 # ~ Chapter 1 ~ Algebra I Algebra I Tools of Algebra

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~ Chapter 1 ~ Algebra I Algebra I Tools of Algebra
Lesson Using Variables Lesson Exponents & Order of Operations Lesson Exploring Real Numbers Lesson Adding Real Numbers Lesson Subtracting Real Numbers Lesson Multiplying & Dividing Real Numbers Lesson The Distributive Property Lesson Properties of Real Numbers Lesson Graphing Data on the Coordinate Plane Chapter Review

Using Variables Lesson 1-1 Notes
Variable – a symbol that represents one or more numbers. Examples – x, y, q, r, s, n … Algebraic Expression – a mathematical phrase that can include numbers, variable, and operation symbols. (no equal sign) Examples ~ 2n , , n , 27x – 4y … 9 Main Menu

Lesson 1-1 Using Variables Notes Lesson 1-1 Using Variables Notes
Writing an Algebraic Expression Add – Terms -> sum, altogether, more than, greater than… Subtract – terms -> difference, minus, less than… Multiply – terms -> product, times, multiplied by, twice, triple… Divide – terms -> quotient, divided by, half, third… Writing an Algebraic Expression Add – Terms -> sum, altogether, more than, greater than… Subtract – terms -> difference, minus, less than… Multiply – terms -> product, times, multiplied by, twice, triple… Divide – terms -> quotient, divided by, half, third… Main Menu

Using Variables Lesson 1-1 Notes Examples: Five more than a number
The difference of five and a number 5 - x Five less than x x - 5 The product of five and a number 5n The quotient of a number and five n ÷ 5 Main Menu

Using Variables Lesson 1-1 Notes More complex algebraic expressions:
Two times a number plus five 2n + 5 Seven less than five times a number 5x - 7 Four more than the quotient of a number and six (n ÷ 6) + 4 Main Menu

Using Variables Lesson 1-1 Notes
Equation – a mathematical sentence that uses an equal sign. (Ex: 2+3 = 5, 4x=8,…) Open sentence – an equation that contains one or more variables. (Ex: 2x=8, 3x+2y = 10) Writing an Equation Track One Media sells all CD’s for \$12 each. Write an equation for the total cost of a given number of CD’s. Know: The total cost is 12 times the number of CD’s Define: Let n = of CD’s Let c = total cost Write: c = 12n or 12n = c Main Menu

Using Variables Lesson 1-1 Notes Number of Hours Total Pay 4 \$32 6 \$48
\$64 10 \$80 Know: Number of hours times 8 equals the total pay Define: Let n = number of hours Let t = total pay Write: 8n = t or t = 8n Main Menu

Notes – Practice Problems
Lesson 1-1 Using Variables Notes – Practice Problems the quotient of 6.3 and b 6.3 ÷ b s minus ten s - 10 9 less than a number n - 9 The sum of twice a number and thirty-one 2x + 31 The product of one half of a number and one fourth of the same number ½ n ( ¼ n) Main Menu

Lesson 1-1 Using Variables Homework Practice 1-1 ~ all ~ Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Daily Math Review Main Menu

Using Variables Lesson 1-1 Homework - Answers ?????? Questions ???????

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Notes Simplify – replace an expression with its simplest name or form. Exponents – A number that shows repeated multiplication. (In 24 ~ 4 is the exponent) Base – The number that is multiplied repeatedly in a power. (In 24 ~ 2 is the base) Power – has two parts, a base and an exponent, and has the form an. Order of operations – GEMS – (1) grouping symbols; (2) Exponents; (3) Multiply & Divide (left to right) (4) Subtract & Add (left to right) Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Notes Simplifying a Numerical Expression 25 – 8 * * 4 – 22 3 + 5 – 6 ÷ 2 6 – 10 ÷ 5 3 2 4 1 18 3 2 4 1 18 2 3 1 5 2 1 4 Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Notes Evaluating an Algebraic Expression 3a – 23 ÷ b for a = 7 and b = 4 3 * 7 – 23 ÷ 4 Example: A shirt costs \$22.85 plus sales tax. What is the total cost of the shirt? Expression - p + p * r ( p = price; r = tax) c = \$ \$22.85(0.07) = \$ \$ = c = \$24.45 2 4 3 1 19 Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Practice 3 * 6 – 42 ÷ 2 4 * ÷ 22 ÷ 10 Evaluate the following for c = 2 and d = 5 4c – 2d ÷ c c4 – d * 2 d + 6c ÷ – d2 + cd * 3 Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Notes Expressions with parenthesis 15(13 – 7) ÷ (8 - 5) (5 + 3) ÷ 2 + (52 – 3) 15(6) ÷ (3) (8) ÷ 2 + (25 – 3) 90 ÷ Expressions with Exponents (cd)2 for c = 7 & d = 19 (7 * 19)2 (133)2 = 17,689 Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Notes m2n for m = 5 & n = 4 52 * 4 = 25 * 4 = 100 Evaluate the following for m=3, q=4, p=7 qp2 + q2p m(pq)2 4* *7 3(7*4)2 4* *7 3(28)2 = (784) = 2,352 Simplifying an expression 2[(13-7)2 ÷3] 24 Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Practice 5[4 + 3(22+1)] 28 ÷ [(19 -7) ÷ 3] 5[4 + 3(4+1)] 28 ÷ [(12) ÷ 3] 5[4 + 3(5)] 28 ÷  = 7 5[4 + 15] 5 = 95 9 + [4 – (10 – 9)2]3 9 + [4 – (1)2]3 9 + [4 – 1]3 9 + 3 = 36 Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Homework Practice ~ even ~ Main Menu

