Grade 6 Math · Topic 27

Opposites and Absolute Value

Two numbers are opposites if they are the same distance from zero on the number line but on different sides. The absolute value of a number is its distance from zero, which is always positive (or zero). We write |x| for the absolute value of x.

Lesson alignment: 6.NS.C.7 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Compare opposites and absolute value

Move one integer. Its opposite appears the same distance from zero on the other side.

Think first: If n is −5, where should its opposite appear? What should both distances from zero be?

Ready? Reveal the model and try your prediction

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Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find |-12| and the opposite of -12.

Start by writing the calculation clearly: |-12| is the distance from 0 to -12, which is 12. The opposite of -12 is the number on the other side of zero, the same distance away: 12.

Answer: |-12| = 12; opposite of -12 is 12.

Worked example 2

Evaluate |9| + |-4|.

Start by writing the calculation clearly: |9| = 9 and |-4| = 4. So 9 + 4 = 13.

Answer: 13

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. |-6| =
    Check

    6

  2. |15| =
    Check

    15

  3. |0| =
    Check

    0

  4. Opposite of -9 =
    Check

    9

  5. Opposite of 14 =
    Check

    -14

  6. |-7| + |3| =
    Check

    10

  7. |-10| - |4| =
    Check

    6

  8. |-8| + |-2| =
    Check

    10

Try this situation 1

A scuba diver is at -25 feet (relative to the water surface). How far below the surface is she?

Show a worked solution

Answer: 25 feet below.

Distance from the surface (0) is |-25| = 25.

Try this situation 2

Town A is at elevation -150 ft and Town B is at +150 ft. How are these elevations related?

Show a worked solution

Answer: They are opposites; both are the same distance (150 ft) from sea level.

Start by writing the calculation clearly: |-150| = |150| = 150, and the signs are different.

Fresh questions · saved on this device

Practice this skill

88 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. What is |-9| + |4|?

2. Point P is at -6 and point Q is at 2 on a number line. What is the distance between them?

3. What is |-12| - |3|?

4. What is the value of |-4| - |-4|?

5. What is the value of |-6|?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Integers & the Coordinate Plane quiz ↗Try a full practice test ↗