Transcript Equations - Mathsrevision.com

Algebra
General
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Tidying up terms
Multiplying terms
Multiplying out Brackets
Solving Simple Equations
Solving Harder Equations
Solving Equations with Brackets
Two sided equations
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Starter Questions
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General
2
66 % of £270
3
Q1.
Calculate
Q2.
Convert 60% to fraction and simplify.
Q3.
Convert
Q4.
What is the time difference 09:28 and 10:50
Q5.
The answer to the question is 90. What is the
question.
30-Apr-20
4
5
to a percentage.
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Aim of the Lesson
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General
Tidying Terms
a+2b+3a+b
1. Tidying up expressions.
2. Show steps when tidying up.
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Tidying Terms
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General
First Row :
2c
c
2d
+
+
+
=
4c = 7c
+
+
2nd Row :
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+
+
2d
+
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=
3d
= 7d
Tidying Terms
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General
+
3rd Row :
3f
+
f
+
=
+
2f = 6f
In Total we have
7c + 7d + 6f
CANNOT
TIDY UP
ANYMORE
WE CAN ONLY TIDY UP “LIKE TERMS”
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Tidying Terms
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General
WE CAN ONLY TIDY UP “LIKE TERMS”
Tidy up the following:
Q1.
6x + 2y
2x + 4x + 5y - 3y
9a + 2b
Q2. 4a + 3b + 5a - b
Q3. 10f + 15g + 5f + g
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15f + 16g
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Tidying Terms
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General
Chapter 7
Page 85
Ex 1
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Q1 and Q2
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Starter Questions
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General
Q1.
Tidy up the expression 2y+3x+4x+10
2
of 84
3
Q2.
Calculate
Q3.
Round to 1 decimal place.
(a)
Q4.
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2.34 (b)
10.25 (c)
Write 4 x 4 in terms of powers
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3.23
Multiplying Terms
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General
Learning Intention
1. To explain how to multiply
terms.
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Success Criteria
1. Understand process of
multiplying terms.
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Multiplying Terms
General
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Find the area of each square in terms of powers
2 x 8 = 16
3 x 4 = 12
8
2
6
3
2 x y =2y
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6 x 5 = 30 5
4
2
y
7 x b = 7b
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7
b
Bracket Equations
Solve the following equations:
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Examples
(1)
2xw
= 2w
(2)
4 x 2y
= 8y
(3)
3a x 3b
= 9ab
(4)
5h x 5g
= 25gh
(5)
9e x 4m
= 36em
(6)
8p
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x
a
Always put letters in
alphabetical order !
= 8ap
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Multiplying Terms
General
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Find the area of each square in terms of powers
32
52
3
3
5
y2
y
y
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82
5
8
b2
b
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b
8
Bracket Equations
Solve the following equations:
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(a)
2xd
(d)
= 2d
(b)
3 x 2y
= d2
(e)
= 6y
(c)
5a x 4b
6e x 3e
= 18e2
(f)
2p x 3p x 4p
= 24p3
= 20ab
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dxd
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Multiplying Terms
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General
Your turn !
Chapter 7
Page 86 Exercise 2
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Starter Questions
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General
1. Tidy up a - 4a -13d +11a + a -3d
2. 70 % of 150
3. Find two numbers that add
to give 15 and divide to give 2.
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Removing brackets (1)
3(b + 5) = 3b
This means 3 times b
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Removing brackets (1)
3(b + 5) = 3b + 15
This means 3 times 5
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Removing brackets (2)
5(8 - f) = 40
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Removing brackets (2)
5(8 - f) = 40 - 5f
Tip: Draw lines to keep you right.
5(8 – f) = 40 - 5f
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Removing brackets (3)
4(3b + 2) =12b
4 x 3b = 4 x 3 x b = 12 x b = 12b
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Removing brackets (3)
4(3b + 2) =12b + 8
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Removing brackets (4)
3(7a – 2b) = 21a
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Removing brackets (4)
3(7a – 2b) = 21a - 6b
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Removing brackets (5)
c(3c + b) = 3c²
c x 3c = 3c x c = 3c²
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Removing brackets (5)
c(3c + b) = 3c² + bc
Tip: Remember to draw lines to keep you right.
c(3c + b) = 3c² + bc
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Removing brackets (6)
6(5e + 3f - 2) = 30e
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Removing brackets (6)
6(5e + 3f - 2) = 30e + 18f
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Removing brackets (6)
6(5e + 3f - 2) = 30e + 18f - 12
Careful!
Tip: Remember to draw lines to keep you right.
6(5e + 3f -2) = 30e + 18f - 12
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Simplifying (1)
4(3a + 5) - 8 = 12a
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Simplifying (1)
\
4(3a + 5) - 8 = 12a + 20 - 8
This is not inside
the brackets
So don’t multiply!
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Simplifying (1)
4(3a + 5) - 8 = 12a + 20 - 8
This can be tidied up
= 12a + 12
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Simplifying (2)
3b + 2(5b – 6) = 3b + 10b
This is not inside
the brackets
So don’t multiply!
