Chapter 1-1 Variables and Expressions In this section you will learn how to,  Write mathematical expressions given verbal expressions  And how to write verbal expressions given mathematical expressions

 Variable  Algebraic expression  Factors  Products  Power  Base  Exponent  Evaluate Vocabulary

* A variable is a letter or a symbol used to represent a value that can change. * An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Writing Mathematical Expressions * Many algebraic expressions contain multiplication. The quantities being multiplied are called factors, and the result is called the product.

These expressions all mean “2 times y”: 2y 2(y) 2 y (2)(y) 2 y (2)y Writing Math

You will need to translate between algebraic expressions and words to be successful in math. The diagram below shows some of the ways to write mathematical operations with words. Plus, the sum of, increased by, total, more than, added to Minus, the difference of, less than, decreased by Times, the product of, equal groups of “of”, Divided by, quotient, per +– x÷

Write a verbal expression for each algebraic expression. A. 9 + r B. q – 3 the sum of 9 and r the sum of 7 times m and n the difference of q and 3 the quotient of j to the third power and 6 Example 1: Translating from Algebra to Words C. 7m + n D. j 3  6

Write an algebraic expression for each verbal expression. A. Seven minus x B. the sum of 7 and 4 times r 7 + 4r Example 2: Translating from Words to Algebra 7 – x

A pizzeria sells one cheese pizza for $14 and two sodas for $3. Write an equation for the cost of buying p pizzas and s sodas. Example 3: Real World Application C = 14p + 3s

Exponents An expression like x n is called a power and is read “x to the n th power” The variable x is called the base and n is called the exponent

SymbolsWordsMeaning to the first power to the second power or 3 squared to the third power or 3 cubed to the fourth power3 3 xnxn x to the nth powerx x … x

Evaluate each expression. A. 2 5 B. 4 2 C. 5 3 Example 4: Evaluating Powers = = 44= 555 = 32 = 16 = 125 My hint: Write out the exponent in expanded form first and then evaluate the exponent. This way you don’t quickly try to evaluate the exponent in your head and make a quick mistake.

Chapter 1-2 Order of Operations In this section you will learn how to,  Evaluate numerical and algebraic expressions by using the order of operations

When there is more than one operation in an expression we have to know which operation to perform first. This rule is called order of operations. Evaluate expressions inside grouping symbols. Evaluate all exponents Do all divisions and/or multiplications from left to right Do all subtractions and/or additions from left to right.

Example 1 – Evaluate each expression a.) – 5 b.) (3 + 4) – 5 20 – 5 15 (7)

Example 2 – Evaluate the given expressions if a = 2, b = 3 and c = 5.

Chapter 1.5 ~ The Distributive Property Today we will learn about the distributive property and how to use this property to evaluate and simplify expressions. New vocabulary today: –Term –Like terms –Equivalent expressions –Simplest form –Coefficient

The Distributive Property  For any numbers a, b, and c, a(b + c) = ab + ac and a(b – c) = ab – ac  For example, 3(2 + 5) = 3∙2 + 3∙5 3(7) = = 21 ** We can also use the distributive property to find products of large numbers. This hopefully will help you simplify mental math.

Example 1 - Write each product using the Distributive Property. Then simplify. a. 9(51) 9(51) = 9(50 + 1) = 9(50) + 9(1) = = 459 b. 12(98) 12(98) = 12(100 – 2) = 12(100) – 12(2) = 1200 – 24 = 1176 c.

Example 2 – Rewrite each product using the distributive property and then simplify. c.) 4(y 2 + 8y + 2) = 4(y 2 ) + 4(8y) + 4(2) = 4y y + 8 b.) 3(5x – 1) = 3(5x) – 3(1) = 15x – 3 a.) 12(y + 3) = 12(y) + 12(3) = 12y + 36

The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. 4x – 3x + 2 Like terms Constant

A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. 1x 2 + 3x Coefficients

3x + 8x and 11x are called equivalent expressions because they denote the same number An expression is in simplest form when it is replaced by an equivalent expression having no like terms or parentheses.

Example 3 – Simplify each expression by combining like terms a.) 17a + 12a b.) 15x + 3y – 2x c.) 4x + 5x 2 d.) 5r + 4w – 3r + w 29a 13x + 3y simplified2r + 5w e.) 9g – (h + 5) + 4(g + 2h) 9g – h – 5 + 4g + 8h 13g + 7h – 5

Classwork Assignment Study Guide1-1, 1-2 & (Front & Back) Homework Assignment Page 820 – Lesson 1-1 (Odds) Page 820 – Lesson 1-2 (Odds) Page 821 – Lesson 1-5 (Odds)

Homework Hints Homework hints  Do one problem at a time. Do NOT pre-number the whole page. Leave room for work.  Show ALL work. No work = no credit  Never EVER just put a question mark. This will get you NO credit for HW.  Please do NOT use a calculator! You won’t be allowed to use one on the Quizzes or the Test in this Unit.