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Unit 7 · Standard 6.NOS.8

Understand Absolute Value of Rational Numbers

Lesson 7-3 · Learn It — how the math works

Why we're learning this

Claire is performing a science experiment with two liquids. The temperatures of the two liquids in Celsius are shown. She needs to use the beaker with the temperature that is closer to 0°C. Which beaker should Claire use?

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What is absolute value?

A rational number is any number that can be written as a fraction: integers like -6, fractions like -3/4, and decimals like 2.5 are all rational numbers. The absolute value of a number is how far it is from zero on the number line. Distance is never negative.

Picture itSee what the math looks like before you read about it

Claire is performing a science experiment with two liquids. The temperatures of the two liquids in Celsius are shown, and she needs to use the beaker with the temperature closer to 0°C.
Where you see this in real lifeClaire is performing a science experiment with two liquids. The temperatures of the two liquids in Celsius are shown, and she needs to use the beaker with the temperature closer to 0°C.

Watch me solve itI do — read one step at a time

The problem looks like this
A number line with -6 marked, showing how many steps it sits from zero. -8-6-4-202468-6
  1. I want to find the of -6, written |-6|.
  2. I find -6 on the number line. It sits 6 steps to the left of zero.
  3. Distance does not care about direction, so -6 is 6 units from zero.
  4. So |-6| = 6. Even though -6 is , its is 6.

Watch out — mistakes students make here

  • Its absolute value is 80, not 8 — check the distance from zero.
  • Zero's absolute value is 0, not 8 — find distance 8 left.
  • 8 is to the RIGHT of zero — you need the negative side.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now let's find |3|. Where is 3 on the number line?
    Check this step
    It is 3 steps to the right of zero.
  2. How far is it from zero?
    Check this step
    It is 3 units away.
  3. So |3| equals what?
    Check this step
    It equals 3.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Find |−2.5|. Where does −2.5 sit on the number line, and how far is it from zero?
  • Now find |3/4|. Distance does not care whether the number is whole.
  • Plot each treasure location — like −4, 6, −2.5 and 3/4 — and give its .
  • Say the rule in your own words: what do all four answers have in common?

Solve: Which statement about is TRUE?

My answer

Stuck? Open one hint at a time.

Hint 1

Remember the definition: absolute value measures DISTANCE from zero, and a distance is never negative.

Hint 2

Test each statement against the definition. Ask: how far is -4 from zero? How far is 4? Can distance be negative?

Hint 3

First count -4's units from zero, then count 4's units from zero. Compare the two counts before judging.

Check my answer
✅ Answer: |-4| = |4| because both are 4 units from zero
Absolute value measures distance from zero. Both -4 and 4 are 4 units from zero, so |-4| = |4| = 4.

Turn & TalkSay it out loud with a partner

Why are -5 and 5 both the same distance from zero on the number line, even though one is and one is ?

Try starting with:

  • Both numbers are ___ units from zero.Ambos numeros estan a ___ unidades del cero.
  • They are different because one is ___ and one is ___.Son diferentes porque uno es ___ y el otro es ___.
Use these wordsintegerabsolute valueoppositepositivenegative