Plotting rational numbers on a number line worksheet with six problems requiring students to place fractions and mixed numbers accurately on labeled number lines.

Absolutely! Let’s solve each problem step by step, explaining how to plot each rational number on the given number lines.

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General Strategy:

- Rational numbers include fractions and mixed numbers.
- To plot them:
- Convert mixed numbers to improper fractions if helpful (but not always necessary).
- Divide the space between two integers into equal parts based on the denominator.
- Count the appropriate number of parts from the left (for negative) or right (for positive).

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## Problem 1: Plot −1/3 and 1 2/3

Number line: from −1 to 2, with marks at integers and evenly spaced tick marks in between.

- −1/3: This is one-third of the way from 0 to −1. So, divide the segment from 0 to −1 into 3 equal parts. The first mark to the left of 0 is −1/3.

- 1 2/3: This is 1 + 2/3. So, go to 1, then divide the segment from 1 to 2 into 3 equal parts. Count 2 parts to the right — that’s 1 2/3.

✔ Plot:
- −1/3 → first tick to the left of 0.
- 1 2/3 → second tick to the right of 1.

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## Problem 2: Plot 2/3 and 1 1/3

Number line: from 0 to 2, with integer marks and ticks in between.

- 2/3: Between 0 and 1, divide into 3 equal parts. The second tick is 2/3.

- 1 1/3: Between 1 and 2, divide into 3 equal parts. The first tick after 1 is 1 1/3.

✔ Plot:
- 2/3 → second tick after 0.
- 1 1/3 → first tick after 1.

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## Problem 3: Plot −1/2 and 1 3/4

Number line: from −1 to 2, with integer marks.

- −1/2: Halfway between 0 and −1. So, exactly in the middle of 0 and −1.

- 1 3/4: Between 1 and 2, divide into 4 equal parts. The third tick after 1 is 1 3/4.

✔ Plot:
- −1/2 → midpoint between 0 and −1.
- 1 3/4 → third tick after 1.

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## Problem 4: Plot 1/4 and 1 2/4

Note: 1 2/4 = 1 1/2 (simplified), but we’ll use 2/4 for plotting since the denominator is 4.

Number line: from 0 to 2.

- 1/4: Between 0 and 1, divide into 4 equal parts. First tick is 1/4.

- 1 2/4: Between 1 and 2, divide into 4 equal parts. Second tick after 1 is 1 2/4 (which is same as 1.5).

✔ Plot:
- 1/4 → first tick after 0.
- 1 2/4 → second tick after 1.

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## Problem 5: Plot −1 1/2 and 1 4/6

Note: 1 4/6 simplifies to 1 2/3, but again, we’ll use 4/6 for plotting — meaning divide into 6 parts.

Number line: from −2 to 2.

- −1 1/2: This is halfway between −1 and −2. So, midpoint between −1 and −2.

- 1 4/6: Between 1 and 2, divide into 6 equal parts. The fourth tick after 1 is 1 4/6.

✔ Plot:
- −1 1/2 → midpoint between −1 and −2.
- 1 4/6 → fourth tick after 1.

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## Problem 6: Plot 1 1/3 and 2 5/6

Number line: from 0 to 3.

- 1 1/3: Between 1 and 2, divide into 3 equal parts. First tick after 1 is 1 1/3.

- 2 5/6: Between 2 and 3, divide into 6 equal parts. Fifth tick after 2 is 2 5/6.

✔ Plot:
- 1 1/3 → first tick after 1.
- 2 5/6 → fifth tick after 2.

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## ✔ Final Answer Summary (for your worksheet):

You would mark each point as follows:

1. −1/3 ← left of 0, 1st tick; 1 2/3 ← right of 1, 2nd tick
2. 2/3 ← 2nd tick after 0; 1 1/3 ← 1st tick after 1
3. −1/2 ← midpoint between 0 and −1; 1 3/4 ← 3rd tick after 1
4. 1/4 ← 1st tick after 0; 1 2/4 ← 2nd tick after 1
5. −1 1/2 ← midpoint between −1 and −2; 1 4/6 ← 4th tick after 1
6. 1 1/3 ← 1st tick after 1; 2 5/6 ← 5th tick after 2

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📌 Tip for students: Always count the number of equal divisions based on the denominator, then count the numerator steps from the nearest whole number.

Let me know if you’d like a visual sketch or printable version!