Let's convert each given improper fraction to a mixed number. The process involves finding the integer part and the fractional part.
### a) [tex]\(\frac{3}{2}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{3}{2} \right\rfloor = 1\)[/tex]
2. Fractional part: [tex]\(\frac{3 - 1 \cdot 2}{2} = \frac{1}{2}\)[/tex]
3. Mixed number: [tex]\(1 \frac{1}{2}\)[/tex]
### b) [tex]\(\frac{5}{2}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{5}{2} \right\rfloor = 2\)[/tex]
2. Fractional part: [tex]\(\frac{5 - 2 \cdot 2}{2} = \frac{1}{2}\)[/tex]
3. Mixed number: [tex]\(2 \frac{1}{2}\)[/tex]
### c) [tex]\(\frac{7}{2}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{7}{2} \right\rfloor = 3\)[/tex]
2. Fractional part: [tex]\(\frac{7 - 3 \cdot 2}{2} = \frac{1}{2}\)[/tex]
3. Mixed number: [tex]\(3 \frac{1}{2}\)[/tex]
### d) [tex]\(\frac{9}{2}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{9}{2} \right\rfloor = 4\)[/tex]
2. Fractional part: [tex]\(\frac{9 - 4 \cdot 2}{2} = \frac{1}{2}\)[/tex]
3. Mixed number: [tex]\(4 \frac{1}{2}\)[/tex]
### e) [tex]\(\frac{4}{3}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{4}{3} \right\rfloor = 1\)[/tex]
2. Fractional part: [tex]\(\frac{4 - 1 \cdot 3}{3} = \frac{1}{3}\)[/tex]
3. Mixed number: [tex]\(1 \frac{1}{3}\)[/tex]
### f) [tex]\(\frac{5}{3}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{5}{3} \right\rfloor = 1\)[/tex]
2. Fractional part: [tex]\(\frac{5 - 1 \cdot 3}{3} = \frac{2}{3}\)[/tex]
3. Mixed number: [tex]\(1 \frac{2}{3}\)[/tex]
### g) [tex]\(\frac{10}{3}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{10}{3} \right\rfloor = 3\)[/tex]
2. Fractional part: [tex]\(\frac{10 - 3 \cdot 3}{3} = \frac{1}{3}\)[/tex]
3. Mixed number: [tex]\(3 \frac{1}{3}\)[/tex]
### h) [tex]\(\frac{5}{4}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{5}{4} \right\rfloor = 1\)[/tex]
2. Fractional part: [tex]\(\frac{5 - 1 \cdot 4}{4} = \frac{1}{4}\)[/tex]
3. Mixed number: [tex]\(1 \frac{1}{4}\)[/tex]
### i) [tex]\(\frac{9}{4}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{9}{4} \right\rfloor = 2\)[/tex]
2. Fractional part: [tex]\(\frac{9 - 2 \cdot 4}{4} = \frac{1}{4}\)[/tex]
3. Mixed number: [tex]\(2 \frac{1}{4}\)[/tex]
### j) [tex]\(\frac{6}{5}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{6}{5} \right\rfloor = 1\)[/tex]
2. Fractional part: [tex]\(\frac{6 - 1 \cdot 5}{5} = \frac{1}{5}\)[/tex]
3. Mixed number: [tex]\(1 \frac{1}{5}\)[/tex]
### k) [tex]\(\frac{12}{5}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{12}{5} \right\rfloor = 2\)[/tex]
2. Fractional part: [tex]\(\frac{12 - 2 \cdot 5}{5} = \frac{2}{5}\)[/tex]
3. Mixed number: [tex]\(2 \frac{2}{5}\)[/tex]
### l) [tex]\(\frac{15}{4}\)[/tex]
1. Integer part: [tex]\(\left\lfloor \frac{15}{4} \right\rfloor = 3\)[/tex]
2. Fractional part: [tex]\(\frac{15 - 3 \cdot 4}{4} = \frac{3}{4}\)[/tex]
3. Mixed number: [tex]\(3 \frac{3}{4}\)[/tex]
So, the mixed numbers are:
- a) [tex]\(1 \frac{1}{2}\)[/tex]
- b) [tex]\(2 \frac{1}{2}\)[/tex]
- c) [tex]\(3 \frac{1}{2}\)[/tex]
- d) [tex]\(4 \frac{1}{2}\)[/tex]
- e) [tex]\(1 \frac{1}{3}\)[/tex]
- f) [tex]\(1 \frac{2}{3}\)[/tex]
- g) [tex]\(3 \frac{1}{3}\)[/tex]
- h) [tex]\(1 \frac{1}{4}\)[/tex]
- i) [tex]\(2 \frac{1}{4}\)[/tex]
- j) [tex]\(1 \frac{1}{5}\)[/tex]
- k) [tex]\(2 \frac{2}{5}\)[/tex]
- l) [tex]\(3 \frac{3}{4}\)[/tex]
