Download 1-2 Simplifying Expressions.

Working with
Expressions
Expressions
 A group of symbols used to represent a
number (no ‘=’ sign) e.g.
3x  3 y
SLO
To understand how to use BEDMAS
BEDMAS Revision
1st
Last
(
(
Brackets
Exponents
Division
Multiplication
Addition
Subtraction
)
1st
)
Last
Note 1: This is not a strict order, hence blue brackets
Note 2: Fractions have ‘invisible’ brackets
Using BEDMAS E.g. 1
2+4x5
Multiplication first, addition second
2 + 20
22
Using BEDMAS E.g. 2
( 2 x 4 – 5) + 7
Inside brackets first
Inside the bracket do multiplication first
8–5=3
Put number back into brackets
(3) + 7 = 10
Using BEDMAS E.g. 3
5x6÷2
Multiplication and Division have equal
importance so use Left to Right Rule
30 ÷ 2
15
Using BEDMAS E.g. 4

(
(
)
)
Insert ‘invisible’ brackets
Apply BEDMAS to numerator and denominator separately
Your Turn: Calculate

27
10
23
5
55
15
3
Algebra Revision
SLO
To understand what 7c means
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note book
Understanding what 7c means
A number next to a letter or two letters next
to each other means to multiply.
E.g.
5a
= 5xa
ab
= axb
5 x C + 7 = 5C + 7
Your turn: write the following in another way
7 x c = 7c
8 x d + 6 = 8d + 6
g x h – 5 = gh – 5
SLO

Copy into note book
a
Understanding what means
b
a
Means:
a
divided
by
b
b
E.g.
1 means 1 ÷ 2 = 0.5
2
5
means 5 ÷ a
a
W means W ÷ V
V
Your turn:
Write the following in another way
10 means 10 ÷ 5 = 2
5
R =R÷3
3
x =x÷y
y
SLO
To understand how to substitute numbers for
letters
Copy into
note book
Substitution
Substitution is putting numbers in
place of letters. Each time the value
of the letter might change.
E.g. If a = 5
10a = 10 x a
= 10 x 5
= 50
If b = 5 calculate 3b + 4:
3 x 5b + 4
15 + 4 = 19
Find the value of 2p – 5 when
P=6
2 x 6p – 5 =
12 – 5 = 7
If a = 3 and b = 4 find
ab + 8a
Using the multiplication rule expression
becomes:
3a x 4b + 8 x 3a
Replace letters with numbers
12 + 24 = 36
If a = 3 and b = 4 find
a(5 + 2b)
Using the multiplication rule the expression
becomes:
3a x ( 5 + 2 x b
4)
Replace letters with numbers
Apply BEDMAS and ‘do’ inside brackets first
3 x (5 + 8)
3 x 13 = 39
SLO
To understand how exponents work
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note book
Exponents
exponent – the number of times a number is
multiplied by itself.
base – the number that is being multiplied.
3
base
8
exponent
index form
This is read “8 to the 3rd power” or “8 cubed.” or “8 to the
power of 3”
Copy into
note book
Exponents
5
1
2
3
4
5
2 =2x2x2x2x2
3
6 =6x6x6
3
A =AxAxA
3 2
G H =GxGxGxHxH
Video exponent to expanded form:
http://www.virtualnerd.com/pre-algebra/factors-fractionsexponents/exponential-to-expanded-form-conversion.php?&sid=
Your Turn:

4
R
FxFxSxSxS
AxAxAxPxPxPxP
SLO
To understand how to use exponents and
numbers at the same time
Copy into
note book
Exponents with Numbers and Letters

Exponents with Numbers and Letters
E.g. 3) 7T x 5Y = 35TY
E.g. 4) 4F x 6F x 10
= 4 x F x 6 x F x 10
= 4 x 6 x 10 x F x F
= 240 x F
2
= 240F
2
Your Turn:
 Write the following in index form
1) 4 x F x 3 x F
2) 5 x H x H x 6
 Simplify (put in index form) the following
1) 6H x 2H
2) 4P x 5P x P
SLO
To understand how to use exponents in
substitution
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note book
Substitution with Exponents

10
P
P
10
Swap letters for numbers
Find the answer
10 x 10 = 100

10
P
10
P
Swap letters for numbers
Find the answer (remember BEDMAS)
10 x 10 + 22 = 122

Swap letters for numbers
P
10
BEDMAS states to do inside the bracket first
10 – 7 = 3

10
P
10
P
Swap letters for numbers
Find the answer
4 x 10 x 10 = 400
Substitution with exponents video: http://www.youtube.com/watch?v=S0JHbW3GfdY
Your Turn

= 25
= 35
=9
= 100
SLO
To understand how to multiply exponents and
numbers
Copy into
note book
Simplifying Indices
(Multiplication)

Can you spot a quick
way to do this?
Simplifying Indices

Can you spot a quick
way to do this?
Copy into note book
Product of Powers Property

a a  aaaaa  a
2
3
23
a
Short video explaining product rule: http://www.youtube.com/watch?v=sbfjHOeBOC4
5
Tour Turn: Simplify
SLO
To understand how to divide exponents
Copy into note book
Simplifying Indices (Division)

Cross off pairs of Ds from top and bottom
Write out what you have left
Simplifying Indices (Division)
Quotient rule video explanation: http://www.youtube.com/watch?v=P7edpw6N_uc

Cross off pairs of Ds from the top and bottom
Write out in index form what you have left
Simplifying Indices (Division)

Simplifying Indices (Division)

14 ÷ 7 = 2
21 ÷ 7 = 3
Cross off pairs of Ds from top and bottom
Simplify the number part of the fraction as usual
Write out what you have left
Your Turn: Simplify

2T
Thanks
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