CHAPTER 2 Expressions

2.3 Distributive Property Distributive Property = multiply a single term and two or more terms inside a set of parentheses. a(b + c) = a(b) + a(c)

Example 1 3(2 + 5) = 3 • 2 + 3 • 5 3(7) = 6 + 15 21 = 21

Example 2 Use distributive property and write an equivalent expression. y(5 + x) = y(5) + y(x) 5y + yx

Exercise 3 Combine any like terms. = 3r + 6 + 5 6 + 3r + 5 = 3r + 11

Exercise 4 Use distributive property and combine any like terms. 2(h + 3) + h = 2(h) + 2(3) + h = 2h + 6 + 1h = 3h + 6

Topic: Distributive Property HOMEWORK Topic: Distributive Property examples on pages 55-56 Assignment: Lesson 2.3 in book on page 57 11-27 all (17 total)

2.4 Evaluating Expressions Expression = contains numbers, variables, and operators grouped together to show the value of something (does not have an equal sign) Operator + – Coefficient = a number by which a variable is multiplied 2n + 5 Constant = is a number whose value does not change (no variable) Terms = can be a number, variable, or a product of a number and variable (separated by an operator) Variable = symbol that represents a value (can be any letter in the alphabet)

Example 1 Evaluate when n = 8. n + 6 8 + 6 = 14

Example 2 Evaluate when x = 2. 18 − 4x 18 − 4(2) 18 − 8 = 10

Example 3 Evaluate when x = 9 and y = 3. x − (y + 7) 9 − (3 + 7) 9 − (10) = −1

Topic: Evaluating Expressions HOMEWORK Topic: Evaluating Expressions examples on pages 59-61 Assignment: Lesson 2.4 in book on pages 61-62 17-45 odd (15 total)

Topic: Evaluating Expressions HOMEWORK Topic: Evaluating Expressions examples on pages 59-61 Assignment: Lesson 2.4 in book on pages 61-62 16-44 even (15 total)

2.5 Simplifying Expressions 2x3y + 6 2 is the coefficient. x and y are variables. 3 is an exponent. + is an operator. 6 is a constant.

2.5 Reviewing Expressions Expression = contains numbers, variables, and operators grouped together to show the value of something (does not have an equal sign) Operator = + – Coefficient = a number by which a variable is multiplied 2n + 5 Constant = is a number whose value does not change Terms = can be a number, variable, or a product of a number and variable (separated by an operator) Variable = symbol that represents a value (can be any letter in the alphabet)

Example 1 Use the −6xy + − z to answer the following. 2 Use the −6xy + − z to answer the following. What are the coefficients in the expression? The coefficients are −6, , and −1. 1 2

Example 2 Use the −6xy + − z to answer the following. Does the expression have a constant term? No. All terms contain a variable factor.

Like Terms = are terms with the same variables and the same exponents

Example 3 4x, 4x2 1 2 5x, −7x, x 6xy, −8xy3 5xy2, −7xy2, 0.75xy2 Determine if each expression below is a “like” or “unlike” term 4x, 4x2 unlike term 5x, −7x, x 1 2 like term 6xy, −8xy3 unlike term 5xy2, −7xy2, 0.75xy2 like term

Example 4 Simplify. (x + 2) + 9 x + 2 + 9 = x + 11

Exercise 5 x + 2x + (2x – 3) x + 2x + 2x – 3 = 5x – 3 The sides of a triangle are represented by x, 2x, and 2x − 3. Find the expression that represents its perimeter. x + 2x + (2x – 3) x + 2x + 2x – 3 = 5x – 3

Exercise 6 Each side of a regular octagon (all sides equal in length) is represented by 25x. Find the expression that represents the perimeter of the regular octagon. 8(25x) = 200x

Topic: Simplifying Expressions HOMEWORK Topic: Simplifying Expressions examples on pages 62-65 Assignment: Lesson 2.5 in book on pages 65-66 5-33 odd (15 total)

Topic: Simplifying Expressions HOMEWORK Topic: Simplifying Expressions examples on pages 62-65 Assignment: Lesson 2.5 in book on pages 65-66 6-34 even (15 total)

2.6 Translating Word Phrases Addition Key Words added to sum increased by more than plus

Subtraction Key Words subtracted from difference decreased by less than minus less

Multiplication Key Words multiplied by product times twice (× 2) doubled (× 2)

Division Key Words divided by quotient ratio of halved (÷ 2)

Example 1 Write “9 decreased by 5” as a numerical expression. 9 − 5

Example 2 Write “the product of 9 and 5” as a numerical expression. 9 × 5

Example 3 Write “a number increased by 2” as an algebraic expression. n + 2

Example 4 Write “44 divided by n” as an algebraic expression.  

“the next consecutive integer” Exercise 5 “the next consecutive integer” n + 1

Exercise 6 “an even integer” 2n

“the integer preceding n” Exercise 7 “the integer preceding n” n – 1

Exercise 8 Bill has $46. How much will he have if he does the following? 46 − 5 spends $5:

Topic: Translating Word Phrases HOMEWORK Topic: Translating Word Phrases examples on pages 69-71 Assignment: Lesson 2.6 in book on page 72 3-31 odd (15 total)

Topic: Translating Word Phrases HOMEWORK Topic: Translating Word Phrases examples on pages 69-71 Assignment: Lesson 2.6 in book on page 72 4-32 even (15 total)

2.7 Estimating Highest Place Value = round the number to the far left Estimating A Product = round each number to its highest place value Estimating A Quotient = only round numbers to obtain a whole number for the answer Front-End Estimation = use the far left digit only and make all other numbers zero

Example 1 Round 7,384 to each indicated place. 7,000 thousand: 7,400 hundred: 7,400 ten: 7,380

Example 2 Estimate the sum by rounding to the nearest ten. 42 + 87 = 40 + 90 = 130

Example 3 Estimate the difference by rounding to the nearest ten. 263 – 9 = 260 – 10 = 250

Example 4 Round 15,469.7482 to each place. tenth: 15,469.7 hundredth: 15,469.75 thousandth: 15,469.748

Example 5 Estimate the sum of 17,436 + 43,519 by rounding each addend to its highest place value. 20,000 + 40,000 = 60,000

Example 6 Estimate product by rounding to the highest place value 34 • 76 = 30 • 80 = 2,400

Example 7 Estimate a quotient by only rounding numbers to obtain a whole number answer. 1,144 ÷ 34 = 1,140 ÷ 30 = 38

Example 8 Estimate the sum of 373 + 224 using front-end estimation. Then adjust the answer to get a more accurate estimate. = 300 + 200 = 500

Example 9 Mr. Brown drove his new car for 76,845 mi. He sold the car to his brother, who drove it for 34,923 mi. Estimate the total mileage to the nearest thousand miles. 77,000 + 35,000 = 112,000 mi.

HOMEWORK Topic: Estimating examples on pages 74-77 Assignment: Lesson 2.7 in book on pages 77-78 1-27 odd, 43-49 odd (18 total)

HOMEWORK Topic: Estimating examples on pages 74-77 Assignment: Lesson 2.7 in book on pages 77-78 2-28 even, 42-48 even (18 total)