Math 094 Section 1.3 Exponents, Order of Operations, and Variable Expressions

Objective A: Exponents and the Order of Operations Exponents indicate repeated multiplication base exponent Notice that since indicates repeated multiplication and 2∙3 indicates repeated addition.

Objective A: Exponents and the Order of Operations Evaluate (find the value of) each expression (Read as “5 squared” or “5 to the second power”) (Read as “6 cubed” or “6 to the third power”) (Read as “2 to the fourth power”)

Objective A: Exponents and the Order of Operations Order of operations (PEMDAS)  If grouping symbols such as parentheses are present, simplify those first starting with the innermost set  Evaluate exponential expressions, roots, and absolute values  Perform multiplication and division in order from left to right  Perform addition and subtraction in order from left to right

Objective A: Exponents and the Order of Operations Common grouping symbols  Parentheses ( )  Brackets [ ]  Braces { }  Fraction bars  Radical signs  Absolute value bars

Objective A: Exponents and the Order of Operations Simplify each expression.

Objective B: Evaluating algebraic expressions Variables are letters used to represent a quantity. An algebraic expression is a collection of numbers, variables, operation symbols, and grouping symbols. If we give a specific value to a variable, we can evaluate the algebraic expression.

Objective B: Evaluating algebraic expressions If someone gives you an expression like 3x + 5, you can substitute in numbers for x, and figure out the expression’s new value (evaluate it). Let’s say x=2. Then 3x + 5 would become 3(2) + 5 = = 11 What if x = 0. Then 3x + 5 would become 3(0) + 5 = = 5 What if x = ☺? When 3x + 5 would become 3(☺) + 5 = 3☺ + 5. There’s nothing else we can do! Recommend you use parentheses around the new number. Remember: Whatever value you’re given, just stick it in wherever the original variable was, compute it, and you’ll be fine!

Objective C: Solutions to equations An equation is a mathematical sentence that says two expressions are equal. The difference between an expression and an equation is an equation has the equal sign. When an equation contains a variable, deciding which value(s) the variable can be that make the equation true is called solving the equation.

Objective C: Solutions to equations What value of the variable makes the statement true?  x + 6 = 10 Is 3 a solution of 5x – 10 = x + 2? Is 10 a solution?

Objective D: Translating words to symbols See p.23 for a table of common phrases that indicate certain operations. Order matters when subtracting or dividing, so be careful when translating things involving these operations. OperationWhat we call the answer for this operation AdditionSum SubtractionDifference MultiplicationProduct DivisionQuotient

Objective D: Translating words to symbols Write an algebraic expression or equation for each phrase  A number subtracted from 8  A number decreased by 8  8 less than a number  A number less 8  Five more than twice a number  The ratio of a number and 6 is 24.  Three is not equal to one half of 10.  Six increased by two equals the product of 4 and two.