Algebra A branch of mathematics characterized by the use of variables and operations relating these variables. Importance of Algebra Algebra serves as a foundation of various concepts and applications of mathematics. How can Algebra be used in real life? An engineer uses algebra to solve physical problems such as how to build a bridge or design a house. Businessmen use algebra to calculate costs, revenues, and profits. Bankers use Algebra to calculate interests
Word Problem A Filipino citizen is said to be of legal age when he or she turns 18 years old. Romulo, who is a Filipino, was born in 2001. a. In what year will he be of legal age? Solution: 2001 + 18 = 2019 b. In what year will he be 30 years old? Solution: 2001 + 30 = 2031 c. In what year will he be 65 years old? Solution: 2001 + 65 = 2066 Questions (Word Problem) 2001 + 18 2001 + 30 2001 + 65 a. What is the commonality among the solutions? 2001 does not change. b. What is the difference among the solutions? The addend changes depending on the given age. Constant & Variable A constant represents a fixed value. Any number in an expression is a constant. A variable is a symbol used to represent values that can change or vary in an expression Example: 2001 + n Constant = 2001 Variable = n
Everyday Constants and Variables The electric bill each month - Variable The number of days in a week - Constant The number of hours of daylight in a day - Variable
Algebraic Expressions An algebraic expression is a combination of one or more constants, and variables along with at least one mathematical operation. Examples: 70r, 70(r), 3x/2y
Translating English Phrases to Mathematical Symbols Addition: The sum of a number and 2 (or 2 + x since addition is commutative – can be reversed) 2 added to a number 2 more than a number A number increased by 2 2 greater than x exceeds x by 2 total of a number and 2 can be translated to: x + 2 Subtraction: the difference of x and 2 a number x decreased by 2 x reduced by 2 x take away 2 a number x less 2 2 subtracted from x 2 less than x can be translated to: x - 2 Multiplication: 2 times x the product of 2 and x 2 multiplied by x twice x can be translated to: 2x Division: x divided by 2 the quotient of x and 2 the ratio of x to 2 can be translated to: x ÷ 2 Exponents: x raised to 2 can be translated to: x^2 Note: "^" is the symbol for exponents.