To draw a number line and locate the fractions on it, follow these steps:
### Part (i): Locating [tex]\(1 \frac{1}{4}\)[/tex] and [tex]\(2 \frac{3}{4}\)[/tex]
1. Identify Whole Numbers:
- [tex]\(1 \frac{1}{4}\)[/tex] falls between 1 and 2.
- [tex]\(2 \frac{3}{4}\)[/tex] falls between 2 and 3.
2. Draw the Number Line:
- Mark the integers 1, 2, and 3.
3. Divide the Segments:
- Divide the segment between each pair of integers into 4 equal parts to accommodate quarters (since [tex]\(4\)[/tex] is the denominator of the rest).
4. Locate Each Fraction:
- [tex]\(1 \frac{1}{4}\)[/tex]: This is one-quarter (or one-fourth) past the integer 1.
- [tex]\(2 \frac{3}{4}\)[/tex]: This is three-quarters past the integer 2.
### Number Line for Part (i):
```
0 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
|----|----|----|----|----|----|----|----|----|----|
^ (1 1/4) ^ (2 3/4)
```
### Part (ii): Locating [tex]\(2 \frac{3}{7}\)[/tex] and [tex]\(2 \frac{6}{7}\)[/tex]
1. Identify Whole Numbers:
- Both [tex]\(2 \frac{3}{7}\)[/tex] and [tex]\(2 \frac{6}{7}\)[/tex] fall between 2 and 3.
2. Draw the Number Line:
- Mark the integers 2 and 3.
3. Divide the Segments:
- Divide the segment between 2 and 3 into 7 equal parts to accommodate sevenths (since [tex]\(7\)[/tex] is the denominator).
4. Locate Each Fraction:
- [tex]\(2 \frac{3}{7}\)[/tex]: This is three-sevenths past the integer 2.
- [tex]\(2 \frac{6}{7}\)[/tex]: This is six-sevenths past the integer 2.
### Number Line for Part (ii):
```
2 2.14 2.28 2.42 2.57 2.71 2.85 3
|----|----|----|----|----|----|----|
^ (2 3/7) ^ (2 6/7)
```
### Part (iii): Locating [tex]\(3 \frac{1}{5}\)[/tex] and [tex]\(3 \frac{4}{5}\)[/tex]
1. Identify Whole Numbers:
- Both [tex]\(3 \frac{1}{5}\)[/tex] and [tex]\(3 \frac{4}{5}\)[/tex] fall between 3 and 4.
2. Draw the Number Line:
- Mark the integers 3 and 4.
3. Divide the Segments:
- Divide the segment between 3 and 4 into 5 equal parts to accommodate fifths (since [tex]\(5\)[/tex] is the denominator).
4. Locate Each Fraction:
- [tex]\(3 \frac{1}{5}\)[/tex]: This is one-fifth past the integer 3.
- [tex]\(3 \frac{4}{5}\)[/tex]: This is four-fifths past the integer 3.
### Number Line for Part (iii):
```
3 3.2 3.4 3.6 3.8 4
|----|----|----|----|----|
^ (3 1/5) ^ (3 4/5)
```
And that's how to draw a number line and locate each of the given fractions on it.
