Algebra 1 CHAPTER 2

Practice together:

Properties And simplifying expressions

Warm up – Tuesday **Copy homework in agenda** Solve each question when a = -2, b = 4, c = -1, d = 3

Properties and simplifying expressions Must be able to identify all the properties! 1) Commutative property of addition Numbers can be added in any order and the answer is the same! =

2) Commutative property of multiplication Numbers can be multiplied in any order and the answer is the same! 3 x -4 x 2 = 2 x 3 x -4

3) Associative property of addition Numbers are kept in the same order, but are grouped differently. 3 + (5 + 6) = (3 + 5) + 6

4) Associative property of multiplication Just like the last one (but with multiplication) 3 x (6 x 2) = (3 x 6) x 2

5) Addition property of zero If you add zero to any number it does not change the number = 456

6) Multiplication property of zero If you multiply any number by zero you get zero 12,568 x 0 = 0

7) Multiplication property of one If you multiply any number by one you get the original number. 12,568 x 1 = 12,568

8) Inverse property of addition ** Also called the “additive inverse” -Add the opposite to get zero. -Used to solve equations (to cancel addition)

9) Inverse property of multiplication ** Also called the “multiplicative inverse” - Multiply by the reciprocal in order to get one. -Used to solve equations (to cancel multiplication)

10) Distributive property

Write down your answers only for questions 1-10.

Section 2.2 PROPERTIES AND COMBINING LIKE TERMS

Warm up – Wednesday **don’t forget about the quiz** Evaluate each expression when a=4, b= -3, c = -2

Quick properties review 1.(7 + 8) + 22 = 7 + (8 + 22) 2)13 x 4 x 5 = 13 x 5 x 4 3)8(5m – 3) = 8(5m) – 8(3) 4)22 x 5 x 1 = 110 5)5 x 1/5 = 1 6)-3(4m + 2) = -12m )8 x 7 x 0 = 7 x 8 x 0 8)3 x (5 x 9) = (5 x 9) x 3 9) 2 x = 2 x 7 10) 8 x 11 x 2 = 11 x 8 x 2

2.2 Combining like terms Like terms are terms with the same variable. Note:

Coefficient The number in front of the variable! NOTE: if there is not a number in front of the variable then it is a one!

More challenging! Simplify each expression: 1)4(x – y) – 2(-3x + 6y) = 2) 7(x – 2y) – 3(-x – 2y) = 3) 2x – 3[2x – 3(x + 7) =

Quiz tomorrow *Evaluate variable expressions *Identify all properties *Combine like terms

Review simplifying expressions from yesterday. 1)-5x + 9 – 2x + 8 = 2) -4(3m – 5) + 6m = 3) 3(2x – 6) – 2(x – 3) =

Partner review sheet Each person will work on their assigned side. All of your answers should match your partners answers. You must show your work. You may help your partner solve a problem, but you cannot do the problem for them. Teach them how to solve it! Once you agree and match all your answers raise your hand.

Objective check: 1)3(x – 5) + 2(x + 9) = 2) -3x – x – 3 = 3) -4(2x – 5) + 6(x – 3) =

Quiz on expressions and properties. HAVE YOUR HOMEWORK OUT ON YOUR DESK

Homework check Get out your homework from Monday – Wednesday Monday – Chapter review #15 – 55 odds Tuesday - # 36 – 66 evens Wednesday - # 16 – 24, 40 – 56, 114 – 134

Translating variable expressions SECTION 2.3

Agenda for the week: Tuesday – notes on translating words into expressions. Wednesday – review for Test on chapter 2 Thursday – TEST on chapter 2 Friday – Solving equations

Notes: 2.3 Translating words into variable expressions. Review of vocabulary: Addition: 1)Added to: (8 added to m) = 2)More than: (7 more than e) = 3)The sum of: (The sum of nine and g) = 4)Increased by: (nine increased by w) = 5)The total of: (the total of 7 and e) 6)Plus: (six plus f) = 1)m + 8 2)e + 7 3)9 + g 4)9 + w 5)7 + e 6)6 + f

Subtraction 1)Minus (12 minus e) = 2)Less than (7 less than g) = 3)Less (15 less f) = 4)Subtracted from (12 subtracted from n) = 5)Decreased by (e decreased by 13) = 6)The difference between(the difference between y and 6) = 1)12 – e 2)g – 7 3)15 – f 4)n – 12 5)e – 13 6)y – 6

Multiplication 1)Times (Eight times f) = 2)of (Half of 3e) = 3)The product of (the product of -3 and m) = 4)Multiplied by (e multiplied by 12) = 5)twice (twice m) = 1)8f 2)½ (3e) 3)-3m 4)12e 5)2m

Division 1)Divided by: (12 divided by e) 2)The quotient of: (the quotient of d and 15) 3) The ratio of: (the ratio of 12 and m)

Exponents: 1)The square of: (the square of x) 2)The cube of: (the cube of m)

Practice: 1)The total of five times b and c. 2)The quotient of 8 less than n and five. 3)Thirteen more than the sum of x and 9. 4)The difference between the square of m and the sum of x and y.

Practice (you try) 1)y decreased by the sum of e and six. 2)n added to the product of 8 and the square of e. 3)Twenty decreased by y less 8. 4)Five times the product of seven and a number e. ** Seven increased by a number added to twice the difference between a number and 2.

Practice with word problems: 1)The length of the swimming pool is 20 feet longer than the width. Express the length of the pool in terms of width. 2)An investor divided 5000 between two accounts. Use one variable to express the amounts invested in each account. 3)A coin bank contains thirty-five coins in nickels and dimes. Use the same variable to express the number of nickels and the numbers of dimes in the coin bank.

Practice(Solve and then check) 1)d increased by the difference between sixteen times d and 3. 2)Four less than the product of seven and the square of a number 3)The cube of e decreased by the product of 12 and e. 4)Five more than the quotient of four times e and two. 5)Seven more than the total of eight and a number. 6)Eight less m divided by the total of e and 6.

Practice (you try) 1)y decreased by the sum of e and six. 2)n added to the product of 8 and the square of e. 3)Twenty decreased by y less 8. 4)Five times the product of seven and a number e.

Review for test CHAPTER TWO