Exploring Real Numbers
Lesson 1-3 Exploring Real Numbers Daily Math Review Main Menu

Exponents & Order of Operations
Lesson 1-2 Exponents & Order of Operations Homework - Answers ?????? Questions ??????? Main Menu ?????? Questions ???????

Exploring Real Numbers
Lesson 1-3 Notes Natural Numbers – counting numbers ~ 1, 2, 3… (not 0) Whole Numbers – non-negative integers ~ 0, 1, 2, 3, 4… Integers – whole #’s & their opposites ~ …-2, -1,0,1,2… Rational Numbers – numbers that can be written as a/b where b ≠ 0. Decimal form is a terminating or repeating decimal. Irrational Numbers – numbers that cannot be expressed in the form a/b where a & b are integers. (Ex ~ π, √10, …) Classify the following integer, rational number rational number /12 natural number, whole number, rational number integer, rational number Main Menu

Exploring Real Numbers
Lesson 1-3 Notes Counterexample – Any example that proves a statement false… All Whole numbers are rational numbers T or F All integers are whole numbers. T or F The square of a number is always greater than the number. T or F All whole numbers are integers. T or F No fractions are whole numbers. T or F Inequality (>, <, ≥ , ≤ , ≠ ~ used to compare the value of two expressions) Ordering fractions Write fractions as a decimal and then compare Find the common denominator, convert, and then compare Absolute value – distance a number is from l-19l = l22l = 22 Main Menu

Lesson 1-4 Notes Adding Real Numbers
Identity Property of Addition - n + 0 = n, for every real number n. Inverse Property of Addition – n + (-n) = 0 (additive inverse is the opposite of a number) Rules for Adding Numbers with the same signs – add and keep the sign. Numbers with different signs – subtract, answer takes the sign of the number with the greatest absolute value. Examples -7 + (-4) -3/4 + (-1/2) 8/9 + (-5/6) -1 ¼ 1/18 Main Menu

Lesson 1-4 & 1-5 Notes Evaluating Expressions -n for n = t + (-4.3) for t = -7.1 Matrix Subtracting Real Numbers Leave, change, opposite… (then use the rules for addition) 3 – 5 = 3 + (-5) = (-5) = = 8 ¾ - (-11/12) = Main Menu

Subtracting Real Numbers
Lesson 1-5 Notes Absolute Values l 5-11 l = l 7 – 8 l = Evaluating Expressions -a – b for a = -3 & b = -5 -(-3) – (-5) = = 8 Subtract with Matrices _ Main Menu

Homework Real Numbers Practice 1-3 - every 3rd problem
Lesson 1-3, 1-4, & 1-5 Real Numbers Homework Practice every 3rd problem Practice 1-4 – every 3rd problem Practice 1-5 – every 3rd problem & #35 Main Menu

Homework - Answers Real Numbers Lesson 1-5 ?????? Questions ???????

