Upload
katherine-phelps
View
223
Download
0
Tags:
Embed Size (px)
Citation preview
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Simplifying Algebraic Expressions
Removing Brackets
AlgebraAlgebraw
ww
.math
srevis
ion
.com
Removing Brackets & Simplifying
Evaluating Expressions
Factorising – The common factor
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
ww
.math
srevis
ion
.com
1. A TV has been reduced in the sale
by 20%. I t was £250. How much is it now.
3. 30% of £300
4. Tidy up the expression
5y + 3d +4d + 10y
5. Find the area and
2. Simplif y the ratio 16:64
perimeter of the shape.6cm
2cm
2cm
3cm
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To remember the To remember the phrase phrase
‘ ‘ like terms.’like terms.’
1. To review tidying up expressions.
AlgebraAlgebraSimplifying Algebraic Expressions
2.2. To be able to simplify To be able to simplify simple algebraic simple algebraic expressions by collecting ‘ expressions by collecting ‘ like terms.’like terms.’
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraSimplifying Algebraic Expressions
Reminder !We can only add and subtract “ like terms “
x x x x 4x9 7p p 2p
10 6 1w 3 6a b a b
2 2 2x x x
2 7a b9 6w
23x
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraSimplifying Algebraic Expressions
Reminder !Multiplying terms
7 a 7a5w 5w
2 4m m b b 2b
28m
( NOT 2b )
( NOT 8m )
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraSimplifying Algebraic Expressions
y 2
y
2
Question : Find the area of each of the 3 sections of this shape. What is the total area.
1 2A y 2A y y
3 2A y
2y
2y
2y
2 2 2TA y y y 2 4y y
1 2 3
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 1Ch11 (page 46)
ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraSimplifying Algebraic Expressions
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
ww
.math
srevis
ion
.com
1. Find the perimeter and area of the shape.
3. Find all the missing angles.
2. Calculate (a) (-3m) x (-4m) (b) (2b) x (3a)
6h
2a
100o
60o
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Understand the key steps Understand the key steps in removing brackets.in removing brackets.
1. To explain how to multiply out simply algebraic brackets.
AlgebraAlgebra
2.2. Apply multiplication Apply multiplication rules rules for integers numbers for integers numbers when when removing brackets.removing brackets.
Removing brackets
3(b + 5) =3b + 15
Example 1
4(w - 2) =4w - 8
Example 2
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
2(y - 1) =2y - 2
Example 3
7(w - 6) =7w- 42
Example 4
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
8(x + 3) =8x+ 24
Example 5
4(3 -2m) = 12 - 8m
Example 6
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
Example 7 : Write down an expressionfor the amount indicate belowin two difference ways.
3(x + 3) =3x + 9
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
x+3
x+3
x+3
Example 8 : Write down an expressionfor the amount indicate belowin two difference ways.
5(y - 2) = 5y - 10
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
y-2
y-2 y-2
y-2y-2
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebra
Y + 5
4
Question : Find the area of the rectangle (i) With brackets(ii) Without brackets.
(i) 4( 5)A y
(ii) 4( 5)A y 4 20y
Removing brackets
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 2Ch11 (page 48)
ww
w.m
ath
srevis
ion
.com
AlgebraAlgebra Removing brackets
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
ww
.math
srevis
ion
.com
1. My shape has 2 pairs of parallel lines
and equal angles and lengths.
What is my shape?
1 12. Calculate of
2 4
3. Remove brackets 4(5d - 6)
4. Calculate the area of the rectangle.
7cm
(x+2)cm
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. Explain how to remove brackets and simplify.
1. Understand how to remove brackets
AlgebraAlgebraRemoving Brackets & Simplifying
3. Tidy up after removing brackets.
2. Apply rules integer numbers.
a(b + 5) =ab + 5a
Example 1
p(w - 2) =pw - 2p
Example 2
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
y(y - 1) = y2 - y
Example 3
7w(w - 3) =7w2 - 21w
Example 4
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
a(a2 + 3b) =a3 + 3ab
Example 5
y2(3y -2c) =3y3 - 2cy2
Example 6
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
-(x + y) = -x - y
Example 7
-5(a - 7) =-5a + 35
Example 8
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
7 + 3(4 - y) =7 + 12
Example 9
9 - 3(8 - y) =9 - 24
Example 10
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
- 3y= 19 - 3y
Tidy Up
+ 3y
Tidy Up
= -15 + 3y
A = 10(x – 2)
Example 11
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
Find my Area (x - 2)
10
Find my Areax
12
A = 12x
A = L x B A = L x B
Example 12 : Find area of the orange border
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Removing aRemoving aSingle BracketSingle Bracket
(x - 2)10
x
12
Area =Big Rec – Small Rec
= 12x – 10(x - 2)
= 12x – 10x + 20
= 2x + 20
4(m - 3) - (m + 2) =4m - 12 - m - 2
Example 13
Example 14
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
= 3m - 14
Tidy Up
7(y - 1) - 2(y + 4) =7y - 7 - 2y - 8 = 5y - 15
Tidy Up
Removing Two Single Removing Two Single BracketsBrackets
3 x 14 – 8= 34
A = 4(y – 5)
Example 15 : Find an expression for the difference inthe areas.
