Sure, let's convert each mixed number to an improper fraction step by step.
### a) [tex]\(1 \frac{1}{2}\)[/tex]
To convert [tex]\(1 \frac{1}{2}\)[/tex] to an improper fraction:
1. Multiply the whole number part by the denominator: [tex]\(1 \times 2 = 2\)[/tex].
2. Add the numerator: [tex]\(2 + 1 = 3\)[/tex].
3. The denominator remains the same: [tex]\(2\)[/tex].
So, [tex]\(1 \frac{1}{2} = \frac{3}{2}\)[/tex].
### b) [tex]\(1 \frac{1}{3}\)[/tex]
To convert [tex]\(1 \frac{1}{3}\)[/tex] to an improper fraction:
1. Multiply the whole number part by the denominator: [tex]\(1 \times 3 = 3\)[/tex].
2. Add the numerator: [tex]\(3 + 1 = 4\)[/tex].
3. The denominator remains the same: [tex]\(3\)[/tex].
So, [tex]\(1 \frac{1}{3} = \frac{4}{3}\)[/tex].
### c) [tex]\(1 \frac{2}{3}\)[/tex]
To convert [tex]\(1 \frac{2}{3}\)[/tex] to an improper fraction:
1. Multiply the whole number part by the denominator: [tex]\(1 \times 3 = 3\)[/tex].
2. Add the numerator: [tex]\(3 + 2 = 5\)[/tex].
3. The denominator remains the same: [tex]\(3\)[/tex].
So, [tex]\(1 \frac{2}{3} = \frac{5}{3}\)[/tex].
### d) [tex]\(2 \frac{1}{2}\)[/tex]
To convert [tex]\(2 \frac{1}{2}\)[/tex] to an improper fraction:
1. Multiply the whole number part by the denominator: [tex]\(2 \times 2 = 4\)[/tex].
2. Add the numerator: [tex]\(4 + 1 = 5\)[/tex].
3. The denominator remains the same: [tex]\(2\)[/tex].
So, [tex]\(2 \frac{1}{2} = \frac{5}{2}\)[/tex].
### e) [tex]\(2 \frac{2}{3}\)[/tex]
To convert [tex]\(2 \frac{2}{3}\)[/tex] to an improper fraction:
1. Multiply the whole number part by the denominator: [tex]\(2 \times 3 = 6\)[/tex].
2. Add the numerator: [tex]\(6 + 2 = 8\)[/tex].
3. The denominator remains the same: [tex]\(3\)[/tex].
So, [tex]\(2 \frac{2}{3} = \frac{8}{3}\)[/tex].
### Final Results
- [tex]\(1 \frac{1}{2} = \frac{3}{2}\)[/tex]
- [tex]\(1 \frac{1}{3} = \frac{4}{3}\)[/tex]
- [tex]\(1 \frac{2}{3} = \frac{5}{3}\)[/tex]
- [tex]\(2 \frac{1}{2} = \frac{5}{2}\)[/tex]
- [tex]\(2 \frac{2}{3} = \frac{8}{3}\)[/tex]
These are the improper fractions for the given mixed numbers.
