kanpur.
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
GeorgeMilliken2
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
Jyoti Chand
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
Priyankaranawat4
 
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
สมใจ จันสุกสี
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
TechSoup
 
The History of Stoke Newington Street Names
The History of Stoke Newington Street NamesThe History of Stoke Newington Street Names
The History of Stoke Newington Street Names
History of Stoke Newington
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
Dr. Mulla Adam Ali
 
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingYour Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Excellence Foundation for South Sudan
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Celine George
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Himanshu Rai
 
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
Academy of Science of South Africa
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
Celine George
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
Dr. Shivangi Singh Parihar
 
A Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdfA Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdf
Jean Carlos Nunes Paixão
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
AyyanKhan40
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Nicholas Montgomery
 
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
Nguyen Thanh Tu Collection
 

Recently uploaded (20)

Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityNatural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
 
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
 
The History of Stoke Newington Street Names
The History of Stoke Newington Street NamesThe History of Stoke Newington Street Names
The History of Stoke Newington Street Names
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
 
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingYour Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
 
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
 
A Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdfA Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdf
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
 
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
 

Sec 2 Maths Notes Change Subject

  • 1. 4048 2EM Algebra – Change Subject (1) Math Academy® All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, or stored in any retrieval system of any nature without prior permission. Math Academy® 1 Knowing is not enough; we must apply. Willing is not enough; we must do. Johann Wolfgang von Goethe Notes: Changing Subject of a Formula Example 1: Make the letter in the brackets the subject of the given formula. Example 2: Example 3: (3 ) 2 w x y c+ = ( )x z yx m = - ( )y 1x y m z - = m x y z - = m x y z - = 2 a b c x = + ( )x 2 1 a b c x + = 2 1x a b c = + 2 a x b c = + 2( ) a x b c = + Common mistake m m z x y - = FLIP EACH side Multiply on both sidesm ALONEy LHS and RHS one term each FLIP EACH side (not flip individually) Multiply on both sidesa Common mistake 1 1 2 x a b c = + LHS: ALONEx Technique: Flip
  • 2. 4048 2EM Algebra – Change Subject (1) Math Academy® All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, or stored in any retrieval system of any nature without prior permission. Math Academy® 2 Example 4: Example 5: Example 6: 3 2x y k k y - = ( )x 2 R r T r + = - ( )r 1 11 =+ ba ( )b 1 1 1 b a = - 1 1a b a a = - 1 1a b a - = 1 1 b a a = - 1 a b a = - appears oncex Do not Cross-multiply appears twicer Cross-multiply Group terms with r Cross- Multiply Factorise r Make the term containing on one side.b Make Same Denominator Flip Do not make same denominator at this stage (else appear everywhere --- Tedious !!) b