To help you mark the fractions and mixed numbers $\frac{1}{6}, \frac{1}{3}, \frac{2}{3}, \frac{5}{6}, \frac{1}{2}, \frac{2}{3}, 2 \frac{1}{3}$ on the number line, let’s break this into steps and calculations.

Step 1: Understand the divisions on the number line

The number line is divided into 18 equal sections. These divisions help us place the fractions in the correct spots.

Step 2: Convert fractions to equivalent terms based on 18ths

To place the fractions accurately:

1. $\frac{1}{6} = \frac{3}{18}$
2. $\frac{1}{3} = \frac{6}{18}$
3. $\frac{2}{3} = \frac{12}{18}$
4. $\frac{5}{6} = \frac{15}{18}$
5. $2 \frac{1}{3} = 2 + \frac{6}{18} = 2 \frac{6}{18}$

Step 3: Mark each value on the number line

1. Start at $0$:
   • $\frac{1}{6}$ ($3/18$) is 3 small divisions to the right of $0$.
   • $\frac{1}{3}$ ($6/18$) is 6 small divisions to the right of $0$.
   • $\frac{2}{3}$ ($12/18$) is 12 small divisions to the right of $0$.
   • $\frac{5}{6}$ ($15/18$) is 15 small divisions to the right of $0$.
   • $2 \frac{1}{3}$ ($2 + \frac{6}{18}$) is 2 full units plus 6 divisions to the right.

Would you like me to add a detailed explanation for each placement? Let me know!

5 Related Questions:

1. How can you simplify fractions to find equivalent fractions?
2. How do you identify the scale of a number line when dividing into parts?
3. What are mixed numbers, and how are they converted to improper fractions?
4. How would you place fractions on a number line with uneven divisions?
5. How do you estimate positions of fractions between whole numbers?

Tip:

When working with fractions on a number line, always convert them to a common denominator based on the divisions of the line for precise placement!