Ordering signed numbers; absolute value

About this lesson

Grade 6 › Rational numbers

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Ordering signed numbers; absolute value

Discover

It is −8-8 °C in one town and −3-3 °C in another. Which is warmer?

  1. −3-3 °C
  2. −8-8 °C

Key idea

Order on the number line; absolute value is distance from 0.

Numbers increase from left to right on the number line, so −8<−3-8 < -3. The absolute value ∣a∣|a| is the distance from aa to 0, never negative: ∣−5∣=5|-5| = 5. The distance between numbers on opposite sides of 0 is the sum of their absolute values.

Worked example

Order −2-2, 44, −6-6, 00.

−6<−2<0<4-6 < -2 < 0 < 4
Left to right.

Your turn, guided

Your turn: ∣−9∣+∣−1∣|-9| + |-1|.

1010
9 + 1.

Practice ★

  1. Which number is greater: −5-5 or −12-12?
    1. −5-5
    2. −12-12
    3. They are equal
  2. Which number is greater: −5-5 or −10-10?
    1. −5-5
    2. −10-10
    3. They are equal
  1. Compute ∣−4∣+∣10∣|-4| + |10|.

Watch out!

Practice ★★

  1. How far apart are −7-7 and 66 on the number line?
  2. How far apart are −15-15 and 11 on the number line?

Exit ticket

Three questions to check you have got it.

  1. Compute ∣−4∣+∣10∣|-4| + |10|.
  2. Compute ∣−2∣+∣10∣|-2| + |10|.
  3. Compute ∣−8∣+∣3∣|-8| + |3|.

Summary card

Ordering and absolute value

Right is greater; |a| is the distance to 0.

Watch out: −8 is less than −3.

End of the lesson

Next lesson: The coordinate plane: quadrants and distances along grid lines Back to the chapter

Answers: Ordering signed numbers; absolute value

A

  1. −5-5
  2. −5-5

B

  1. 1414

C

  1. 1313
  2. 1616

D

  1. 1414
  2. 1212
  3. 1111

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