Algebra I. Ch. 2. Notes and Worksheets

Transcription

1 Algebra I Ch. Notes and Worksheets

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3 Rational Numbers: Natural Numbers: Whole Numbers: Integers: Rational Numbers: Date: Section : Rational Numbers on the Number Line Notes Example #: Name the coordinates of the points graphed on each number line. Example #: Graph each set of numbers. a.),0,, b.) {.5,0,.5,... } c.) {integers less than 6, or greater than or equal to }

4 Absolute Value: Example #: Find each absolute value. a.) 5 b.) 0. 5 c.) 5 8 Example #4: Evaluate the following expressions. a.) y if y =. b.) x 5 if x = 5.

5 Steps to Add Decimals:.. Section -: Adding and Subtracting Decimals Notes Part Example #: Find the sum. Show all work! a.) = b.) = Date: c.) = d.) Example # : Mr. Coles has $40. in his pocket. Mrs. Wilkes gives him another $5.75. Mrs. Hart also gives him $0.08. How much does Mr. Coles now have? Show all work!

6 Steps to Subtract Decimals:... Example #: Find the difference. Show all work! a.) = b.) -.7 (- 5.) = c.) = d.) = Example #4: In the past year the price of a Steeler s game ticket went from $55.76 to $ Find the change in the price of a ticket. Show all work!

7 Steps to Add Fractions: Least Common Denominator Section -: Adding and Subtracting Fractions Notes Part 4 Date: Example #: Find the sum. Show all work! 5 a. + = b. + = c. = d. =

8 Steps to Subtract Fractions: Example #: Find the difference. Show all work! 4 4 a.) = 5 b.) = c.) = 5 d.) = 0 7 Example #: Gabrielle and Nick are subtracting fractions. Who is correct? Explain your reasoning in a few sentences.

9 Section -: Adding Rational Numbers Notes Part Using your counters, find each sum of the following problems. Date:.) ) +.) ) - + (- 4) 5.) ) ) 8 + (- ) 8.) ADDITION RULES When numbers have the same sign: When numbers have different signs: Find each sum of the following problems using the Addition Rules..) ) 5 + (- 9).) ) ) ) ) ) + 4 4

10 Example #: Kevin was playing a computer trivia game. His scores for each round were + 00, + 00, + 500, - 00, + 400, and 500. What was his total score at the end of his game? Show all work. Example 4: The Pittsburgh Steelers offense began a drive from their 0 - yard line. They gained 6 yards on the first down, lost 8 yards on the second down, then gained yards on the rd down. a.) What yard line were they on at the fourth down? Show all work. b.) How many yards do they need to gain to get another first down?

11 Section -: Subtracting Rational Numbers Notes Part ADDITION RULES When numbers have the same sign: Date: When numbers have different signs: SUBTRACTION RULE Find each difference of the following problems using the Subtraction Rule..) 4 -.) 8-5.) ) - 0 (- 4) 5.) 6 (- 4) 6.) ) (-.9) 8.) Example #: In the past year, a publishing company s stock went from $5 per share to $7 per share. Find the change in the price of the stock. Show all work!

12 MULTIPLICATION RULES Section -: Multiplying Rational Numbers Notes Date: Example : Find each product. a.) (- 4) (- ) = b.) 6 8 = c.) five times negative = d.) (- 9) x ( 7) = 4 8 e.) = f.) = 5 Example : Evaluate each expression if a = -, b = 5, and c = Show all work. a.) 5b b.) 4ab c.) ab d.) b e.) ( b) a f.) ac + ( a)

13 Example : Americans use about.5 million plastic bottles every hour. a.) How many plastic bottles are used in one day? Show all work. b.) How many bottles are used in one week? Show all work. Example 4: In a United States flag, the length of the union is 5 of the fly, and the width is 7 of the hoist. If the fly is 6 feet, how long is the union? Show all work. Example 5: The value of a company s stock dropped by $.5 per share. By what amount did the total value of the company s stock change if the company has issued 500,000 shares of stock? Show all work.

14 Section -4: Dividing Rational Numbers Notes Date: DIVIDING RULES: Example : Find each quotient. a.) 60 5 = b.) = 4 c.) 0 divided by 5 d.) 6 = e.) -.6 f.) g.) = h.) 4 4 = Example : Evaluate each expression if g = -, h = 7, and k = - 4. Show all work. a.) g h k b.) hk g

15 Example : The perimeter of a square baseball diamond is 60 feet. Find the length of one side of the diamond. Show all work. Example 4: Carlesha is making pillows. The pattern states that she needs of fabric for each pillow. If she has make? Show all work. yards 4 4 yards of fabric, how many pillows can she Example 5: Germal works 9 days at the mall and earns $ If he works eight hours each day, what is his hourly pay? Show all work.

16 - NAME DATE PERIOD Practice Rational Numbers on the Number Line Name the coordinates of the points graphed on each number line Graph each set of numbers ,,,,, 4. {integers less than 4 or greater than } Find each absolute value Evaluate each expression if a 4, b, c, x 4, y.4, and z z 0. a 0. x y 0. b 4. b 5. c 6. c 4 ASTRONOMY For Exercises 7 9, use the following information. The absolute magnitude of a star is how bright the star would appear from a standard distance of 0 parsecs, or.6 light years. The lower the number, the greater the magnitude, or brightness, of the star. The table gives the magnitudes of several stars. 7. Use a number line to order the magnitudes from least to greatest Which of the stars are the brightest and the least bright? Star Magnitude Altair. Betelgeuse 7. Castor 0.5 Deneb 4.7 Pollux 0.7 Regulus 0. Rigel 8. Sirius.4 9. Write the absolute value of the magnitude of each star Source: 0. CLIMATE The table shows the mean wind speeds in miles per hour at Daytona Beach, Florida. Source: National Climatic Data Center Graph the wind speeds on a number line. Which month has the greatest mean wind speed? Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Glencoe/McGraw-Hill 78 Glencoe Algebra

