Which one is the algebraic ?

Key Words 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 = 2s8 x y = 8y

A. Identifying an Algebraic Term

Term Coefficient Variable

p 1 p

-8a -8 a

½ y ½ y

2k/3 2/3 k

-5n/7 -5/7 n

Algebraic ExpressionA 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 TermLike 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 Termsex. –x, 1/3 p, 4hSo, 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 subtractedex.10y + 3x + 8y = 10y + 8y + 3x

= 18y + 3x10y + 3x = 3x + 10y

Group the like terms

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

MULTIPLICATIONSIMPLIFY

Simplify a x 2 = 2 x a = 2a

p x 1 = 1 x p = p, a x b = b x a =ab

Simplifya. 12 x a e. -3 x (-4) x 5pb. -7 x a f. 8 x (-4p) x 3qc. k x 5 g. -2y x (-4x) x 6d. h x (-1) h. -7a x (-3b) x (-2a)

EXPANDING

•EXPANDING

ab + ac = a(b+c) = (b+c)aORa(b+c) =ab - ac = a(b-c) = (b-c)aORa(b-c) =

DISTRIBUTIVE LAW

ab ac+

ab ac-

DIVISIONDefinition of Division

ex , 2 : 3 = 2 x 1/3 3 : y = 3 x 1/y

So, DIVISION = INVERSE OF MULTIPLICATION

FACTOR OF TERMS

DivisionObserve the same factor

1. 2a : a = 2 2. 6xy : 2y = 3x

Simplify1.12ab : 4a2. x3 : x3.6x5y2 : 2x2y4.8x4y2z : 2xy2

DIVISION

= 3x

= 4m

= -7x

= 1/3(x)

= 1/3m

= 1/3(ab)

= 3m

= 4m

= 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

Describea. (2a)2

b. (-3a)2

c. -(2ab)3

d. -3(-2a2)3

MATHEMATICAL EXPRESSIONNumerical expressionVerbal ExpressionAlgebraic expressionExample: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 expressionCost for the Keene family = 3g + 2k Cost for the Norman family = 5g + 4kOffer = - gTotal 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 = 3gCost for 2 adults = 2kTotal 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 phrases1. Four more than s2. The product of 7 and c3. Nine less than x4. A number divided by the sum of 4 and 7.5. Twice the sum of a number plus 4.6. The sum of ¾ of a number and 7.7. Ten times a number increased by 150.

Write an algebraic phrase for these situations1. 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

AnswersThe 2nd tier cake is p cm wide and q - 5 cm long:So the formula for the length of ribbon isp + q - 5 + p + q - 5 + 1Simplifying 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 b. p + 2r = 2 + 2(6) c. 3p2 – 2r = 3(2)2 - 2(6)

= 5 = 14 = 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 + 7And 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 + 7When g = 14 , g + 7 = 14 + 7 = 21So 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?

AnswersThe formula for working out the time in Santiago, Chile is g - 4

When g = 20, The g - 4 = 16So if you worked out that at 20.00 hours in London, the time in Santiago is 16.00 hours

Terms in brackets

Worked exampleHere 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 exampleThis is the formula to find the area of a trapezium: (a + b) h /2Find the area of this trapezium: