Intro to Algebra PDF

ALGEBRA: AN INTRODUCTION Sir Jerald Lambon Jalos  PRELIMINARY When you wish to add, subtract, multiply, or divide a certain number in a numerical expression, how will you represent that number?  VARIABLES Is any symbol (usually letters) t...

ALGEBRA: AN INTRODUCTION Sir Jerald Lambon Jalos  PRELIMINARY When you wish to add, subtract, multiply, or divide a certain number in a numerical expression, how will you represent that number?  VARIABLES Is any symbol (usually letters) that represents an arbitrary value. The value of variable may vary depending on what value it may present. Examples: 4ab 6b 7x  CONSTANTS On the other hand, real numbers or known quantities. Any number that has a fixed value Examples: 4ab 6b 7x ALGEBRAIC EXPRESSIONS Is a mathematical phrase that contains integral or fractional constants, variables and algebraic operators. These expressions are expressed in the form of terms, factors, and coefficients. ALGEBRAIC EXPRESSIONS Example: 2abc Factors: 2, a, b, c Constant: 2 Variables: a, b, c  PARTS OF EXPRESSION In mathematics, an algebraic expression is an expression that is made up of variables, constant, coefficients, and arithmetic operations. Example: 2x + 4y – 9 Coefficients: 2 and 4 Constant: 9 Variables: x and y Terms: 2x, 4y and 9  TERMS It can be a number, a variable, product of two or more variables or product of a number and a variable. An AE is formed by a single term or by a group of terms. For example, in the expression 4x + y, the two terms are 4x and y.  COEFFICIENTS In a term, the constant multiplied by the variable is called coefficient. NUMERICAL COEFFICIENT is the numerical factor of a term. LITERAL COEFFICIENT is the product of the variables in a term.  WHAT IS MEANT BY TERMS IN EXPRESSION?. An algebraic expression is made up of terms. A term can be a constant or a variable, or variables with coefficients  WHAT ARE THE FACTORS IN AN ALGEBRAIC EXPRESSION? A factor in an expression is something that is multiplied by something else. It can be a number, variable, term or any other longer expression. For example, the factors of 2xy are 2, x and y.  WHAT IS A COEFFICIENT? A coefficient is a numerical value that is multiplied by a variable. For example, the coefficient of 7x is 7.  WHAT IS A COEFFICIENT, TERM OF AN EXPRESSION 5X+8Y? In an expression 5x+8y, the coefficients are 5 and 8, and the terms are 5x and 8y.  WHAT IS MEANT BY CONSTANT? A constant is a numerical value that should not change its value. For example, in the expression 2x+6, 6 is a constant.  IDENTIFY THE VARIABLES, TERMS, CONSTANT, AND COEFFICIENTS 1.9x + 2y – 3  VARIABLE CONSTAN COEFFICIENT TERMS S S T 9x + 2y – 3 x, y 9x, 2y, -3 -3 9, 2 X ,, 17 22, -6 x, y , 1, 2, -14 P 3p, 16 16 3 x, y -19 15, 3, 4, -1  SIMILAR TERMS AND DISSIMILAR TERMS Similar terms (sometimes called like terms) are those identical variables and with equal exponents. Dissimilar terms (unlike terms) are those with different variables and with unequal exponents.  EXPONENT An exponent is a number or variable written above and to the right (superscript) of another number or variable to denote how many times the number or variable being multiplied by itself. Example: 4 x 4 x 4 = 3 is the exponent of 4  EXPONENT Examples: 1. IDENTIFY THE LIKE AND UNLIKE TERMS LIKE UNLIKE In each algebraic expression, identify the numerical and literal coefficient, and write a term similar to it. Algebraic Numerical Literal coefficient Similar term expressions coefficient 1. –a -1 a 23a 2. 2 78 3. 101 4. 33 stv 4stv 5. -79 bc bc 6. -3/4 7. -7/11 8. - -8/17 9..001 10.  Simplifying Algebraic Expression An algebraic expression is considered simplified when: a.the grouping symbols are removed; b.All similar terms or like terms are combined Steps in Simplifying Algebraic Expression 1.Remove the grouping symbols of algebraic expressions 2.Start with the terms in the parenthesis then the brackets and then the braces. 3.Combine all the like terms by performing the operations among the terms.  Remember Terms that can be combined are those with the same variable and equal exponents. 1. Commutative Property of Equality If a and b are real numbers, then a+b=b+a Examples: 1. -16 + 23 = 23 + (-16) 7=7 2. 12x + 9x = 9x + 12x 21x = 21x 3. 35xy + (-19xy) = -19xy + 35xy 16xy = 16xy  2. Associative Property of Equality If a, b, and c are real numbers, then a + (b + c) = (a + b) + c. Examples: 1. 1 + (3 + 5) = (1 + 3) + 5 1+8=4+5 9=9 2. y + (2y + 10y) = (y + 2y) + 10y y + 12y = 3y + 10y 13y = 13y  3. Distributive Property of Equality If a, b, and c are real numbers, then a (b + c) = ab + ac. Examples: 1. 4(3 + 9) = 4(3) + 4(9) 4(12) = 12 + 36 48 = 48 2. 2(5x + x) = 2(5x) + 2(x) 2 (6x) = 10x + 2x 12x = 12x Example of combining like terms:  Simplify the following Algebraic Expressions 1. +7