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Simplifying (2)
3b + 2(5b – 6) = 3b + 10b - 12
Careful!
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Simplifying (2)
3b + 2(5b – 6) = 3b + 10b - 12
This can be tidied up
= 13b - 12
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Structured Diagrams
Now try Exercise 3
Ch7 (page 86)
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Starter Questions
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General
1. Simplify 3x + x -6 + x + x -3
2. A scale model of a train is 1cm : 5m.
The height of the model train is 10cm.
What is the real height of the train.
3. 80 % of 350
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Equations
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General
Solving Equations
Learning Intention
1. To solve simple equations
using the rule
‘change side change sign’.
Success Criteria
1. Know rule
‘change side change sign’.
2. Solving simple algebraic
equations.
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Equations
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General
Solving Equations
The rule we use to solve equations is
The rule “change side change sign”
Write down the opposite of the following :
+
x opposite is ÷
opposite is
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- opposite is +
opposite is x
÷
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Equations
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General
Solving Equations
The rule “change side change sign”
Examples
-5
opposite
is +5
x  5  11
 x  11  5
 x  16
Check to see if correct !
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+8
opposite
is -8
x8 8
 x  88
x0
Check to see if correct !
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Equations
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General
Solving Equations
The rule “change side change sign”
Examples
3 y  18
18
y
3
 y6
times by 3
opposite
is divide
by 3
Check to see if correct !
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times by 8
opposite
is divide
by 8
8m  72
72
m
8
m9
Check to see if correct !
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Equations
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General
Solving Equations
Now try Exercise 4
Ch8 (page 87)
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Starter Questions
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General
1. Simplify 5 y  6 x  7 x  3 x  3 xy
2. The ratio of apples to pears is 4 : 5.
If there are 72 pieces of fruit in total.
How many apples are there.
3.
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Find HCF of 15 and 21
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Equations
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General
Solving Equations
Learning Intention
1. To solve harder equations
using the rule
‘change side change sign’.
repeatedly.
Success Criteria
1. Know rule
‘change side change sign’.
2. Solving harder algebraic
equations by using rule
repeatedly.
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Created by Mr.Lafferty Maths Dept
Equations
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General
Solving Equations
The rule we use to solve equations is
The rule “change side change sign”
Write down the opposite of the following :
+
x opposite is ÷
opposite is
30-Apr-20
- opposite is +
opposite is x
÷
Created by Mr.Lafferty Maths Dept
Equations
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General
Solving Equations
The rule “change side change sign”
Examples
+1
opposite
is -1
2 x  1  11
times by 2
 2 x  11  1  10
opposite
is divide
 2 x  10
by 2
10
 x   5 Check to see if correct !
2
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Equations
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General
Solving Equations
The rule “change side change sign”
Examples
-6
opposite
is +6
4 x  6  30
times by 4
 4 x  30  6  36
opposite
is divide
 4 x  36
by 4
36
x
 9 Check to see if correct !
4
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Equations
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General
Solving Equations
Now try Exercise 5
Ch7 (page 88)
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Starter Questions
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General
1. I have an infinite amount of line symmetry.
What is my shape?
2. Calculate
3
1
of
4
8
3. Remove brackets 4(5k - 8)
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Bracket Equations
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General
Equations with Brackets
Learning Intention
1. To show how to solve
equations with brackets .
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Success Criteria
1. Multiply out brackets.
2. Apply ‘change side change
sign’ rule.
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Bracket Equations
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General
Equations with Brackets
Multiply out the brackets first
and then
Apply ‘change side change sign’ rule
Example
2(2 x  3)  18
 4 x  6  18
 x  12  4  3
 4 x  12
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Bracket Equations
General
Equations with Brackets
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Example
5(3x  2)  20
 15 x  10  20
 15 x  20  10
 15 x  30
 x  30  15  2
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Equations
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General
Bracket Equations
Now try Exercise 6
Ch7 (page 89)
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Starter Questions
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General
1. Simplify 7 a  4a  9b  11b  ab  3
2. The ratio of apples to pears is 6 : 7.
If there are 52 pieces of fruit in total.
How many apples are there.
3.
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Find LCM of 4 qand 7
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Equations
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General
Two sided equation
Learning Intention
1. To explain how to solve
two sided equations using
knowledge we already have
Success Criteria
1. Know the rule
change side change sign
2. Solving two sided equations
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Both Sides Equations
4m + 8 = 3m + 12
4m - 3m
=
m
=
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12 - 8
4
(1) letters to one side
(2) Solve as normal
Check correct answer !
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Both Sides Equations
7h - 9 = 4h + 7
7h – 3h
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(1) letters to one side
=
7+9
(2) Solve as normal
4h
=
16
h
=
h
=
16 ÷ 4
Check correct answer !
4
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Both Sides Equations
Solve the following equations:
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(a)
3x - 5 = 2x + 1
x=6
(b)
12x - 4 = 4x + 12
x=2
(c)
5x + 6 = 3x + 20
x=7
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Equations
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General
Two sided equation
Now try Exercise 7
Ch7 (page 89)
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