714 Gluck 1/4-1 k. Me 4- e-7- r I L -j LJ 'J [ -Z Integers Integers greater than 0 are positive integers. Integers less than 0 are negative integers. negative integers positive integers 7 6 5 4 3 2 1 I) 1 2 3 4 Two numbers are opposites if, on the number line, they are the same distance from 0, but on opposite sides of 0. The number line below shows that 5 and 5 are opposites. ( 1 5 units 5 units 1 1 1-1 1 1 1 1 1 1 I 1 1 7 6 5 4 3 2 1 0 1 2 3 4 5 6 The absolute value of an. integer is its distance from 0 on the number line. 5 is 5 units from 0. The absolute value of 5 is 5. 5 is 5 units from 0. The absolute value of 5 is 5. 151=5 I 5 1 5 Write an integer for each situation. 1. 6 F below zero 2. a gain of 40 pounds 3. a profit of $4 4. a loss of 10 points 5. 68 F above zero 6. falling 3 feet Write the integer represented by the point for each letter. Then find its opposite and its absolute value. <- Q Z S V Y R W T I 4 7 6 5 4 3 2 1 0 1 2 3 7. Q 8. R X + I + 6 7 8 9. S 10. 7' 11. V 12. W 13.X 14. Y 15. Z Glencoe/McGraw-Hill Mathematics: Applications 34 and Connections, Course 2
Date Integers Write an integer for each situation. 1. a gain of 14 yards 2. a loss of $15 3. 24 above zero 4. 3 points lost 5. a deposit of $40 6. a withdrawal of $100 7. 9 below zero 8. a profit of $49 9. a drop of 18 10. a loss of 10 pounds 11. a bonus of $140 12. a wage increase of $150 Write the integer represented by the point for each letter. Then find its opposite and its absolute value. A 8 C D E F G 10 8 6 10 13. A 14. B 15. C 16. D 17. E 18. F 19. G 20. H 21. I 22. What is the least positive integer? 23. A submarine is 2,000 meters below sea level. Write this depth as an integer. Glencoe/McGraw-Hill 34 Mathematics: Applications and Connections, Course 2
Name Date Practice Decimals and Fractions Write each repeating decimal using bar notation. 1. 0.4666666... 2. 0.5833333... 3. 0.1272727... Express each fraction or mixed number as a decimal, If the decimal is a repeating decimal, use bar notation. 3 z 19 4. 20 6. 31 7 23 19 50 25 n 46 "' 180 11 40 12. 37 13. 14-50 14. 8i 15. 3+ Replace each 16. 4 0 4 9 0 with <, >, or = to make a true sentence. 17. 1121-0:3) 18. 1 1.375 19 2 22 20. 2.78 2-1-9 ' 25 250 50 Glencoe/McGraw-Hill Mathematics: Applications 14 and Connections, Course 2
Warne Date Decimals and Fractions To express a fraction as a decimal, divide the numerator of the fraction by the denominator. Example 1 Express 8as a decimal. 0.375 8)3.000 g 8 = 0.375 A decimal like 0.375 is a terminating decimal The decimal equivalents for some fractions are repeating decimals rather than terminating decimals. Use a bar to indicate the digits that repeat. Examples 2 Express 2as a decimal. 0.41666 = 0.416 12)5.00000 3 Express 3 as a decimal. 0.393939... = 0.39 33)13.000000 4 Express 51as a decimal. 0.4 5T276 = 0.4 <2 < Express each fraction or mixed number as a decimal. If the decimal is a repeating decimal, use bar notation. 4 1. 2 20 10 3. -34-. 4. 5 *-. 5. 0 6 -I- 7 ±7-- 50 99 11 8. 10 1-7 11 8 ' 200 12' ' 25 Mathematics: Applications Glencoe/McGraw-Hill 14 and Connections, Course 2
24,16.1=, L.L5r44e. Henry runs up 10 fliqhts of stairs. Then, he runs down 10 flights of stairs. Does this situation represent additive inverses? Explain. 2. FiVe out of six students said baseball was-their-favorite sport:what-is-the decimal equivalent for the number of students who chose baseball? 0 0.56 0.56 0.83 O 0.83 3. The outside temperature decreases by 7 F in 31 hours. How would you represent the temperature change as a unit rate? Express your answer as an integer. If the temperature continues to decrease at this rate, what will be the change in temperature after 5 hours? Topic Assessment Form B 4 Which expression i s equivalent to 4 5? Select all that apply. 2 ' 5 O O 45- ( -54) x _ 25 ) O (A) ( 3) ( -54) X ( -2) 5. Josie deposited $450 in a bank account at the beginning of the month. A payment of $35.20 is automatically deducted each month for her gym membership. If she makes no other deposits or withdrawals, how much money is in Josie's account at the end of four months? r- 6. Sean started with 15 points during a trivia game. Then, he lost 15 points on one turn and an additional 20 points on his final turn. Show the change in Sean's score using the number line below. 11111111111111111111111111111111111111111 20 15.-10 5 0 5 10 15 20 What is Sean's final score? Assessment, Form B Copyright 0 Pearson Education, Inc, or its affiliates. All Rights Reserved. 7