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
(y - 5)
47 A = 7(y- 4)
(y- 4)Difference = 7(y - 4) - 4(y – 5)
= 7y - 28 - 4y + 20= 3y - 8
Calculate difference if
y = 14
Removing Two Single Removing Two Single BracketsBrackets
2 x 4 + 20=28
A = 7(x + 1)
Example 16 : Find an expression for the difference inthe areas.
Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
(x + 1)
79 A = 9(x + 3)
x + 3Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7
= 2x + 20
Calculate difference if
x = 4
Removing Two Single Removing Two Single BracketsBrackets
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebra
x
6
Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section.
6LA x 4( 3)SA x 4 12x
4x-3
6 (4 12)RA x x 2 12x
Removing Brackets & Simplifying
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 3Ch11 (page 50)
ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraRemoving Brackets & Simplifying
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
ww
.math
srevis
ion
.com
1. My shape has 2 pairs of parallel lines
equal lengths and opposite angles are equal.
What is my shape?
1 12. Calculate of
3 4
3. Remove brackets and simplif y 4e- (8e -12)
4. Calculate the perimeter of the rectangle.
7cm
(x+2)cm
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. To show how to evaluate an expression given values for the letters.
1. Be able to substitute numbers for letters in an expression.
AlgebraAlgebra
2. Use previous knowledge to evaluate expression.
Evaluating Expressions – number for letter
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraEvaluating Expressions – number for letter
Given the following information find the values of :-
a = 3 ; b = 4 and c = -1
BODMAS
5 a 5 3 15 2a c 2 3 ( 1)
22b
2 2b a (4 4) (3 3)
2 4 4
516 9 7
2 b b 32
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraEvaluating Expressions – number for letter
Given the following information find the values of :-
a = 3 ; b = 4 and c = -1
25c 5 ( 1) ( 1) 5 c c 5
22 3 30a b c
(2 3 3) (3 4) (30 ( 1)) (2 ) (3 ) (30 )a a b c
18 12 30 0
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 4Ch2 (page 51)
ww
w.m
ath
srevis
ion
.com
AlgebraAlgebraEvaluating Expressions – number for letter
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
ww
.math
srevis
ion
.com 1. My shape has 1 line of symmetry, 1 pair of equal
angles and adjcent lengths are equal.
What is my shape?
2. Find the highest common f actor f or
(a) 12 and 24 (b) 2x and 10x
3. Calculate 6a+ 5ab when a=(-1) b=(-2)
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. To show how to reverse the process of removing bracket ‘factorising’.
1. Be able to recognise the HCF for set of values.
AlgebraAlgebra
2. Understand the term factorising.
Factorising – The Common Factor
3. Factorise simple expressions.
19 Apr 202319 Apr 2023 Created by Mr. [email protected] by Mr. [email protected]
FactorisingFactorisingw
ww
.math
srevis
ion
.com
Example Factorise 3x + 15
1. Find the HCF for 3x and 15 3
2. HCF goes outside the bracket 3( )
3. To see what goes inside the bracketdivide each term by HCF
3x ÷ 3 = x 15 ÷ 3 = 5 3( x + 5 )
Check by multiplying out the bracket to get back to where
you started
S3 Credit
19 Apr 202319 Apr 2023 Created by Mr. [email protected] by Mr. [email protected]
FactorisingFactorisingw
ww
.math
srevis
ion
.com
Example
1. Find the HCF for 4x2 and 6xy 2x
2. HCF goes outside the bracket 2x( )
3. To see what goes inside the bracketdivide each term by HCF
4x2 ÷ 2x =2x 6xy ÷ 2x = 3y 2x( 2x- 3y )
Factorise 4x2 – 6xy
Check by multiplying out the bracket to get back to where
you started
S3 Credit
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebra
Simply find the HCF for a given set of data and write the data using brackets :-
Factorising – The Common Factor
6 12x
HCF ?6
6( )x 2
8 12a b
HCF ?4
4( )2a 3b
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
AlgebraAlgebra
Simply find the HCF for a given set of data and write the data using brackets :-
Factorising – The Common Factor
am an
HCF ?a
( )a m n
29 6x x
HCF ?3x
3 ( )x 3 2x
19 Apr 202319 Apr 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.comw
ww
.math
srevis
ion
.com
FactorisingFactorising
Factorise the following :
(a) 3x + 6
(b) 4xy – 2x
(c) 6a + 7a2
(d) y2 - y
3(x + 2)
2x(2y – 1)
a(6 + 7a)
y(y – 1)
Be careful !
S3 Credit