Sure! To label the fractions [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] on the number line, let's follow these steps:
1. Convert Fractions to Decimals:
- [tex]\(\frac{4}{5}\)[/tex] is equivalent to 0.8.
- [tex]\(\frac{6}{7}\)[/tex] is approximately 0.8571428571428571.
2. Draw the Number Line:
- Start by drawing a horizontal line.
- Label the line with integers. For ease, let's label from 0 to 1 since both fractions are between these values.
3. Mark the Positions of Decimals on the Number Line:
- First identify the position of 0.8:
- 0.8 is 4/5 of the way from 0 to 1. Mark a point closer to 1 than 0, specifically four segments out of five.
- Next identify the position of approximately 0.8571428571428571:
- This number is 6/7 of the way from 0 to 1. Mark a point slightly closer to 1 than the 0.8 mark, as 0.8571428571428571 is greater than 0.8.
4. Label the Points:
- Write [tex]\(\frac{4}{5}\)[/tex] (or 0.8) at the position you marked for 0.8.
- Write [tex]\(\frac{6}{7}\)[/tex] (or approximately 0.8571428571428571) at the position you marked for 0.8571428571428571.
Visually, the number line should look like this:
```
0 0.5 0.8 0.8571 1
|----|------|-------|-----|
```
Here the vertical lines represent where the fractions are located on the number line and the decimal approximations show their respective positions.