7. Which expression is equivalent to the distance between 2 and 15 on a number line? Select all that apply. 1-15 (-2)1 O 1-15-2 15 ± (-2)1 O 1-2 + ( -15 )1 (-15) 8. A jewelry company loses $450 as a result of a delivery delay. The 9 owners of the company must share the loss equally. Which integer represents the change in profit for each owner? $50 $35 $5 @ $50 9. A half-marathon is 13.1 miles long. There is a water station every 1,1W3, miles along the race trail. Which expression represents the total number of water stations? 0 13.1-1 11210 13.1 +11120 10. A crew is shingling a roof.they complete 6.8 square feet every hour. How many square feet will they complete in 12-1f hours of work? 11. Alexis and Mariana are hiking. Alexis climbs to the toppf a ridge 417 feet above sea levelrmariana goes to the bottom of a valley, 30 feet below sea level. What is the vertical distance between Alexis and Mariana? 12. Mackenzie has 32 books, including 12 books by her favorite author. Express as a decimal the number of books by her favorite author out of the total number of books she owns. Is the decimal terminating or repeating? Explain. 13.1 11 1 fti) QD 13.1 ± 1 1110 Assessment, Form B Copyright V Pearson Education, Inc., or its affiliates. All Rights Reserved. 7
Harne, Late 8 Ake 41 fifrt t. t, LIZMARICIMEereeMerCELS.WeiwnlYa.M1SeenamaResiJ Adding Integers To add integers, think of a number line. Locate the first addend on the number line. Move right if the second addend is positive. Move left if the second addend is negative. Example 1 Solve t = 4 + (-10). Start at 0. Since 4 is positive, go 4 units to the right. Since 10 is negative, go 10 units to the left. --10 7 6 5 4 3 2 1 So, t = 6. When you add integers, remember the following. The sum of two positive integers is positive. The sum of two negative integers is negative. The sum of a positive integer and a negative integer is: positive if the positive integer has the greater absolute value. negative if the negative integer has the greater absolute value. Examples 2 Solve n = 14 + (-11). 3 Solve 24 + 16 = k. 1141 > 1-111, 1-241 > 1161, so the sum is positive. so the sum is negative. 14 11 = 3 24 16 = 8 So, n = 3. So, k = 8. Solve each equation. 1. p = 16 + (-11) 2. 22 + (-7) = g 4. 50 + 50 = v 5. c= 10 + (-10) 7. 100 + (-25) = w 8. n 38 + (-6) 10. r= 89+29 11. 85 + (-10) = 3. y= 6+36 6. k= 12+9 9. 50 + (-20) = v 12. 4 + (-10) = z Evaluate each expression if a = 8, b = 8, and c = 4. 13. a + 16 14. b + (-9) 15. b + c 16. 10 + c 17. a + (-21) 18. 12 + b Mathematics: Applications Glencoe/McGraw-Hill 37 and Connections, Course 2
Name Date Practice Adding Integers Tell whether the sum is positive, negative, or 0. 1. 5 + (-5) 2. 8 + (-3) 4. 9 + (-3) Solve each equation. 7. d = 5 + (-8) 8. 6 + 6 = t 9. v= 4 + (-9) 10. 7 + 13 = h 11. = 9 + (-9) 12. b = 14 + (-27) 13. y -= 15 + (-10) 14. 19 + (-10) = k 15. 12 + (-18)=s =p 17. m = 12_+ (-8) 18. c 28 + 16 Evaluate each expression if a = 8, b = 12, and c = a + (-6) 20. 10 + b 19. 21. c (-7) 22. a + b 23. c + 0 24. b + c Glencoe/McGraw-Hill 37 Mathematics: Applications and Connections, Course 2
