Algebra 1 Notes Section 2.1: Use Integers and Rational Numbers Name: Hour: Objective: You will graph and compare positive and negative numbers. Vocabulary: I. Whole Numbers: The numbers 0, 1, 2, 3,... II. Integers: The numbers consisting of the (see the glossary) integers,, and the integers. a III. Rational Number: A number that can be written as b where (see the glossary) and are and. Rational numbers belong to the set of numbers called the real numbers. In decimal form, a rational number either or..., 3, 2, 1, 0, 1, 2, 3,... negative zero positive a b integers b 0 repeats terminates numbers IV. Opposites: Two that are the same distance 0 number line from on a but are on opposite sides of 0. V. Absolute Value: The absolute value of a number is the between and on a number line. The symbol represents the a distance a 0 a absolute value of a Absolute Value of a Number Words Example If a is positive, then a = a 2 = 2 If a is 0, then a = 0 0 = 0 If a is negative, then a = a 2 = ( 2) = 2 statement hypothesis VI. Conditional Statement: A with a and a conclusion. If a is a positive number, then a = a. false counterexample satisfied An if-then statement is if for just one example, called a, the conclusion is when the hypothesis is. false
Examples: Notes 2.1 page 2 1 1 1 1 1. Order the numbers from least to greatest:,,,, 2, 0 10 9 7 8 2. Tell whether each of the following numbers is a whole number, an integer, and/or a rational number: (List each term that applies.) 1 a. -19 b. 7 c. 0.3 d. 1 e. 0. 6 5 3. The apparent magnitude of a star is its brightness as observed from Earth. The greater the magnitude, the dimmer the star. Order the stars from brightest to dimmest. Star Arcturus Sirius Vega Magnitude 0.06 1.47 0.03 4. For the given value of x, find x. a. x = 3 b. x = 0.65 c. x = 1.75 8 5. For the given value of x, find x. a. x = 16.2 b. x = 3.45 c. x = 2 3 6. Identify the hypothesis and conclusion of the statement below. Then tell whether the statement is true or false. If false, give a counterexample. "If a number is an integer, then the number is either positive or negative."
Algebra 1 Notes Section 2.2: Add Real Numbers Date: Section 2.3: Subtract Real Numbers Section 2.4: Multiply Real Numbers Objectives: Section 2.2: Section 2.3: Section 2.4: You will add positive and negative numbers. You will subtract real numbers. You will multiply real numbers. Vocabulary: Section 2.2: I. Rules of Addition: To add two numbers with the same sign, add their absolute values. The sum has the same sign as the numbers added. different To add two numbers with signs, lesser absolute value the from the greater absolute value. The sum has the same sign as the number with the greater absolute value. subtract II. Properties of Addition: Commutative Prop. of Addition: order The in which you two numbers does not change the sum. add Associative Prop. of Addition: The way in which you in a does not group three numbers sum change the sum. Identity Prop. of Addition: sum of a number and 0 is the number The (p. 76) 0 additive identity The number is the Inverse Prop. of Addition: sum of a number and its opposite is 0 The (p. 76) a additive inverse The opposite of is its Section 2.3: III. Subtraction Rule: b a add the opposite of b to a To subtract from, (p. 81) The change in a quantity is the difference of the amount and original the amount. new
Notes 2.2-2.4 page 2 Section 2.4: same IV. The Sign of a Product: The product of two real numbers with the sign is. different positive negative The product of two real numbers with signs is. V. Properties of Multiplication: Commutative Prop. of Mult: order The in which you two numbers does not multiply change the product. Associative Prop. of Mult: The way in which you in a product does not group three numbers change the product. Identity Property of Mult.: product of a number and 1 is that number The (p. 89) 1 multiplicative identity The number is called the Multiplication Property of Zero: product of a number and 0 is 0. The Multiplication Property of 1: product of a number and 1 is the opposite of The the number
Examples: Notes 2.2-2.4 page 3 1. Perform the indicated operation. a. 8.4 + ( 0.7) b. 9 ( 12) c. 8 ( 6) d. 12.6 + 7.3 e. 18 3 f. 2(3.5)( 4) g. 25 ( 14) h. 12 3 2. Identify the property being illustrated. a. 11.9 + 11.9 = 0 b. 7 0 = 0 c. 2 + 0 = 2 1 4 d. x 1 = x e. 1 ( 13) = 13 f. 8 + ( x) = x + ( 8) g. a b = b ( a) h. ( 2.5 x) ( 4) = 2.5 (x ( 4)) 3. The following is a step-by-step way to simplify 2 (x ( 0.5)). Justify each step with the name of the property used. 2 (x ( 0.5)) = 2 ( ( 0.5) x) = (( 2) ( 0.5)) x = (1) x = x 4. The table shows how much weight two dieters lost or gained per month. Which dieter had the greater weight loss at the end of three months? Month Dieter A Dieter B 1 3.3 7.8 2 5.1 +1.2 3 +0.5 0.8 5. Evaluate the expression 2x y + ( 5) (( 2) x) when x = 3 and y = 4. 6. The temperature one morning was 14 C. By midday, the temperature was 3 C. What was the change in temperature? 7. From 1900 to 1940, a 250-foot wide beach on the Atlantic coast was eroding at a rate of about 0.02 feet per year. From 1940 to 2000, it was eroding at a rate of about 0.12 feet per year. Approximate the width of the beach in 2000.
