Transcript Algebraic Expression

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Which one is the algebraic ?
Key Words
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Algebraic Expression : Bentuk Aljabar
Unknown : Tidak diketahui
Term : Suku
Like term : suku sejenis
Unlike term : suku tidak sejenis
Variable : Variabel
Coefficient : Bilangan Pengali
Exponent : bilangan pangkat dari variable
Constant : bilangan yg berdiri sendiri
Simplify : Sederhanakan
 What do you do when you want to refer a number
but you do not know?
Suppose you wanted to refer the number of shops
in your town, but haven't counted them yet.
May be “You say 'blank' number of shops, or
perhaps ' ? ' number of shops.
 In mathematics a letter is often used to represent
the number of shops that unknown - so you could
say ' x ' number of shops, or ' q ' number of shops.
 In the lesson we will take for using letters to
represent numbers.
Terms
 Term is a letter on its own or multiplied by a
number.
example :
r is a term and 2s is a term.
 When we write algebraic terms we leave the
multiplication signs out.
2 x s = 2s
8 x y = 8y
A. Identifying an Algebraic Term
Term
p
-8a
½y
Coefficient Variable
1
p
-8
a
½
y
2k/3
2/3
k
-5n/7
-5/7
n
Algebraic Expression
 A sign of numbers and letters joined together by
mathematical operations, such as + and -, is called an
Algebraic Expression (forms) .
Ex : r + 2s is an algebraic expression
How many term does it have ?
 3a + y consists of 2 terms( 3a and y)
 3a + p - 4a Consist of 3 terms(3a, p, -4a)
 7x – 2a + b
consists of 3 terms(7x, -2a, b)
B. Identifying Like term and Unlike Term
 Like Terms
ex. 1. 7y, -6y, 1/3 y
2. x2, -3x2
3.
4.
Thus, Like Terms are terms that have same variable
and same exponent of variable
 Unlike Terms
ex. –x, 1/3 p, 4h
So, Unlike Terms are terms that have different
variables
Simplifying Algebraic forms
(Addition and Subtraction)
In algebra, when like terms are added and subtracted it
is called simplifying.
Only like terms can be added or subtracted
Group the like terms
ex.
10y + 3x + 8y = 10y + 8y + 3x
= 18y + 3x
10y + 3x = 3x + 10y
How to simplify the algebraic expressions
Question:
Simplify ; 4x + y - 2x + 6y.
Answers
4x + y - 2x + 6y = 4x - 2x + y + 6y
= 2x + 7y
EXERCISE
MULTIPLICATION
SIMPLIFY
EXPANDING
MULTIPLICATION
SIMPLIFY
EXPANDING
Simplify
 a x 2 = 2 x a = 2a
p x 1 = 1 x p = p,
a x b = b x a =ab
Simplify
a. 12 x a
e. -3 x (-4) x 5p
b. -7 x a
f. 8 x (-4p) x 3q
c. k x 5
g. -2y x (-4x) x 6
d. h x (-1)
h. -7a x (-3b) x (-2a)
DISTRIBUTIVE LAW
•EXPANDING
 ab + ac = a(b+c) = (b+c)a
OR
a(b+c) =
ab +
ac
 ab - ac = a(b-c) = (b-c)a
OR
a(b-c) =
ab
-
ac
DIVISION
 Definition of Division
ex , 2 : 3 = 2 x 1/3
3 : y = 3 x 1/y
So, DIVISION = INVERSE OF MULTIPLICATION
 FACTOR OF TERMS
Division
Observe the same factor
1. 2a : a = 2
2. 6xy : 2y = 3x
Simplify
1.12ab : 4a
2. x3 : x
3.6x5y2 : 2x2y
4.8x4y2z : 2xy2
DIVISION
…..
= 3x
= 4m
= 4m
= 3m
= -7x
= 1/3(x)
= 1/3m
= 1/3(ab)
= 3m
…..
…..
= 2/9m
= 1/2a
= 3m
Exponents/Powering