Pfy e Topics 2 Cumulative/ Benchmark Assessment For choosr, Yes or No to tr- t1 Whether each number is rational. a. 3.02859... b. 3 c. 3.14159... d. O Yes O Yes O Yes O Yes O No O No O No O No 2. Six cell phones weigh 46.2 ounces. Fourteen cell phones weigh 107.8 ounces. Does this represent a proportional relationship? Explain. If so, state the constant of proportionality. 5 The 7:3.0 represents the cost of renting a generator from a hardware store. Tota l Cost ($) Time (h) What does the point (0, 0) mean in the problem situation? 3. A scuba diver is 15.5 feet below the surface of the water. If the diver continues to swim downward at a rate of 2.5 feet per second, what integer represents her location relative to the surface after 7 seconds? How far does the diver have to go to return to the surface? Choose one ordered pair on the graph and explain what it means in the problem situation. 4. The record high temperature on January 15 is 41 F.The record low temperature on that day is 16 F. What is the difference in the record temperatures? Topics 1-2 Cumulative/Benchmark Assessment Copyright O Pearson Education, Inc, or its affiliates. All Rights Reserved. 7
6. Marcelo had $49.13 in his bank account. He paid two fees of $32.50 each, and then he made two deposits of $74.25 each. Write an expression to represent the situation. 9. An overweight dog is put on a special diet. Use the table to determine the dog's average weight change per week. Week Number Weight Change (oz) 1 1.5 2 2.2 3 0.8 4 1.6 5-0.6 What is the balance in Marcelo's account now? 7. Which expression is equivalent to (-60) 5? Select all that apply. 60 ± (-5) O (-60) (-5) 10. Tomic and Brooke make a game of shooting free throws. Each basket is worth 22 points. Each miss is worth 3 4 points. Out of 30 free throws, they make 16 baskets. Tomic calculated incorrectly that they had scored 502 points. Explain his likely error. U (-60) x 60 X (- 35) (-60) X (-4) 8. A family drives 42 miles in of an hour. What is their rate of speed in miles per hour? What is the correct number of points that Tannic and Brooke scored? Topics 1-2 Cumulative/Benchmark Assessment Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. 7
?'t,-atenny bought a 50-pound bag of chicken feed for $29,98 and a 25-pound bag for $15.49. Can you use proportional reasoning to find the price of a 40-pound bag? Explain. Water evaporates from a pond at a rate of 0.05 inches per hour: What is the change in the water level - of the pond after 24 hours? Express your answer as a rational number. 14. The dimensions of the box below are reduced by half. What is the constant of proportionality between the volume of the new box and the volume of the original box? 12. Which of the following tables represent a proportional relationship? Select all that apply. X 2 4 6 8 10 y 5 10 15 20 25 20 inches O 11 12 20 28 36 44 X 4 6 8 10 12 y 10 16 24 34 46 X 21 35 49 63 77 y 3 5 7 9 11 X 6 8 10 12 14 Y J )1 19 31. 47 15. For a-d, choose Positive or Negative to tell the sign of the simplified expression. Positive Negative a. 13 25 0 0 b. 10.5+11 c. 4.25 (-1.25) d. (-30) ± (-10) Topics 1-2 Cumulative/Benchmark Assessment Copyright 0 Pearson Education, Inc, or its affiliates. All Rights Reserved. 7
16. Which pair of numbers is opposite? Select all that apply. CD 1-61 and 6 I-61 and 6 O O 6 and 36-6 and 6 O 0 and 6 17. Each year, the students in seventh grade go to an environmental camp. This year, the total cost is $1,580 for 79 students. How much does it cost for each student to attend the camp? L Write an equation to represent the cost, y, of attending the camp for x number of students. 18. Which of the following represents the lowest speed in miles per hour? 6 miles in -18- hour 11 miles in 4 hour 3 16 miles in -8- hour 20 miles in zhour 19. The results of a board game are shown in the table below. Player Amount Joseph $500 Sarah $1,500 Malachi $2,200 Tyson $400 Shaun $600 Summer $300 What is the total of the players' scores? a Part C Graph the equation from. Label the graph. 1600 1200 800 400 T 0 0 20 40 60 80 20. Which of the following products is negative? Select all that apply. O (- 4)(=9) (-4)(9) O (6)(6) O (-6)(-6) O (6)(-6) Topics 1-2 Cumulative/Benchmark Assessment Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. 7