Integers Opposites Absolute Value Worksheet Answer Key – Grade 6

Problem 1 Writing signed numbers

1. Below zero is negative: −8.
2. A deposit adds money: +35.
3. Above sea level is positive: +40.
4. A debt is owed money: −12.

Problem 2 Finding opposites

The opposite changes the sign: −14, 9, 0, −3.5. Zero is its own opposite.

Problem 3 Reading a number line

Count units from 0: A is 4 left, B is 1 left, C is 3 right, D is 5 right.

A = −4, B = −1, C = 3, D = 5.

Problem 4 Comparing integers

1. −3 is left of 2: −3 < 2.
2. −7 is left of −4: −7 < −4.
3. 0 is right of −1: 0 > −1.
4. Same value: −2.5 = −2.50.

Problem 5 Absolute values

Each is a distance from 0: 12, 8, 0 and 3.5.

Problem 6 Ordering integers

Negatives first, with −8 farthest left: −8, −3, −1, 2, 9.

Problem 7 Thermometer readings

The 7 AM reading is −8 °F and noon is 3 °F. −8 is lower. From −8 up to 0 is 8 degrees, then 3 more: 11 degrees. 7 AM is lower; the rise was 11 °F.

Problem 8 Ordering rational numbers

As decimals: 0.5, −0.75, −1.25, 0.2.

−1.25, −34, 0.2, 12.

Problem 9 Opposite of an opposite

−(−8) = 8. −(−(−3)): the inner −(−3) = 3, then the opposite of 3 is −3. −|−6| = −(6) = −6. −(5) = −5. 8, −3, −6, −5.

Problem 10 Absolute value comparisons

1. 9 and 5: |−9| > |5|.
2. −9 is left of 5: −9 < 5.
3. 4 and 4: |−4| = |4|.
4. −2 and 2: −|−2| < |−2|.

Problem 11 Closer to sea level

|−32| = 32 and |20| = 20. The smaller distance belongs to the seagull. The seagull is closer, 20 feet from sea level versus 32 feet.

Problem 12 Half-unit number line

Each tick is 0.5. M is 5 ticks left of 0, P is 1 tick left, N is 3 ticks right.

M = −2.5, P = −0.5, N = 1.5.

Problem 13 Ordering elevations

Lowest is the most negative: −186, then −54, then 0, then 940. Dry Gulch Basin, Salt Sink, Pelican Bay, Cedar Ridge.

Problem 14 Same distance from zero

One point is 7 units right of 0 and the other is 7 units left. The numbers are 7 and −7, which are opposites.

Problem 15 Daily low temperatures

Coldest is the least number, −11. Order from greatest to least: 6, 0, −2, −4, −11. Wednesday was coldest; warmest to coldest: Tuesday, Thursday, Friday, Monday, Wednesday.

Problem 16 Trivia game scores

Higher score wins: 10, −5, −15, −25. Distances from 0: 10, 5, 15, 25, so the greatest is 25. Luis is winning. Order: Luis, Kai, Priya, Omar. Omar’s score is farthest from 0.

Problem 17 Ocean and sky

Order: −240, −75, 90, 3,600. Distances from sea level: 240, 75, 90, 3,600; the smallest is 75. Submarine, whale, gull, plane. The whale is closest to sea level.

Problem 18 Mirror points

The first point is −4.5, and its opposite is 4.5. |−4.5| = 4.5 and |4.5| = 4.5. They match because each point is 4.5 units from 0, just on opposite sides.

Problem 19 Account balances

Compare on a number line: −12.25 is farthest left, then −8.50, then 0, then 3.75. Zoe, Mia, Ben, Eli in that order, and Zoe owes the most ($12.25).

Problem 20 True or false

1. True. Negatives lie left of 0 and positives right of it, e.g. −100 < 1.
2. False. |−9| > |2| but −9 < 2.
3. True. The opposite of 6 is −6.
4. True. Distance cannot be negative, e.g. |−3| = 3.