UNIT 1: ALGEBRA

OSH 1162:

MATHEMATICS

by miss najwa CHAPTER 1:

Algebra

Algebra

1.1Introduction to Algebra1.2Formulate Algebraic Equations in One Unknown1.3Formulate Algebraic Equations in One Unknown1.4Formulate Algebraic Equations in One UnknownA) Using Letters To Represent NumberIn algebra, we can use letters to represent numbers. The number represented by a letter is called an unknown.

Expressions formed by numbers, unknowns and the signs +, , , etc. are called algebraic expressions.1.1 Introduction To Algebra

A student buys 4 boxes of building block and 10 pieces of screw for his science project. If each box of building block already has m pieces of screw inside, use algebraic language to write the total number of screw that student has now.1.1 Introduction To Algebra

SOLUTION The total number of students screw now= 4 m + 10= 4.m + 10= 4m + 10Aina is t years old now and her brother is 4 years older than her. Use algebraic language to write the sum of the ages of Aina and her brother.1.1 Introduction To Algebra

SOLUTION The age of her brother = t + 4The sum of the ages of Aina and her brother= t + t + 4

B) The Advantages of Using Algebraic LanguageIt is simple and direct, so it is easy to read and understand.It can be an international language.

1.1 Introduction To Algebra

1.1 Introduction To Algebra

Add 9 to an unknown number.x + 9Word phaseAlgebraic expressionSubtract 6 from an unknown number and multiply the difference by 2.Divide an unknown even number by 2 and then add 1 to the quotient.(y 6) 2(z 2) + 11.1 Introduction To Algebra

SOLUTION

9C) More About Algebraic ExpressionFor the algebraic expression x + 2y 3x + 5,

x, 2y, 3x, 5 are the terms of the algebraic expression, 5 is the constant term, x and 3x are like terms, x and 2y is a pair of unlike terms.

1.1 Introduction To Algebra

C) More About Algebraic ExpressionIn an algebraic expression,

numbers and letters that are separated by the signs or are not considered as two different termsE.g. +2 a (can be written as +2a) is considered as one term.

the + sign before a single term or the first term is usually skipped. E.g.+2a is written as 2a, +7b 6 is written as 7b 6.1.1 Introduction To Algebra

C) More About Algebraic ExpressionIn an algebraic expression,

like terms can be combined by addition, subtraction, multiplication or division

unlike terms, on the other hand, can be combined by multiplication or division.

1.1 Introduction To Algebra

1.1 Introduction To Algebra

SOLUTION There are 4 terms in the algebraic expression 2 a + 5 a 6 4a b + 5 7 which isHow many terms are there in the algebraic expression2 a + 5 a 6 4a b + 5 7 ?Identify the terms as constant term, like terms and unlike terms.

1.1 Introduction To Algebra

SOLUTION 1.1 Introduction To Algebra

1.1 Introduction To Algebra

SOLUTION 1.1 Introduction To Algebra

SOLUTION A) Formulate Algebraic Equations in One Unknown

An equation contains an equal sign = and also one or more unknowns.The equation that contains one unknown only is called an algebraic equation in one unknown.To solve an equation is to find the value of the unknown in that equation. That value is called the solution of the equation.To find the solution of an equation is to solve the equation.

1.2 Algebraic Equation in One Unknown

In each of the following, formulate an algebraic equation to find the value of the unknown.The cost of a doll is $x and that of a ball is $25. It is known that the total cost of the doll and the ball is $43.There are 150 candies in a jar. Kenny has y jars of candies and it is known that he has 600 candies.

SOLUTION x + 25 = 43, x = 18150y = 600, y = 4

1.2 Algebraic Equation in One Unknown19B) Properties of Equations

1.2 Algebraic Equation in One Unknown

There are a red flowers and b yellow flowers in the vase. Mrs Law picks c red flowers and c yellow flowers from the vase. How many red flowers and yellow flowers in the vase now? If the original numbers of red flowers and yellow flowers are the same, write down the relationship between the numbers of the flowers by using the algebraic expression.

SOLUTION Numbers of flowers in the vase:Red flowers = a c ; Yellow flowers = b cIf the original numbers of red flowers and yellow flowers are the same, then a c = b c 1.2 Algebraic Equation in One Unknown

21Helen has a pears and b oranges. She divides the pears and oranges among her brothers. It is known Helen has c brothers. How many pears and oranges that each of Helens brothers can get? If the numbers of pears and oranges are the same, write down the relationship between the numbers of the fruits by using the algebraic expression.

SOLUTION 1.2 Algebraic Equation in One Unknown

22C) Solving Algebraic Equations in One Unknown

We may apply guessing and checking or apply the same operation to the two sides of the equation to solve algebraic equations.

Skills to solve algebraic equationTransposing TermsRemoving BracketsCancelling Denominators

1.2 Algebraic Equation in One Unknown

C) Solving Algebraic Equations in One Unknown

Skills to solve algebraic equation

Transposing TermsThe terms in an equation can be transposed from one side of the equal sign to the other. At the same time, the signs of the terms must be change

For example: If x a = b, after transposing terms, we have x = b + a. If x + a = b, after transposing terms, we have x = b a. If a = b x, after transposing terms, we have x + a = b.

1.2 Algebraic Equation in One Unknown

C) Solving Algebraic Equations in One Unknown

Skills to solve algebraic equation

Removing BracketsWhen brackets are involved in an equation, they should be removed first in order to simplify the equation.In general, we can remove brackets in the following way:

a(b + c) = ab + ac OR(b + c)a = ba + ca

1.2 Algebraic Equation in One Unknown