Sure, let's convert each of the given improper fractions to mixed numbers step by step.
### a) [tex]\(\frac{3}{2}\)[/tex]
1. Divide the numerator by the denominator:
[tex]\[
3 \div 2 = 1 \quad \text{(quotient)}
\][/tex]
2. Find the remainder:
[tex]\[
3 \mod 2 = 1 \quad \text{(remainder)}
\][/tex]
3. Construct the mixed number:
[tex]\[
1 \frac{1}{2}
\][/tex]
So, [tex]\(\frac{3}{2} = 1 \frac{1}{2}\)[/tex].
### b) [tex]\(\frac{5}{2}\)[/tex]
1. Divide the numerator by the denominator:
[tex]\[
5 \div 2 = 2 \quad \text{(quotient)}
\][/tex]
2. Find the remainder:
[tex]\[
5 \mod 2 = 1 \quad \text{(remainder)}
\][/tex]
3. Construct the mixed number:
[tex]\[
2 \frac{1}{2}
\][/tex]
So, [tex]\(\frac{5}{2} = 2 \frac{1}{2}\)[/tex].
### c) [tex]\(\frac{7}{2}\)[/tex]
1. Divide the numerator by the denominator:
[tex]\[
7 \div 2 = 3 \quad \text{(quotient)}
\][/tex]
2. Find the remainder:
[tex]\[
7 \mod 2 = 1 \quad \text{(remainder)}
\][/tex]
3. Construct the mixed number:
[tex]\[
3 \frac{1}{2}
\][/tex]
So, [tex]\(\frac{7}{2} = 3 \frac{1}{2}\)[/tex].
### d) [tex]\(\frac{9}{2}\)[/tex]
1. Divide the numerator by the denominator:
[tex]\[
9 \div 2 = 4 \quad \text{(quotient)}
\][/tex]
2. Find the remainder:
[tex]\[
9 \mod 2 = 1 \quad \text{(remainder)}
\][/tex]
3. Construct the mixed number:
[tex]\[
4 \frac{1}{2}
\][/tex]
So, [tex]\(\frac{9}{2} = 4 \frac{1}{2}\)[/tex].
### e) [tex]\(\frac{4}{3}\)[/tex]
1. Divide the numerator by the denominator:
[tex]\[
4 \div 3 = 1 \quad \text{(quotient)}
\][/tex]
2. Find the remainder:
[tex]\[
4 \mod 3 = 1 \quad \text{(remainder)}
\][/tex]
3. Construct the mixed number:
[tex]\[
1 \frac{1}{3}
\][/tex]
So, [tex]\(\frac{4}{3} = 1 \frac{1}{3}\)[/tex].
### Summary
- [tex]\(\frac{3}{2} = 1 \frac{1}{2}\)[/tex]
- [tex]\(\frac{5}{2} = 2 \frac{1}{2}\)[/tex]
- [tex]\(\frac{7}{2} = 3 \frac{1}{2}\)[/tex]
- [tex]\(\frac{9}{2} = 4 \frac{1}{2}\)[/tex]
- [tex]\(\frac{4}{3} = 1 \frac{1}{3}\)[/tex]