Multiplying & Dividing Real Numbers
Lesson 1-6 Notes Identity Property of Multiplication ~ 1 * n = n Multiplication Property of Zero ~ n * 0 = 0 Multiplication Property of -1 ~ -1 * n = -n Rules for Multiplying & Dividing Like/same signs – answer is positive. Different signs – answer is negative. Simplifying Expressions -6 * -5 = ( -15/3) = * 4.1 = (-2) (3/4)2 -(4*4*4) (-2)(-2)(-2)(-2) ( ¾ * ¾) /16 Main Menu

Multiplying & Dividing Real Numbers
Lesson 1-6 Notes Evaluating Expressions -(cd) (-2)(-3)(cd) for c= -8 and d= -7 -(-8*(-7)) (-2)(-3)(-8*(-7)) 3x ÷ 2z + y ÷ z+x/2y for x = 8, y = -5, & z = -3 3(8) ÷ 2(-3) + (-5) ÷ [2(-3) + (8)]/2(-5) 24 ÷ (-6) + (-5/10) [-6 + 8]/-10 -4 + (-1/2) /-10 -4 ½ /5 Inverse Property of Multiplication ~ a ≠ 0, a (1/a) = 1 x/y x = -3/4 and y = -5/2 -3/4 ÷ (-5/2) (the reciprocal or multiplicative inverse is used) -3/4 x (-2/5) = 6/20 = 3/10 Main Menu

Properties of Real Numbers

The Distributive Property
Lesson 1-7 Notes Distributive Property ~ a(b + c) = ab + ac; (b + c)a = ba + ca a(b – c) = ab – ac; (b – c)a = ba – ca Simplifying Expressions 13(103) = 13( ) (98) = = 13(100) + 13(3) = = 1339 6(m + 5) (3-7t) ( c)(3) 6m – 14t c Terms, constants, and coefficients… 6a2 – 5ab + 3b – (a2, ab, and b are all unlike terms) Like terms are combined to simplify an expression… 3x2 + 5x y + 6y w3 - 3w3 Main Menu

Multiplying & Dividing Real Number & The Distributive Property
Lesson 1-6 & 1-7 Notes & Homework Writing an Expression… -2 times the quantity t plus 7 -2(t + 7) The product of 14 and the quantity 8 plus w 14(8 + w) Main Menu

Properties of Real Numbers
Lesson 1-8 Notes Commutative Property of Addition ~ a + b = b + a Commutative Property of Multiplication ~ a * b = b * a Associative Property of Addition ~ (a + b) + c = a + (b + c) Associative Property of Multiplication ~ (a * b) * c = a * (b * c) Identity Property of Addition ~ a + 0 = a Identity Property of Multiplication ~ a * 1 = a Inverse Property of Addition ~ a + (-a) = 0 Inverse Property of Multiplication ~ a (1/a) = 1 Distributive Property Multiplication Property of Zero Multiplication Property of -1 Identify the property… = m = m np = pn =2 Main Menu

Properties of Real Numbers
Lesson 1-8 Notes Using Deductive Reasoning – logically justifying the reason (the why) for each step in simplifying an expression using properties, definitions, or rules. Simplify the expression… Justify each step 7z – 5(3 + z) Step Reason 7z – z Distributive Property 7z +(-15) + (-5z) Rules for subtraction 7z + (-5z) + (-15) Commutative property of addition 2z + (-15) addition of like terms 2z – rules for subtraction Main Menu

Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9 Notes 2(3t – 1) + 2 Step Reason 6t – Distributive property 6t +(-2) Rules/defn of subtraction 6t addition Homework Practice 1-7 & 1-8 even;-) Main Menu

Subtracting Real Numbers
Lesson 1-5 Subtracting Real Numbers Quiz Lesson 1-1 to 1-4 Main Menu

Properties of Real Numbers

Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9 Properties of Real Numbers & Graphing on the Coordinate Plane Homework Answers Main Menu

Graphing on the Coordinate Plane
Lesson 1-9 Notes Graphing Data on the Coordinate Plane A coordinate plane has an x-axis (horizontal) and a y-axis (vertical) An ordered pair (x, y) are the numbers that identify the specific location of a point. y-axis (0,0) origin origin (-,+) (+,+) Quadrant II Quadrant I x-axis Quadrant IV Quadrant III (+,-) (-,-) Main Menu

Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9 Notes Identifying & Graphing Points Use the (x, y) location to identify the location of a point. Graph C(0,3); D (2,4); E(-1,-4); F(-3,0) Quadrant? (-2,0) (4,-1) (-3,-5) (2.7,3.6) Can we find the dimensions of a shape when we graph it? Scatter Plot Graph that relates data of two different sets. Scattered points do not form a line. (Usually graphed in Quadrant I) A trend line can show trend of the data in a scatter plot. Main Menu

Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9 Properties of Real Numbers & Graphing on the Coordinate Plane Practice Homework Practice 1-8 & 1-9 odd Main Menu

Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9 Properties of Real Numbers & Graphing on the Coordinate Plane Homework Answers Main Menu