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Worksheet: Applications of Comparing and Ordering Integers

Q1:

Benjamin and Michael are playing a board game. Benjamin’s token moved 3 squares back, while Michael’s token moved 2 squares forward. By representing the movements of the tokens as integers, which has the greater absolute value?

  • A moving back 3
  • B moving forward 2

Q2:

A group of five friends played a card game. Their scores were as follows: Person A, + 2 9 ; Person B, 1 9 ; Person C, 2 1 ; Person D, + 6 ; Person E, 2 . Arrange the players from the worst performing player to the best.

  • APerson B, Person C, Person E, Person D, Person A
  • BPerson A, Person D, Person E, Person B, Person C
  • CPerson A, Person E, Person D, Person B, Person C
  • DPerson C, Person B, Person E, Person D, Person A
  • EPerson E, Person B, Person C, Person D, Person A

Q3:

For three days, the water level in the morning was measured. Then, the changes in the water level, in feet, were recorded for the next low tide and the following high tide. Use the table to determine the day on which the water level was lowest after the high tide.

Day Morning water level (feet) Change at Low Tide Change at High Tide
Monday 20 1 9 + 2 0
Tuesday 30 1 5 + 2 5
Wednesday 21 1 8 + 2 1
  • ATuesday
  • BWednesday
  • CMonday

Q4:

Three university students checked the balances in their bank accounts. Victoria has a debt of $234 and Olivia has a debt of $192. Hannah, on the other hand, has a balance of $293. Which of them owes the most money?

  • AOlivia
  • BHannah
  • CVictoria

Q5:

Four friends played a game, where, at each turn, they either collect or lose points. Olivia finished with 2 3 , Benjamin with 1 2 , Amelia with + 1 5 , and Matthew with 1 7 . Who ranked last at this game?

  • AMatthew
  • BAmelia
  • CBenjamin
  • DOlivia

Q6:

The table shows the players in a card game and their corresponding score. Order the scores descendingly.

Player 1 2 3 4 5 6 7 8
Score
  • A , , , , , , ,
  • B , , , , , , ,
  • C , , , , , , ,
  • D , , , , , , ,
  • E , , , , , , ,

Q7:

The elevations of 4 locations are shown in the table. Elevation is based on a point’s distance from sea level. Sea level has an elevation measured at 0 feet. Decide which of the following statements is true based on the information in the table.

Place Location Elevation
Mt. McKinley Alaska 2 0 3 2 0 feet
Death Valley California 2 8 2 feet
Mt. Everest Nepal 2 9 0 2 9 feet
Lake Assal Djibouti 5 0 9 feet
  • A The Dead Sea is at a lower elevation than Death Valley because 1 3 8 8 > 2 8 2 .
  • B Death Valley is farther from sea level than Mt. McKinley because 2 8 2 > 2 0 3 2 0 .
  • C Mt. McKinley is taller than Mt. Everest because | 2 0 3 2 0 | > | 2 9 0 2 9 | .
  • D The Lake Assal is at a lower elevation than Death Valley because | 5 0 9 | > | 2 8 2 | .

Q8:

Three friends are comparing the distances they travelled in a month; Liam travelled a distance of 4 405 km, Anthony travelled a distance of 3 212 km, and Daniel travelled a distance of 1 300 km. Who travelled the longest distance?

  • ADaniel
  • BAnthony
  • CLiam

Q9:

The table shows the records of four football teams in one year. The achievements of a team can be determined by the number of the matches won compared to the total number of matches played. List these teams according to their achievements from best to worst.

Team Barcelona A.C. Milan Manchester United Bayern Munich
Number of Matches Won 33 45 16 44
Number of Matches Played 56 72 32 48
  • ABayern Munich, Barcelona, A.C. Milan, Manchester United
  • BA.C. Milan, Bayern Munich, Barcelona, Manchester United
  • CA.C. Milan, Barcelona, Manchester United, Bayern Munich
  • DBayern Munich, A.C. Milan, Barcelona, Manchester United

Q10:

Chloe, Liam, and Ethan were all waiting for their turns at the bank. Chloe’s turn comes at 25 minutes after noon, Liam’s turn 3 minutes before noon, and Ethan’s turn 16 minutes before noon. Arrange the three according to who will be attended to first.

  • AEthan, Chloe, Liam
  • BChloe, Liam, Ethan
  • CChloe, Ethan, Liam
  • DEthan, Liam, Chloe
  • ELiam, Ethan, Chloe

Q11:

Daniel pays for 500 minutes of international calls a month. The table shows his usage over the past 4 months. Positive values indicate the number of minutes he went over his allotted minutes, and negative values indicate the number of minutes he was under. Order the months according to Daniel’s usage from least to greatest.

Month June July August September
Time 78 2 2 26 8 4
  • ASeptember, August, July, June
  • BJune, August, July, September
  • CJune, July, August, September
  • DSeptember, July, August, June
  • EJuly, September, August, June

Q12:

The table shows the net profit and loss of a used-car dealership from last March to last September. Order the months from the lowest net value to the highest, and then determine the median value.

Month March April May June July August September
Net Profit/Loss $ 3 4 0 0 $ 3 9 0 0 $ 4 7 0 0 $ 5 7 0 0 $ 1 0 0 0 $ 1 8 0 0 $ 1 9 0 0
  • AMay, April, September, July, August, March, June, $5 700
  • BMay, April, September, July, August, March, June, $1 000
  • CJune, March, August, July, September, April, May, $5 700
  • DJune, March, August, July, September, April, May, $1 000
  • EMay, April, September, July, August, March, June, $4 700

Q13:

The table shows the net profit and loss of a used-car dealership from last March to last September. Order the months from the lowest net value to the highest, and then determine the median value.

Month March April May June July August September
Net Profit/Loss $ 7 4 0 0 $ 3 3 0 0 $ 2 5 0 0 $ 5 1 0 0 $ 3 0 0 $ 1 7 0 0 $ 3 2 0 0
  • AMarch, September, May, July, August, April, June, $5 100
  • BMarch, September, May, July, August, April, June, $300
  • CJune, April, August, July, May, September, March, $5 100
  • DJune, April, August, July, May, September, March, $300
  • EMarch, September, May, July, August, April, June, $7 400

Q14:

The table shows the average normal January temperatures of four cities in Alaska. Order the cities from the highest to the lowest temperature.

City A B C D
Temperature (°F) 2 6 6 1 8 13
  • AA, B, C, D
  • BA, C, B, D
  • CD, C, B, A
  • DD, B, C, A
  • EC, A, B, D

Q15:

The temperature inside a house is 5 5 F , while the temperature outside the house is 5 2 F . If we represent these temperatures by integers, which has the greater absolute value?

  • Athe temperature inside the house
  • Bthe temperature outside the house

Q16:

Before deciding whether to go out for shopping, four friends checked their bank account balances. Sophia found she has a debt of $143, Madison a debt of $203, and Victoria a debt of $178. However, Hannah found she has a balance of $350. Which of them owes the most money?

  • AVictoria
  • BSophia
  • CHannah
  • DMadison