Sure, let's break down the solution step-by-step.
### Part (a): Represent [tex]\( \frac{3}{4} \)[/tex] on a number line
To represent [tex]\( \frac{3}{4} \)[/tex] on a number line:
1. Number Line Setup: Draw a horizontal line and mark points to denote whole numbers such as 0, 1, 2, etc.
2. Division into Equal Parts: Since we need [tex]\( \frac{3}{4} \)[/tex], divide the segment between 0 and 1 into 4 equal parts.
3. Marking [tex]\( \frac{3}{4} \)[/tex]: [tex]\( \frac{3}{4} \)[/tex] is equivalent to three parts of these four. Mark the third division point from 0, which is [tex]\( \frac{3}{4} \)[/tex].
Hence, [tex]\( \frac{3}{4} \)[/tex] is placed at the point 0.75 on the number line.
### Part (b): Identify three rational numbers between [tex]\( \frac{25}{30} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex]
We need to identify three rational numbers between the fractions:
1. Simplification of [tex]\( \frac{25}{30} \)[/tex]:
- Simplify [tex]\( \frac{25}{30} \)[/tex]:
[tex]\[
\frac{25}{30} = \frac{25 \div 5}{30 \div 5} = \frac{5}{6}
\][/tex]
- [tex]\( \frac{5}{6} \)[/tex] is approximately 0.8333.
2. Simplification of [tex]\( \frac{1}{2} \)[/tex]:
- [tex]\( \frac{1}{2} = 0.5 \)[/tex]
We are looking for three rational numbers between 0.5 and 0.8333 (or [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{5}{6} \)[/tex]).
3. Identifying Rational Numbers:
- First rational number:
[tex]\[
\frac{7}{12} \approx 0.5833
\][/tex]
- Second rational number:
[tex]\[
\frac{5}{8} = 0.625
\][/tex]
- Third rational number:
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
Therefore, three rational numbers between [tex]\( \frac{25}{30} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex] are:
1. [tex]\( \frac{7}{12} \approx 0.5833 \)[/tex]
2. [tex]\( \frac{5}{8} = 0.625 \)[/tex]
3. [tex]\( \frac{3}{5} = 0.6 \)[/tex]
### Summary:
- [tex]\( \frac{3}{4} \)[/tex] on the number line is represented at 0.75.
- Three rational numbers between [tex]\( \frac{25}{30} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex] are 0.5833, 0.625, and 0.6.
