1. CHAPTER 2
Expressions

2. 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)

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

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

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

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

7. 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)

9. 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)

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

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

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

13. 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)

14. 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)

16. 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.

17. 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)

18. 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

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

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

21. 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

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

23. 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

24. 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

25. 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)

26. 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)

28. 2.6 Translating Word Phrases
Addition Key Words
added to
sum
increased by
more than
plus

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

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

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

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

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

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

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

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

37. Exercise 6
“an even integer” 2n

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

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

40. 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)

41. 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)

43. 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

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

45. Example 2
Estimate the sum by rounding to the nearest ten.
= = 130

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

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

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

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

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

51. Example 8
Estimate the sum of using front-end estimation. Then adjust the answer to get a more accurate estimate.
= = 500

52. 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 = 112,000 mi.

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

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