Basic Math 1 Section 1.2 United Arab Emirates University University General Requirement Unit

is called the quotient of x and y, or x divided by y. Operations and Properties Binary operation: The process of combining two elements of a set to produce a third element is called a Binary operation. There are 4 operations: 1.Addition 2.Subtraction 3.Multiplication 4.Division x+ y is called the sum of x and y, or x plus y. x- y is called the difference of x and y, or x minus y. xy(or x y ) is called the product of x and y, or x times y.

… Expression: an expression is a meaningful collection of numbers, variables, and operations. Example 1 2x+3y is an expression that involves numbers, ( 2 and 3 ), variables ( x and y ) operations ( addition and multiplication ) Example 2 Write the following statements using symbols StatementSymbol(s) The sum of 10 and x 10 + x 12 more than p n increased by 1 The product of m and n The quotient of b and 2 4 less than the product of r and s

… StatementSymbol(s) 7 times b The sum of c and 4, divided by d x square 4 less than the square of m The square of the sum of x and y s divided by 4 Class Exercise

Order Of Operation Rules and Properties: Order of operations 1.Simplify within innermost grouping symbol, and work outward until all grouping symbols are removed. 2.Evaluate any expressions involving exponents. 3.Perform any multiplication and division, working from left to right. 4.Then do any addition and subtraction, again working from left to right. Example 1 Evaluate each expression Multiply first Then do the addition Simplify within the grouping symbols Then multiply

… Add inside parentheses Evaluate the power Multiply Multiply Add and then subtract from left to right

… Class Exercise Evaluate each expression

Properties of Addition and Multiplication over Real numbers Inverse Identity Commutative Associative Closure MultiplicationAdditionProperty ExamplePropertyExampleProperty

Rules and Properties Rules and Properties:Distributive Property a ( b + c ) = ab + ac Example 1 Use the distributive property to simplify each expression First Use Distributive property Simplify Class Exercise Use the distributive property to simplify each expression

… Class Exercise

Combining Like Terms Like Terms: If two or more terms have the same variable and same power( exponent), then, these terms are called like terms. Example 1 3x and 8x are like terms 7y and –5y are like terms 3x 2 and 5x 2 are like terms Unlike Terms: If two or more terms have different variable or different powers ( exponents ), then these terms are called unlike terms Example 2 2x and 4y are unlike terms because they have different variables

… 4x and 2x 2 are unlike terms because they have different powers Class Exercise Check if these terms in the table below are like terms (Type Yes ) or unlike terms ( Type No ). TermsLike Terms 2m and 15m 3n and 4y 2x and 3x and 4x 2 6n and –3n

Adding Like Terms To add ( or subtract ) two like terms, we add ( or subtract ) their coefficients. Example 3 Add or subtract. x and y are unlike terms Class Exercise Add or subtract.

Home Work Do the Home Work Exercises as written in the Syllabus