FOUR OPERATION LEARNING OBJECTIVE Algebra is an important branch of mathematics it is used in Physics, Chemistry, Biology, Economics and Statistics.

Presentation By

Mrs. Saira BanoDAHS Ph-VIIISubject: Math’s

ALGEBRAFOUR OPERATION

LEARNING OBJECTIVE Analysis By the end of the lesson students

will be able to analysis the basic concepts of four operations in algebra by making charts and solving question.

Evalution By the end of the lesson students will be able to compare the different method of solving of four operations and investigate the rules of four operations.

Creation By the end of the lesson students will be able to improve their knowledge about four operations in Algebra and They prepare their project.

Topic21st

Century Approache

s

Techniques/

Modes

21st century skills

Algebra(Four

Operation)

Giving direction ,liste

ning and speaking

skills.

Investigation plan and

charts.

Formulation system thinking, Self Direction and solution.

INSTRUCTIONAL STRATEGIES

ALGEBRA

Algebra is an important branch of mathematics it is used in Physics, Chemistry, Biology, Economics and Statistics these days. The Muslim mathematician did the spade work on this branch.

Muslim mathematician “Muhammad Bin Musa Al- Khowarizimi” was one of the greatest mathematician who made this branch prominent.

He wrote a book on algebra ‘Al Jabar-wa-Al-Muqabalatah’. The word algebra has been taken from the title of his book. ‘Al Jabar’. In the arithmetic we deal with specific numbers…., -2-1,0,1.2…., while

in algebra we deal with number as well as letters of the alphabet a,b,c,…..,x,y,z…. Where alphabets represent unspecified numbers. The same basic operations of arithmetic +, - , x ,÷ are also used in algebra.

A statement connecting variables and constants by operation of addition, subtraction, multiplication, division etc, is called an algebraic expression

ALGEBRAIC EXPRESSION

Types of Algebraic Expression

a) Involving only one term“monomial”

e.g., (i) 2ab(ii) 4x²

b) Involving two or more terms or sum of two or more expression is know as “polynomial”

e.g., (i) 2x²– 5 (ii) x² + 4x - 3

VERTICAL ADDITIONIn vertical addition the second expression is written below the first expression such that the like terms are in the same column. In case of more than two expressions the third expression is written below the second expression in the same manner and so on.

Same signs always add up but the sign remains the same.Different signs always subtracts but the sign of greater quantity is used.

ADDITION OF POLYNOMIAL EXPRESSION

SOLUTION a³+2a²-6a +7 a³+2a² +5

2a³- a²+2a-8 4a³+3a²-4a+4

HORIZONTAL ADDITION

Write the given polynomials in brackets in horizontal form and then add like terms.

SOLUTION

= (a³+2a²-6a+7) + (a³+2a²+5) + (2a³-a²+2a-8)

= a³+2a²-6a+7+a³+2a+5+2a³-a²+2a-8

= a³+a³+2a³+2a²+2a²-a²-6a+2a+7+5-8

= 4a³+3a²-4a+4

VERTICAL SUBTRACTION:

The expression to be subtracted is written the below the other expression such that like terms are in the same column. Since subtraction means addition of additive inverse, therefore the signs of the lower expression are changed then added with the other expression.

Subtraction of polynomial Expression

EXAMPLE:-

Subtract a³-3a²b+3ab²-b³ from a³+3a²b-3ab²+b³

SOLUTION:-

a³+3a² b-3ab²+b³

+a³-3a² b+3ab²-b³

- + - +

6a²b-6ab²+2b³

Write the given polynomial in brackets in horizontal form and change the sign of second expression and then add them.

HORIZONTAL SUBTRACTION

=(a³+3a²b-3ab²+b³) – (a³-3a²b+3ab²-b³)

= a³+3a²b-3ab²+b³-a³+3a²b-3ab²+b³

= a³-a³+3a²b+3a²b-3ab²-3ab²+b³+b³

= 6a²b-6ab²+2b³

SOLUTION:-

MULTIPLICATION OF POLYNOMIAL EXPRESSION

While multiplying two polynomials, the co-efficients and variables of the terms in each polynomial are multiplied separately. If the bases are the same, then the powers are simply added. We have two forms for multiplication of two polynomials.i) Horizontal formii) Vertical FormLet us explain these forms with the help of examples.

EXAMPLE:-Find the product of

(x+3) (3x²+2x-6)

Vertical form

Solution:

3x²+2x – 6

x x +3

3x³+2x² - 6x

+9x²+6x – 18

3x³+11x² - 18 or 3x³+11x² - 18

SOLUTION:

(x + 3 ) (3x² + 2x – 6) = x (3x² + 2x – 6) +3 (3x²+2x – 6)

= 3x³ + 2x² - 6x + 9x² + 6x – 18

= 3x³ + 2x² + 9x² - 6x + 6x - 18

= 3x³ + 11x² - 18

HORIZONTAL FORM

DIVISION OF POLYNOMIALS EXPRESSION

To division a polynomial by another polynomials, the various steps to follow are:i) The dividend and the divisors are arranged either in ascending or in descending powers of the same variable.ii) The first term of the dividend is divided by the first term of the divisor and the quotient is written in the first position scheduled for the quotient,iii) Each term of the divisor is multiplied by the quotient and the product is subtracted from the dividend.iv) The remainder is then divided by the divisor and the process is continued until the remainder is zero.

Example: Divide x²-5x+6 by x-2

Solution:

x-2﴿ x²-5x+6﴾ x-3

x²-2x - + -3x+6 -3x+6 + - 0

END