Neft Teacher · Learn It

Unit 7 · Standard 6.NOS.6

Represent Rational Numbers and Their Opposites on the Number Line

Lesson 7-2 · Learn It — how the math works

Why we're learning this

Arihi planted a flower. The height and depth of the plant are shown. How do the height of the plant and the depth of the roots compare?

✱ Math Workbench

Learn It

How do you place rational numbers on a number line?

A rational number can be written as a ratio of two integers with a nonzero denominator. Integers and terminating or repeating decimals are rational. A rational number that is not an integer lies between two neighboring integers.

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

Captain Vega zoomed in on a stretch of the treasure map between -3 and -2. One point sits about halfway between those two marks, and a second point sits a little to the right of -2.
Where you see this in real lifeCaptain Vega zoomed in on a stretch of the treasure map between -3 and -2. One point sits about halfway between those two marks, and a second point sits a little to the right of -2.

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

The problem looks like this
A number line with -2.5 plotted. -4-3-2-101234-2.5
  1. I will plot -2.5 on the .
  2. First, the it falls between: -2.5 is between -2 and -3.
  3. The .5 means halfway, so I split the space between -2 and -3 in half.
  4. I place my dot exactly halfway between -2 and -3. That is -2.5.

Watch out — mistakes students make here

  • -3.5 is past -3 — you need a value between -2 and -3.
  • -1.5 is to the right of -2, not between -2 and -3.
  • 2.5 is positive — look on the negative side.

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

Same steps, new numbers.

  1. Now let's plot 0.75. Which two is it between?
    Check this step
    It is between 0 and 1.
  2. The 0.75 equals the 3/4. The denominator 4 splits one unit into four equal parts; the numerator 3 counts three parts.
  3. So we split 0 to 1 into 4 equal parts and place the dot at the 3rd mark.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the explore, plot each treasure clue like -2.5, 0.75, and -1.5 at its exact spot on the .

Solve: Which is closest to 0 on the ?

My answer

Stuck? Open one hint at a time.

Hint 1

'Closest to 0' means the SMALLEST distance from zero — the sign doesn't matter.

Hint 2

Find each choice's absolute value — for example |0.5| = 0.5 — then look for the smallest distance.

Hint 3

Write every choice as a distance from zero, then compare all four distances and take the smallest.

Check my answer
✅ Answer: -1/4
|-1/4| = 0.25, |0.5| = 0.5, |-2| = 2, |1.75| = 1.75. Since 0.25 is the smallest absolute value, -1/4 is closest to zero.

Turn & TalkSay it out loud with a partner

The flower is 7/8 foot above the ground and the roots are 7/8 foot below. How are those two distances the same, and how are they different?

Try starting with:

  • I think ___ because ___.Pienso que ___ porque ___.
  • I agree / disagree with you because ___.Estoy / no estoy de acuerdo contigo porque ___.
Use these wordsRational Numbers on the Number LineRational numberFractionDecimalNumber line