Comparing and Ordering Integers — Solutions

1. Find the absolute value

   1. |−5|: 5 ▶ View Solution
   2. |3|: 3 ▶ View Solution
   3. |−12|: 12 ▶ View Solution
   4. |0|: 0 ▶ View Solution
   5. |−7|: 7 ▶ View Solution
   6. |15|: 15 ▶ View Solution
   7. |−3|: 3 ▶ View Solution
   8. |8|: 8 ▶ View Solution

2. Compare each pair using <, > or =

   1. −3 __ −7: > ▶ View Solution
   2. −1 __ 0: < ▶ View Solution
   3. 5 __ −5: > ▶ View Solution
   4. −10 __ −4: < ▶ View Solution
   5. 0 __ −2: > ▶ View Solution
   6. −8 __ −9: > ▶ View Solution
   7. −15 __ −15: = ▶ View Solution
   8. 6 __ −100: > ▶ View Solution

3. Order each set from smallest to largest

   1. −5, −3, 0, 1, 4 ▶ View Solution
   2. −7, −2, −1, 3, 7 ▶ View Solution
   3. −10, −8, −4, −1, 0 ▶ View Solution
   4. −6, −2, 0, 2, 6 ▶ View Solution
   5. −15, −10, −5, 0, 5, 10 ▶ View Solution
   6. −100, −50, −25, −10, −1 ▶ View Solution
   7. −9, −4, −1, 0, 4, 9 ▶ View Solution
   8. −30, −3, −3, 3, 30 ▶ View Solution

4. Temperature and depths

   1. −8°C vs −3°C — which is colder?: Monday (−8°C) ▶ View Solution
   2. −80 m vs −12 m — which is deeper?: Submarine ▶ View Solution
   3. Is −20 a warmer temperature than −15?: False — −20 < −15 ▶ View Solution
   4. Is the absolute value of a negative integer always positive?: True ▶ View Solution

5. Number line reasoning

   1. Which is further from zero, −9 or 7?: −9 ▶ View Solution
   2. Integers strictly between −5 and −1: −4, −3, −2 ▶ View Solution
   3. Midpoint of −6 and 4: −1 ▶ View Solution
   4. Two integers 6 units from zero: 6 and −6 ▶ View Solution

6. Real-world contexts

   1. Order temperatures coldest to warmest: −12°C, −9°C, −5°C, 0°C, 3°C ▶ View Solution
   2. Golf scores best to worst: −5, −3, −1, 0, +2, +4 ▶ View Solution
   3. Lowest balance; best off: Bob (−$120); Carla ($30) ▶ View Solution
   4. Diver at −25 m rises 10 m; is she above −20 m?: −15 m; yes ▶ View Solution

7. Order from largest to smallest

   1. 8, 5, 0, −3, −11 ▶ View Solution
   2. 6, 1, −2, −4, −9 ▶ View Solution
   3. 7, 0, −1, −7, −7 ▶ View Solution
   4. 50, 20, 0, −20, −50 ▶ View Solution
   5. 33, 13, 3, −3, −13, −33 ▶ View Solution
   6. 200, 150, −100, −150, −200 ▶ View Solution

8. True or false — justify each answer

   1. Is |−4| > |3|?: True ▶ View Solution
   2. Is −7 > −6?: False — −7 < −6 ▶ View Solution
   3. Is |−10| = |10|?: True ▶ View Solution
   4. Is −1 the largest negative integer?: True ▶ View Solution
   5. Is 0 a positive integer?: False — 0 is neither positive nor negative ▶ View Solution
   6. Is |−3| < |−5|?: True ▶ View Solution

9. Absolute value comparisons

   1. |−9| and |9|: = ▶ View Solution
   2. |−4| and |−6|: ≠ ▶ View Solution
   3. |0| and |−1|: ≠ ▶ View Solution
   4. |−15| and |12|: ≠ ▶ View Solution
   5. |−8| and |8|: = ▶ View Solution
   6. |−100| and |−99|: ≠ ▶ View Solution
   7. |2| and |−2|: = ▶ View Solution
   8. |−30| and |25|: ≠ ▶ View Solution

10. Integer puzzles

    1. Absolute value 8, less than 0: −8 ▶ View Solution
    2. Integers strictly between −10 and −6: −9, −8, −7 ▶ View Solution
    3. x = −13 ▶ View Solution
    4. Order −4, +3, −2, −7, +6 least to greatest: −7, −4, −2, +3, +6 ▶ View Solution
    5. Temperature drop from −6°C to −14°C: 8 degrees ▶ View Solution