To address the math problem involving fractions and their positions on the number line, follow these detailed steps:
### Part (a): Mark Each Fraction on the Number Line
1. Identify the fractions to be marked:
- [tex]\(\frac{2}{10}\)[/tex]
- [tex]\(\frac{1}{4}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex]
2. Convert the fractions to decimals for easier placement:
- [tex]\(\frac{2}{10} = 0.2\)[/tex]
- [tex]\(\frac{1}{4} = 0.25\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
3. Draw a number line ranging from 0 to 1:
- On this number line, place the fractions at their corresponding decimal values.
- 0.2 ([tex]\(\frac{2}{10}\)[/tex]) is slightly less than a quarter.
- 0.25 ([tex]\(\frac{1}{4}\)[/tex]) is exactly at the quarter point.
- 0.5 ([tex]\(\frac{1}{2}\)[/tex]) is halfway between 0 and 1.
### Part (b): Marking the Positions of 1, 2, and 3 on the Number Line
1. Adjust the number line to include points up to 3:
- Extend the number line beyond 1 to include 2 and 3.
2. Identify the positions:
- 1 is at the next whole number after 0.
- 2 is the whole number after 1.
- 3 is the whole number after 2.
### Part (c): Determine the Correct Placement
1. Compare your markings:
- Ensure the fractions are correctly placed relative to their decimal values.
- Confirm that the positions of 1, 2, and 3 are marked correctly.
2. Verification:
- Check with other students or teams to see if they also placed the points at the correct positions.
This comprehensive method ensures that fractions and whole numbers are accurately placed on the number line.
