chapter 1-1 variables and expressions in this section you will learn how to, write mathematical...

Chapter 1-1 Chapter 1-1 Variables and Variables and ExpressionsExpressions

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 mand n

the difference of q and 3

the quotient of j to thethird power and 6

Example 1: Translating from Algebra to Words

C. 7m + n D. j3 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 xn is called a

power and is read “x to the nth power”

• The variable x is called the base and n is called the exponent

Symbols

Words Meaning

31 3 to the first power 3

32 3 to the second power or 3 squared

3 • 3

33 3 to the third power or 3 cubed

3 • 3 • 3

34 3 to the fourth power

3 • 3 • 3 • 3

xn x to the nth power x • x • … • x

Evaluate each expression.

A. 25 B. 42 C. 53

Example 4: Evaluating Powers

= 2•2•2•2•2 = 4•4 = 5•5•5

= 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 Chapter 1-2 Order of Operationsof 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.) 4 + 2 • 8 – 5 b.) (3 + 4)2 - 1 4 + 16 – 5

20 – 5 15

(7)2 - 1 49 - 1

48

cb

a

2

26

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

)5()3(

)2(62

2

59

46

45

10

9

2

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) = 6 + 15

21 = 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)

= 450 + 9

= 459

b. 12(98)

12(98) = 12(100 – 2)

= 12(100) – 12(2)

= 1200 – 24

= 1176

c. )4

12(8

)4

12(8

)4

1(8)2(8

21618

Example 2 – Rewrite each product using the distributive property and then

simplify.

c.) 4(y2 + 8y + 2) = 4(y2) + 4(8y) +

4(2) = 4y2 + 32y + 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.

1x2 + 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 + 5x2 d.) 5r + 4w – 3r + w

29a 13x + 3y

simplified 2r + 5w

e.) 9g – (h + 5) + 4(g + 2h)9g – h – 5 + 4g + 8h

13g + 7h – 5

Classwork Assignment• Study Guide1-1, 1-2 & 1- 5.

(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 hintsDo 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.