Algebra 1 Notes Section 2.5: Apply the Distributive Property Objective: You will apply the distributive property. Vocabulary: expressions same I. Equivalent Expressions: Two that have the value for all values variable of the. property product II. Distributive Property: A that can be used to find the (see the glossary) of a number and a sum or difference. expression III. Term: The parts of an that are added together. number term IV. Coefficient: The part of a with a variable part. term number no V. Constant Term: A with a part but variable part. VI. Like Terms: Terms that have the same variable parts Constant terms are also like terms. The Distributive Property Let a, b, and c be real numbers. Words Algebra Examples The product of a and (b + c): The product of a and (b c): a(b + c) = ab + ac (b + c)a = ba + ca a(b c) = ab ac (b c)a = ba ca 3(4 + 2) = 3(4) + 3(2) (3 + 5)2 = 3(2) + 5(2) 5(6 4) = 5(6) 5(4) (8 6)4 = 8(4) 6(4)
Examples: Notes 2.5 page 2 1. Use the distributive property to write an equivalent expression. a. 3(x + 6) b. (x + 5)x c. x(x 12) d. (8 x)9 e. (x 2)( 4) f. 5x(4 x) g. (3x 9) 2. Identify the terms, like terms, coefficients, and constant terms of the expression 2x 8 + 6x + 5. Terms: Like Terms: Coefficients: Constant Terms: 3. Which expression is equivalent to 6(x + 3) 2(8 + x)? a. 4x + 2 b. 4x + 34 c. 8x + 2 d. 8x + 34 4. Ms. Jenkins rented a rototiller from a garden shop. The rental charge is $28 per day for the first two days and then $15 per day for each additional day. If Ms. Jenkins kept the rototiller for 13 days, what was the total rental charge?
Algebra 1 Notes Section 2.6: Divide Real Numbers Objective: You will divide real numbers. Vocabulary: reciprocal nonzero I. Multiplicative Inverse: The of a number 1 a, written a. II. Reciprocal: III. Mean: IV. Inverse Property of Multiplication: Two nonzero numbers whose product is 1. Every number except 0 has a reciprocal. The sum of the values of a data set divided by the number of values in the set. product The of multiplicative inverse is 1. a nonzero number and its divide a number a by a nonzero number b, V. Division Rule: To multiply a by the multiplicative inverse of b. VI. The Sign of a Quotient: same positive The quotient of two real numbers with the sign is different The quotient of two real numbers with signs is nonzero 0 The quotient of 0 and any real number is negative VII. Rules for Addition, Subtraction, Multiplication, and Division: Let a and b be real numbers Expression a + b a b a b a b Positive if... the number with the greater absolute value is positive. a > b a and b have the same sign (a 0, b 0). a and b have the same sign (a 0, b 0). Negative if... the number with the greater absolute value is negative. a < b a and b have different signs (a 0, b 0). a and b have different signs (a 0, b 0). Zero if... a and b are additive inverses. a = b a = 0 or b = 0 a = 0 b 0 and
Examples: Notes 2.6 page 2 1. Find the multiplicative inverse of the number. a. 1 b. 7 5 c. 3 2 d. 5 9 2. Find the quotient. 8 a. 18 (-3) b. 16 c. 3 3 2 5 5 3. Andy recorded the low temperature each night at his home during January. Over five consecutive nights, he recorded the temperatures -2 C, -10 C, 6 C, -1 C, and 2 C. What was the mean low temperature at his home for these nights? 4. Simplify the expression. a. 40x 32 8 b. 20x 5 5
Algebra 1 Notes Section 2.7: Find Square Roots and Compare Real Numbers Objective: You will find square roots and compare real numbers. Vocabulary: b 2 = a b square root a I. Square Root: If, then is a of. nonnegative The radical symbol represents a square root. II. Radicand: The or inside a symbol. number expression radical III. Perfect Square: (see the glossary) A number that is the square root of an integer cannot quotient IV. Irrational Number: A number that be written as a of two integers decimal form. The of an irrational number neither terminates nor repeats rational irrational V. Real Numbers: The set of all and numbers. Real Numbers
Examples: Notes 2.7 page 2 1. Evaluate the expression. a. 100 b. 121 c. 400 2. The top of a square box has an area of 320 square inches. Approximate the side length of the box top to the nearest inch. 3. Tell whether each of the following numbers is a real number, a rational number, an irrational number, an integer, or a whole number. (circle all terms that apply.) a. 25 Whole Integer Rational Irrational Real b. 121 Whole Integer Rational Irrational Real c. 30 Whole Integer Rational Irrational Real d. 0 Whole Integer Rational Irrational Real e. 4 Whole Integer Rational Irrational Real 4. In the diagram shown, place each number in the one most specific set to which it belongs. Rational Real Numbers Irrational 2 13, 0.7,, 144, 5, 0, 0.3,, 5 6 49 Integers Whole Numbers 19 4. Order the numbers from least to greatest: 10,, 3, 12, 16 5 5. Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. a. All negative numbers are rational numbers. b. All integers are rational numbers.