Chapter 5 Algebra Expression 5.1 Variables and Algebra Expression Representing Variable Example Madam Soh wishes to buy a few pieces of local delicacies from a stall. The number of pieces of delicacies Madam Soh wishes to buy and the price of each delicacy are quantities with unknown values. In mathematics, quantities with undetermined values are represented by letters and are called the variables. For example, letters k and x are variables with the condition: k represents the number of pieces of delicacies Madam Soh wishes to buy and x represents the price per piece of the delicacies. （在数学中，具有未确定值的量⽤字母表⽰，称为变数。） k is a variable whose value varies because the value of k depends on Madam Soh's decision. The unit price of the delicacy is determined by the stall; hence x is a variable with a fixed value. Variable Varies k (Number of pieces of delicacies) Fixed x (unit of delicacies)
Chapter 5 Algebra Expression Deriving Algebraic Expressions 1. Hafiz is 8 years old. After 4 years, his age 8+4 = 12 years old After 7 years, his age 8+7 = 15 years old After c years, his age (8+c) years old. 8+c is an algebraic expression. 2. An algebraic expression is a combination of variables, numbers, and operation signs (+, -, x and ÷) to represent a particular situation. Determining the value of Algebraic Expression 1.The price of one watermelon is RM5 and the price of one pineapple is RM2. To buy one watermelon and two pineapples, Total price in RM = 5 x 1 + 2 x 2 =5+4 =9 2. If the number of watermelons bought is represented by m and the number of pineapples bought is represented by n, then the total price for m watermelons and n pineapples = RM (5m + 2n) 3.To buy one watermelon and two pineapples, the total price can be calculated by substituting m = 1 and n = 2 into the algebraic expression 5m + 2n. Total price in RM = 5m + 2n = 5(1) + 2(2) = 5+4 =9
Chapter 5 Algebra Expression Identifying the term in an expressing and Coefficient of a term 1. In an algebraic expression, the parts separated by the symbols + and ‒ are called terms. 3c + 8y - 7 has three terms, namely 3c, 8y and -7. 2. Note that every term is identified with the symbol + or - before it. The symbol + is normally omitted, for example +8y is written as 8y. 3. 3c and 8y are also known as algebraic terms. An algebraic term is the product of a variable and a number. 4. The numbers 3 and 8 in the algebraic terms 3c and 8y are the coefficients of c and y. Generally, the coefficient of a variable and in an algebraic term is the other factor in the algebraic term. 5. -7 which is a term without a variable is called a constant. Like and Unlike terms 1. Like terms are terms with the same variables and the same power. 2. Unlike terms are terms with different variables or terms with the same variable but different power. 3c+8y-7 3c Variable = c Coefficient = 3 8y Variable = y Coefficient = 8 -7 Constant term
Chapter 5 Algebra Expression Example Look at the following pairs of terms. Both terms have the same variable, h and the power of h is 1. Therefore, 8h and 3h are like terms. Both terms have the same variable, k and the power of k is 2. 2k2 and -7k2 are like terms. Look at the following terms. The terms have different variables. 2p,3d and 9k are unlike terms. The terms have the same variable but different powers. 5c,6c2 and c3 are unlike terms. 5.2 Algebraic Expression involving Basic Arithmetic Operation Addition and subtraction of algebraic expression We can add or subtract two or more algebraic expression by grouping the like term. (我们可以把 like term 相加或者相减。) 1. The sum of pair of positive or negative number with the same figure is zero. 1+(-1) =0 / 2+(-2) =0 Same as number for algebraic terms x +(-x) =0 / y+(-y) =0 Repeated Multiplication of Algebraic Expressions 1. The concept of power can also be applied to variables, thatʼs a x a = a2, a x a x a = a3. (倍数的概念一样可以应用在algebraic上。) 2. Square and cube are the repeated multiplication of a number twice and thrice respectively. If the process of repeated multiplication is continued, the power of higher degree will be produced. (双倍和三倍是重复地相乘同一个数目两次和三次。如果这个步骤一直继续下去 的话，更高的度数会产生。) 8h 3h 2k2 -7k2 2p 3d 9k 5c 6c2 c3 0 (zero pairing)
Chapter 5 Algebra Expression Multiplication and Division of Algebraic Expression 1. The product of algebraic expression in one variable = product of numbers x product of variables Example: Length = pcm, width= qcm Whole = 4pcm, width = 6qcm Area = 4pcm x 6qcm = (4x6) x p x q cm = 24 x p x q cm = 24pqcm2 1. Steps to multiply algebraic expression. Example: a.)6ef x 4g = 6 x e x f x 4 x g = 6 x 4 x e x f x g = 24 x e x f x g = 24efg b.) -2ac2 x 5abc x 3c = -2 x a x c x c x 5x a x b x c x 3 x c = -2 x 5 x 3 x a x a x b x c x c x c x c = -30 x a2 x b x c4 = -30a2bc4 Write the algebraic terms as the product of the numbers and variables Multiply the number with number, and the variable with variables Simplfy the expression. Write the repeated numtiplication of variables in power form.
Chapter 5 Algebra Expression Dividing algebraic expression. 1. Step to divide algebraic expression. Write the division in fraction form that is , a÷b=! " Write the algebraic form as the product and variables Simplify by canceling out the same number and variable in the numerator and denominator.
Chapter 5 Algebra Expression Example