b2 = b x b
(-b)2 = (-b) x (-b)
-(b)2 = - (b x b)
(2b)2 = 2b x 2b
Describe
a. (2a)2
b. (-3a)2
c. -(2ab)3
d. -3(-2a2)3
MATHEMATICAL EXPRESSION
 Numerical expression
 Verbal Expression
 Algebraic expression
Example:
 Verbal expression
The Keene family and the Norman family visit the zoo together.
Because there is more than 10 people they get a special offer : 1 child
goes free.
 Algebraic expression
Cost for the Keene family = 3g + 2k
Cost for the Norman family = 5g + 4k
Offer = - g
Total cost = 3g + 2k + 5g + 4k - g
= 3g + 5g - g + 2k + 4k
= 7g + 6k
Worked example:
g is the cost of child admission and k is the cost of
adult admission to the zoo.
What is the cost for the Keene family of 3 children and
2 adults to visit the zoo?
Solution:
Cost for 3 children = 3g
Cost for 2 adults = 2k
Total cost = 3g + 2k
Sample question:
Write an algebraic forms for the cost for the Norman
family, 5 children and 4 adults, visiting the zoo.
Answers
5g + 4k
WHEN DO WE NEED ALGEBRAIC EXPRESSION
WHEN DO WE NEED ALGEBRAIC EXPRESSIONS
Write algebraic expressions for these word
phrases
1.
2.
3.
4.
5.
6.
7.
Four more than s
The product of 7 and c
Nine less than x
A number divided by the sum of 4 and 7.
Twice the sum of a number plus 4.
The sum of ¾ of a number and 7.
Ten times a number increased by 150.
Write an algebraic phrase for these
situations
1. A car was traveling 35 miles per hour
for a number of hours.
2. Bob ran 7 times a week for a number
of weeks.
3. The plumber added an extra $35 to
her bill.
4. Thirty-five fewer people came than
the number expected.
Simple formulae
A formula is another word for an expression, usually
used when an expression represents a problem in real
life. Formulae (plural of formula) are useful when the
numbers represented by letters in the expression
change according to different situations.
 Worked example:
The size of a rectangular wedding cake changes
according to the tier it sits on. The 1st tier is the
largest cake and is p cm wide and q cm long:
 The length of ribbon to decorate the outside of the
cake is given by a formula that is the perimeter of
the cake plus 1cm, so that the ribbon can overlap.
 So the formula for the length of ribbon is:
p + q + p + q + 1 = 2p + 2q + 1 or 2(p + q) + 1
Sample question:
Write a formula for the length of ribbon for the
cake on the 2nd tier, if the 2nd tier cake has the
same width as the 1st tier but a length that is 5cm
shorter than the 1st tier cake. Now check your
answer
Answers
The 2nd tier cake is p cm wide and q - 5 cm long:
So the formula for the length of ribbon is
p+q-5+p+q-5+1
Simplifying the expression:
p + p + q + q - 5 - 5 + 1 = 2p + 2q - 9 or 2(p + q) - 9
Using formula
While using formulae is usually learnt as part of
algebra, you'll be surprised at how often it creeps into
other areas of mathematics and even other areas of life!
You might use a formula to convert an imperial
measurement to a metric measurement, or to find the
area of a shape, or to calculate a bill.
Substitution
When letters in a formula are replaced by numbers, it
is called substitution
Example
If p = 2, q= 3, and r = 6. Find the results of
a. p + q
b. p + 2r
c. 3p2 – 2r
Answer
a. p + q = 2 + 3
=5
b. p + 2r = 2 + 2(6)
= 14
c. 3p2 – 2r = 3(2)2 - 2(6)
= 12 -12
=0
 Here's an example. For the purpose of time, the Earth's
surface is divided into 24 equal wedges of 15 o, each called
time zones. We work out times around the world beginning
at Greenwich, London; and as we pass over each wedge to
the east we add 1 hour to London time and as we pass over
each wedge to the west we subtract 1 hour from London
time.
 Let's call the time in London g.
Then the formula for working out the time in Bangkok,
Thailand, is: g + 7
And the formula for working out the time in Santiago,
Chile, is: g - 4
 These formulae allow us to substitute g for any time in
London to find out the time in Bangkok or Santiago.
Worked example:
Using the formula above, find the time in Bangkok
when it is 14.00 hours in London.
Solution:
Substitute the 14 for the g in the formula g + 7
When g = 14 , g + 7 = 14 + 7 = 21
So at 14.00 hours in London, the time in Bangkok is
21.00 hours.
Sample question:
What time is it in Santiago, Chile, when the time in
London is 20.00 hours?
Answers
The formula for working out the time in Santiago,
Chile is g - 4
When g = 20, The g - 4 = 16
So if you worked out that at 20.00 hours in London,
the time in Santiago is 16.00 hours
Terms in brackets
 Worked example
Here is the formula to convert the temperature in
oF to the temperature in oC:

where f represents the temperature in oF.
If you want to find the temperature in oC when it is
68 oF, then substitute 68 for the f in the formula:
 if f = 68
so,
=
= 200
Worked example
This is the formula to
find the area of a
trapezium: (a + b) h /2
Find the area of this
trapezium: