Name Class Date. Use a number line to order the integers from least to greatest.

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1 Explore It! 2-1 Integers MA.7.A.3.1 Use and justify the rules for finding the absolute value of integers. Graph each integer and its opposite on a number line Compare the integers. Use < or > Use a number line to order the integers from least to greatest ,, -5, 7, , 8, 0,, , 5, -7, -8, , 3, -, -5, Use a number line to find each absolute value Christy dove to a reef that was 12 feet below the surface of the water. Use an integer to represent the reef s position relative to the surface of the water The temperature yesterday morning was 9 below zero. Write the temperature as an integer. 2-1 Integers 35

2 2-1 Explore It! Integers 1. The coldest place on record in the U.S. was in Alaska in It was 80 F below zero. Write this temperature as an integer. 2. The temperature outside was - F at Jared s house and -8 F at Mario s house. Where was the temperature warmer? 3. A small business reported a net loss of $62,500 during its first year. In its second year, it reported a profit of $3,100. Write each amount as an integer. MA.7.A.3.1 Use and justify the rules for finding the absolute value of integers. The table gives some elevations relative to sea level. Use the table for 7 9. Continent Highest Point (ft) Lowest Point (ft) North America 20, South America 22, Africa 19, Asia 29,028-1,339 Australia 7, Europe 18, Order the elevations of the highest points from least to greatest. Which continent has the highest point?. For one day, Lacy recorded the low temperatures in five U.S. cities. The temperatures were 5 C, -1 C, -3 C, 2 C, and 0 C. Write the temperatures in order from least to greatest. 5. Basha says 5 and -5 have the same value. Danny says 5 and -5 are not equal. Who is correct? Justify your answer. 8. Order the elevations of the lowest points from least to greatest. Which continent has the lowest point? 9. Gridded Response What is the elevation (in feet) of the lowest point in the table? 6. What is the value of the expression 7? Justify your answer Integers

3 Explore It! 2-2 Adding Integers MA.7.A.3.1 Use and justify the rules for adding integers. Also MA.7.A.3.2 Use a number line to find each sum (-6) Find each sum (-9) (-6) (-30) (-25) (-7) (-15) 9. (-23) (-8) 13. (-15) + (-7) (-1) (-2) + (-3) (-30) + 70 Evaluate e + f for the given values. 17. e = 9, f = e = -17, f = e = 32, f = e = -15, f = e = -20, f = e = -30, f = The temperature rose 9 F in three hours. If the starting temperature was -15 F what was the final temperature? Explain. 2. Matt is playing a game. He gains 7 points, loses 10 points, gains 2 points, and then loses 8 points. What is his final score? Justify your answer. 2-2 Adding Integers 3

4 2-2 Explore It! Adding Integers MA.7.A.3.1 Use and justify the rules for adding integers. Also MA.7.A At 3 p.m., the temperature was 9 F. By 11 p.m., it had dropped 31 F. Write and simplify an addition expression to find the temperature at 11 p.m. 6. In Indianapolis, Indiana, the coldest recorded temperature was -27 F. The hottest recorded temperature was 13 F higher. What was the hottest temperature in Indianapolis? 2. The temperature dropped 12 F in 8 hours. The final temperature was -7 F. Write and simplify an addition expression to find the starting temperature. 7. The Aral Sea and the Caspian Sea are actually lakes. The elevation of the Caspian Sea is 92 feet below sea level. The Aral Sea is 217 feet higher. What is the elevation of the Aral Sea? 3. Tad owes Juan $23 and borrows $12 more. Explain how to find the amount Tad owes Juan now. Aral Sea 217. New Orleans, Louisiana, is 6 feet below sea level. The highest point in Louisiana, Driskill Mountain, is 51 feet higher than New Orleans. Explain how to find how high Driskill Mountain is above sea level. 5. An airplane at 20,000 ft drops 2,500 ft in altitude. Then the airplane rises 8,075 feet in altitude. Write and simplify an integer addition expression to find the airplane s final altitude. 92 Sea Level Caspian Sea 8. Short Response Last week, Flore s checking account balance was $27. She made deposits of $6, $25, and $37 into her checking account and then wrote checks for $52 and $9. Does Flore have enough money in her account to spend $75 on a new MP3 player? Justify your answer. 2-2 Adding Integers

5 Explore It! 2-3 MA.7.A.3.1 Use and justify the rules for subtracting integers. Subtracting Integers Use a number line to find each difference (-1) Find each difference ( -12 ) ( -19 ) ( -18 ) ( -23 ) ( -9 ) ( -13 ) ( -8 ) ( -11 ) Evaluate x - y for each set of values. 15. x = 1, y = x = -11, y = x = -8, y = x = -9, y = x = 19, y = x = 20, y = The high temperature one day was -1 F. The low temperature was -5 F. What was the difference between the high and low temperatures for the day? 22. The temperature changed from 5 F at 6 p.m. to -2 F at midnight. How much did the temperature decrease? 23. Camille had $275 in her checking account. She deposited $812 and wrote checks for $75, $60, and $8. How much did she have in the account after all these transactions? 2-3 Subtracting Integers 51

6 2-3 Explore It! Subtracting Integers MA.7.A.3.1 Use and justify the rules for subtracting integers. Also MA.7.A The hottest temperature on Mercury is 67 C. The coldest temperature is -183 C. Write and simplify a subtraction expression to find how much the temperature can vary on Mercury. 6. On Wednesday night in St. Petersburg, Russia, the temperature is -10 C. On the same night in Bombay, India, the temperature is 17 C. What is the difference in temperature? 2. The top of a tree is 35 feet above the ground. Its roots reach a depth of 22 feet below the ground. Write and simplify a subtraction expression to find the distance from the top of the tree to the deepest part of its roots. 3. The lowest point of the Puerto Rico Trench, in the Atlantic Ocean, is -8,380 meters. The lowest point of the Japan Trench, in the Pacific Ocean, is 133 meters lower. Write and simplify an expression to find the depth of the lowest point of the Japan Trench.. The lowest point of the Tonga Trench, in the Pacific Ocean, is -10,882 meters. The lowest point of the Mariana Trench, also in the Pacific Ocean, is 108 meters lower. What is the depth of the lowest point of the Mariana Trench? Bombay, India St. Petersburg, Russia 7. Short Response Lionel finished four rounds of a golf tournament. His combined total score after playing all four rounds was -10. His scores on the first three rounds were -, -2, and -6. What was his score on the last round? Justify your answer. 5. An ice cream company reported a net profit of $2,000 in 2002 and a net loss of $11,000 in Write and simplify a subtraction expression to find how much the company s profits changed from 2002 to Subtracting Integers

7 Explore It! 2- Multiplying and Dividing Integers MA.7.A.3.1 Use and justify the rules for multiplying [and] dividing integers. Also MA.7.A.3.2, MA.7.A.5.2 Solve. Check each answer ( -5 ) ( -3 ) ( -9 ) Multiply ( -6 ) 8. 9 ( -3 ) ( -8 ) ( -7 ) ( -6 ) 1. ( - ) ( -11 ) Find each quotient ( -5 ) ( -6 ) ( - ) ( -7 ) ( -6 ) ( -9 ) ( -9 ) ( -8 ) ( -9 ) 29. Kim was walking downhill. For minutes, the elevation dropped steadily. Altogether it dropped 8 feet. Find the change in elevation per minute. 30. The temperature changed steadily over 6 hours. Altogether it changed -18 degrees. What was the change in temperature per hour for the 6 hours? 2- Multiplying and Dividing Integers 59

8 2- Explore It! Multiplying and Dividing Integers MA.7.A.3.1 Use and justify the rules for multiplying [and] dividing integers. Also MA.7.A.3.2, MA.7.A.5.2 Gerald recorded the temperature at 6-hour intervals for one 2-hour period. The table shows his data. Use the table for 1 3. Time Temperature ( F) 10:00 P.M. 70 :00 A.M :00 A.M. 6 :00 P.M :00 P.M Lee and Di are underwater. Lee s location relative to the surface is 6 times greater than Di s location. Lee is 2 feet below the surface. Explain why the expression 6 (-2) can be used to represent this situation. 1. If the temperature changed steadily, what was the change per hour from 10:00 p.m. the first day to :00 a.m.? 2. If the temperature changed steadily, what was the change per hour from :00 a.m. to 10:00 a.m.? 3. If the temperature changed steadily, what was the change per hour from :00 p.m. to 10:00 p.m. the second day? Explain how you found your answer.. Jorge made four $90 deposits to his savings account one month. The next month he made two $120 withdrawals. He had $1,750 in his account after these withdrawals. How much money did he have before he made all these transactions? 6. A football team must move the ball forward at least 10 yards from its starting point to make a first down. If the team has 2 losses of 2 yards each and a gain of 12 yards, does the team make a first down? Justify your answer. 7. Gridded Response Jeri began with the number -2 and divided by -2. She divided the result by -6 and then multiplied that result by -3. What is Jeri s final number? Multiplying and Dividing Integers

9 Got It? Ready to Go On? Go to thinkcentral.com 2-1 THROUGH 2- Quiz for Lessons 2-1 through Integers (Student Textbook pp. 6 67) 1. Use the number line to order the integers -7, 3, 6, -1, 0, 5, -, and Adding Integers (Student Textbook pp ) Add ( -9 ) ( -11 ) Evaluate p + t for the given values. 8. p = 5, t = p = -, t = p = -37, t = Subtracting Integers (Student Textbook pp ) Subtract ( -7 ) ( -11 ) When Cai traveled from New Orleans, Louisiana, to the Ozark Mountains in Arkansas, the elevation changed from 7 ft below sea level to 2,31 ft above sea level. How much did the elevation increase? 2- Multiplying and Dividing Integers (Student Textbook pp ) Find each product or quotient (-6) ( -9 ) 18. After reaching the top of a cliff, a rock climber descended the rock face using a 65-foot rope. The distance to the base of the cliff was 585 feet. How many rope lengths did it take the climber to complete her descent? 19. A submarine rose 22 feet from its original position underwater. It then descended in 3 increments of 15 feet each. The final position of the submarine is 180 feet below sea level. Find its original position. Chapter 2 Integers and Rational Numbers 61

10 Explore It! 2-5 Solving Equations Containing Integers MA.7.A.3.3 Formulate and use different strategies to solve one-step linear equations Solve. Check each answer. 1. y - 5 = = x q + 6 = h = = -u 11. c = f + 15 = g -19 = n - 9 = -1. p + 18 = = w b = d 5 = S -9 = = 3v = -9s m = = 31 + x = 21 + n = w 20. e -7 = z - 10 = The temperature in Buffalo, New York, was -2 F one day. This was 2 degrees warmer than the temperature in Nome, Alaska, on the same day. Find the temperature in Nome. Justify your answer by writing and solving an equation. 2. A farmstand collected $350 from sales on Wednesday. This amount was $75 greater than the amount collected from sales on Tuesday, and two times as great as the amount collected from sales on Monday. How much more did the farmstand collect from sales on Tuesday than it collected on Monday? Justify your thinking by showing your work. 2-5 Solving Equations Containing Integers 69

11 2-5 Explore It! Solving Equations Containing Integers MA.7.A.3.3 Formulate and use different strategies to solve onestep linear equations Also MA.7.A Sam wants to bicycle a total of 600 miles to prepare for a race. He will bicycle 15 miles each day. Write and solve an equation to find how many days must he bicycle. 2. The measures of two angles of a triangle have a sum of 110. The sum of the measures of all three angles is 180. What equation can you solve to find the measure of the third angle? What is the measure of the third angle? 6. Mr. Marco sold his stock in several companies. The table shows how much money he made from each type of stock. Write and solve an equation to find the selling price per share of the Gizmo stock. Stock Shares Sold Total Price Contraption 0 $3600 Doodad 25 $1575 Gizmo 50 $1250 Widget 15 $ The Statue of Liberty was erected in New York City in Write an equation to find how old the statue is. What operation must you perform to solve the equation?. Lonnie swam 3 miles each day of her vacation. She swam a total of 2 miles. How many days long was her vacation? 5. On the hottest day in Richmond, Virginia, the temperature was 105 F. On the coldest day, the temperature was 117 F lower. Write and solve an equation to find what the coldest temperature in Richmond was. 7. Extended Response Ann has a checking account and a savings account. She must pay a monthly service fee of $.00 for her savings account. a. Ann s checking account had a balance of $50. She then deposited $50 and wrote checks for $0, $2, and $18. What is Ann s new balance? b. During June, Ann deposited $1,250 in her savings account, withdrew $575, and paid the monthly fee. Her final balance for the month was $968. Write an equation that could be used to find the balance b at the beginning of June. c. Solve your equation from Part B to find Ann s savings account balance at the beginning of June Solving Equations Containing Integers

12 Explore It! 2-6 Solving Two-Step Equations MA.7.A.3.3 Formulate and use different strategies to solve two-step linear equations. Also MA.7.A.3. Solve. 1. b + 3 = f = n + 7 = j = y = = 6a x -9-1 = = + m 7 9. h = = e _ k _ 6 = w 3-6 = m 6-3 =1 1. x = = y -9-6 Write an equation and solve. 16. The school track team purchased uniforms for a total cost of $1,00. The shorts cost $600, and the shirts were $32 each. How many shirts did the school purchase? 17. Three years of storage space cost $3,500, including a one-time moving fee of $125. What is the yearly cost? 18. Jeanne s family already owns 1 DVDs. This number is 5 more than 6 times the number of used DVDs Jeanne wants to buy at a yard sale. How many DVDs does Jeanne want to buy? Justify your answer. 2-6 Solving Two-Step Equations 77

13 2-6 Explore It! Solving Two-Step Equations MA.7.A.3.3 Formulate and use different strategies to solve two-step linear equations. Also MA.7.A Sal s movie rental club membership costs $11 per month. With a membership, each movie costs $2. Sal s monthly movie rental charge was $23. How many movies did Sal rent? 5. Alan has saved $60. He needs $700 to go on a trip to Mexico. If he starts saving $0 per month, how many months will he need to save so that he has enough for his trip? 2. Liz earns a weekly salary of $59 and $20 per hour for each overtime hour she works. This week her total pay including salary and overtime pay was $559. Write an equation to represent this situation. How many hours of overtime did Liz work? 3. Chris had some rice cakes and 1 granola bar as a snack. The snack contained a total of 560 Calories. If the granola bar had 120 Calories and each rice cake had 0 Calories, how many rice cakes did Chris have? Explain.. Bella baked 6 dozen cookies. She wants to keep 1 dozen and give the rest to 20 friends. She wants to give an equal number of cookies to each friend. How many cookies does each friend get? Justify your anwer. 6. Extended Response The table shows the hours 3 students spent babysitting in June and the hourly rate each student charged. Student Hours in June Hourly Jan 25 $8 Ted 20 $6 Rob 30 $10 a. How much money did each student make from babysitting in June? b. Rob wants to make a total of $600 in June, July, and August. Write and solve an equation to find how many hours he needs to babysit during July and August. C. Jan and Ted also want to make $600 this summer. Write and solve equations to find how many hours they need to babysit during July and August Solving Two-Step Equations

14 Explore It! 2-11 MA.7.A.5.1 Express rational numbers as terminating or repeating decimals. Equivalent Fractions and Decimals Write each fraction as a decimal Write each decimal as a fraction in simplest form In the 1998 Winter Olympics, a total of 205 medals were awarded. The United States won 13 medals. What portion of the medals did the United States win? Write your answer as a decimal rounded to the nearest thousandth. 26. On a test, Hailey answered 6 out of 75 questions correctly. What portion of her answers was correct? Write your answer as a decimal. 27. Mr. and Mrs. Alvarez shared the job of driving the car on a recent vacation. Mr. Alvarez drove 122 miles. Mrs. Alvarez drove 13 miles. Find the fraction of the total number of miles driven by each person. Write the fraction as a decimal rounded to the nearest thousandth Equivalent Fractions and Decimals 87

15 2-11 Explore It! MA.7.A.5.1 Express rational numbers as terminating or repeating decimals. Equivalent Fractions and Decimals 1. On a test, Shane answered 35 out of 2 questions correctly. What portion of his answers was correct? Write your answer as a decimal. Use the table for 6 7. Energy Consumption (in quadrillions of British Thermal Units in 2003, BTU) North America Sammy Sosa hit 66 home runs in He had 63 at bats. Explain how to write his home run average as a decimal rounded to the nearest thousandth. Far East/Oceania Western Europe Eastern Europe Central/ South America Middle East Africa In February, Chicago receives an average of 1 2_ inches of rain. Explain how to write 5 a decimal to show the number of inches of rain.. On atrue/false test, 51 answers were true and 13 were false. Write the portion of answers that were true as a decimal rounded to the nearest hundredth. 6. Write a mixed number that describes the energy, in quadrillions of BTU, consumed in Eastern Europe in Write a mixed number that describes the energy, in quadrillions of BTU, consumed in the Middle East in Gridded Response What is _ 5 written as a decimal? 5. The high school sold 399 out of 62 tickets to the opening night of a concert series. Write the portion of tickets sold as a decimal Equivalent Fractions and Decimals

16 Got It? Ready to Go On? Go to thinkcentral.com 2-5, 2-6, 2-11 Quiz for Lessons 2-5, 2-6, Solving Equations Containing Integers (Student Textbook pp ) Solve each equation. Check your answer x = k - 25 = y + 16 = -8. This year, 72 students completed projects for the science fair. This was 23 more students than last year. How many students completed projects for the science fair last year? 5. Ana owes $30 to her brother, which is 5 times as much as her brother owes their cousin. Explain why the equation -30 = 5x can represent this situation. What does the solution of the equation represent? 2-6 Solving Two-Step Equations (Student Textbook pp. 8 87) Solve each equation. Check your answer. 6. x + 6 = y 3 = 6 8. z 8 5 = 3 9. A coach has $100 to buy T-shirts. Each shirt costs $6, and the coach must pay a $ shipping charge. How many T-shirts can the coach afford? 10. Jillian has already run 20 miles this month and wants to run a total of 50 miles. There are 15 days left in the month and she plans to run the same distance each day. Write and solve an equation to find how many miles she needs to run each day Equivalent Fractions and Decimals (Student Textbook pp ) Write each fraction as a decimal. Round to the nearest hundredth, if necessary Write each decimal as a fraction in simplest form In one 33-gram serving of snack crackers, there are 27 grams of carbohydrates. What fraction of a serving is made up of carbohydrates? Write your answer as a fraction and as a decimal. Chapter 2 Integers and Rational Numbers 89

17 FLORIDA Name Class Study It! Vocabulary CHAPTER Date 2 Multi-Language Glossary Go to thinkcentral.com (Student Textbook page references) absolute value (65) opposite (6) repeating decimal (106) integer (6) rational number (106) terminating decimal.... (106) Complete the sentences below with vocabulary words from the list above. 1. A(n) can be written as the ratio of one to another and can be represented by a repeating or 2. The. are the set of whole numbers and their Lesson 2-1 (s). Integers (Student Textbook pp. 6 65) MA.7.A.3.1 Use a number line to order the integers from least to greatest. 3,, -2, 1, , -2, 1, 3, Compare the integers. Use < or > Use a number line to order the integers from least to greatest ,, 0, -2, , -3, 2, -8, 1 Use a number line to find each absolute value Lesson Tutorial Videos Chapter 2 Integers and Rational Numbers 91

18 Lesson 2-2 Find the sum. Adding Integers (Student Textbook pp ) MA.7.A.3.1, MA.7.A (-11) -7 + (-11) The signs are the same. -18 Find each sum (-6) (-0) 1. The temperature was -9 F at 5 a.m. and rose 20 by 10 a.m. What was the temperature at 10 a.m.? Lesson 2-3 Subtracting Integers (Student Textbook pp ) MA.7.A.3.1, MA.7.A.3.2 Find the difference (-3) Add the opposite of Find each difference (-5) (-5) (-3) - (-1) Lesson 2- Find each product or quotient. Multiplying and Dividing Integers (Student Textbook pp ) 12 (-3) The signs are different, so -36 the product is negative. -16 (-) The signs are the same, so the quotient is positive. Find each product or quotient. MA.7.A.3.1, MA.7.A.3.2, MA.7.A (-10) (-9) (-8) (-15) 92 Chapter 2 Integers and Rational Numbers Lesson Tutorial Videos

19 Lesson 2-5 Solve. Solving Equations Containing Integers (Student Textbook pp ) x -12 = Add 12 to both sides. x = = -2f = -2f -2 5 = f MA.7.A.3.3, MA.7.A.3. Divide both sides by -2. Solve y = d - 8 = j + 23 = n = = -2c = -7m 36 Lesson 2-6 Solving Two-Step Equations (Student Textbook pp. 8 87) Solve 6a -3 = 15. 6a -3 = 15 6a = a = 18 6a 6 = 18 6 a = 3 Add 3 to both sides. Divide both sides by 6. MA.7.A.3.3, MA.7.A.3. Solve y + 6 = z 6 Lesson 2-11 Equivalent Fractions and Decimals (Student Textbook pp ) Write 0.75 as a fraction in simplest form = = = 3 = = w An isosceles triangle has two angles whose measures are equal. The measure of the third angle is 56. Given that the sum of the angle measures is 180, write and solve an equation to find the measures of the other two angles. Write 5 as a decimal. 5 = 5 = 1.25 MA.7.A.5.1 Write each decimal as a fraction in simplest form. Write each fraction as a decimal Lesson Tutorial Videos Chapter 2 Integers and Rational Numbers 93