17 - Find each sum ( 9) 4. 8 ( ) ( 0.9) 0... NAME DATE PERIOD Practice Adding and Subtracting Rational Numbers ( 9.06) Find each difference ( 7) 5. ( 9) (.4) ( 4.7) FINANCE For Exercises 5 7, use the following information. The table shows activity in Ben s checking account. The balance before the activity was $ Deposits are added to an account and checks are subtracted. Number Date Transaction Amount Balance 5/ deposit /0 check to Castle Music 5.50? 0 6/ check to Comp U Save 5.40? 5. What is the account balance after writing check number 0? 6. What is the account balance after writing check number 0? 7. Realizing that he has just written a check for more than is in the account, Ben immediately deposits $45. What will this make his new account balance? 8. CHEMISTRY The melting points of krypton, radon, and sulfur in degrees Celsius are 56.6, 6.8, and.8, respectively. What is the difference in melting points between radon and krypton and between sulfur and krypton? Glencoe/McGraw-Hill 84 Glencoe Algebra

18 - Find each product.. 4(7). 8( 7). 5( 4) NAME DATE PERIOD 8 Practice Multiplying Rational Numbers 0. (.5)(8.8). (6.8)(.). ( 0.)(.8). (.6)( 0.55) 4. 6.( 0.7) 5. ( 4)(9) Simplify each expression. 6. 5( a) 8a 7. 8(4c) c 8. 9(g g) 9. 7(b 4b) 0. 4x(y) ( b)( d). 5p( q) (4m)( 6n) 4 Evaluate each expression if a, b, c.4, and d b. 4ab 4. 5a ( b) 5. 6d 6. cd 7. c ( 5d) 8. RECIPES A recipe for buttermilk biscuits calls for cups of flour. How many cups of flour do you need for the recipe? COMPUTERS For Exercises 9 and 0, use the following information. Leeza is downloading a file from a Web site at 47. kilobytes per second. 9. How many kilobytes of the file will be downloaded after one minute? 0. How many kilobytes will be downloaded after 4.5 minutes? CONSERVATION For Exercises and, use the following information. A county commission has set aside 640 acres of land for a wildlife preserve.. Suppose of the preserve is marshland. How many acres of the preserve are 5 marshland?. If the forested area of the preserve is.5 times larger than the marshland, how many acres of the preserve are forested? Glencoe/McGraw-Hill 90 Glencoe Algebra

19 - NAME DATE PERIOD Reading to Learn Mathematics Multiplying Rational Numbers Pre-Activity How do consumers use multiplication of rational numbers? Read the introduction to Lesson - at the top of page 79 in your textbook. How is the amount of the coupon shown on the sales slip? Besides the amount, how is the number representing the coupon different from the other numbers on the sales slip? Reading the Lesson. Complete: If two numbers have different signs, the one number is positive and the other number is.. Complete the table. Multiplication Are the signs of the numbers the same Is the product positive or negative? Example or different? a. ( 4)(9) b. ( )( ) c. 5( 8) d. 6(). Explain what the term additive inverse means to you. Then give an example. Lesson - Helping You Remember 4. Describe how you know that the product of and 5 is positive. Then describe how you know that the product of and 5 is negative. Glencoe/McGraw-Hill 9 Glencoe Algebra

20 -4 NAME DATE PERIOD Find each quotient.. 75 ( 5). ( 7) ( 9) (.5) Practice Dividing Rational Numbers Simplify each expression. 68p 5 x t x y 8k h 4c ( 6d) Evaluate each expression if p 6, q 4.5, r.6, and s 5.. Round to the nearest hundredth. qr rs ps qr p q p q r s 9. rs pq 0.. r q. EXERCISE Ashley walks miles around a lake three times a week. If Ashley walks d around the lake in hour, what is her rate of speed? (Hint: Use the formula r, 4 t where r is rate, d is distance, and t is time.). PUBLICATION A production assistant must divide a page of text into two columns. If the page is 6 inches wide, how wide will each column be? 4 ROLLER COASTERS For Exercises 4 and 5, use the following information. f s The formula for acceleration is a t starting speed, and t is time., where a is acceleration, f is final speed, s is 4. The Hypersonic XLC roller coaster in Virginia goes from zero to 80 miles per hour in.8 seconds. What is its acceleration in miles per hour per second to the nearest tenth? Source: 5. What is the acceleration in feet per second per second? (Hint: Convert miles to feet and hours to seconds, then apply the formula for acceleration. mile 80 feet) Glencoe/McGraw-Hill 96 Glencoe Algebra

21 -4 NAME DATE PERIOD Reading to Learn Mathematics Dividing Rational Numbers Pre-Activity How can you use division of rational numbers to describe data? Read the introduction to Lesson -4 at the top of page 84 in your textbook. What is meant by the term mean? In the expression negative? ( 7) 4 ( 65), will the numerator be positive or Reading the Lesson. Explain what the term inverse operations means to you.. Write negative or positive to describe the quotient. Explain your answer. Expression Negative or Positive? Explanation a. 5 7 b. 78 c. ( 5.6)(.4).9 Helping You Remember. Explain how knowing the rules for multiplying rational numbers can help you remember the rules for dividing rational numbers. Lesson -4 Glencoe/McGraw-Hill 97 Glencoe Algebra