Alright, let's solve each part in detail:
1. [tex]\( \frac{2}{3} \times \frac{1}{5} \)[/tex]
- We multiply the numerators: [tex]\(2 \times 1 = 2\)[/tex].
- We multiply the denominators: [tex]\(3 \times 5 = 15\)[/tex].
- So, [tex]\( \frac{2}{3} \times \frac{1}{5} = \frac{2}{15} \approx 0.13333333333333333 \)[/tex].
2. [tex]\( \frac{3}{8} \times \frac{4}{5} \)[/tex]
- We multiply the numerators: [tex]\(3 \times 4 = 12\)[/tex].
- We multiply the denominators: [tex]\(8 \times 5 = 40\)[/tex].
- So, [tex]\( \frac{3}{8} \times \frac{4}{5} = \frac{12}{40} = \frac{3}{10} \approx 0.30000000000000004 \)[/tex].
3. [tex]\( 4 \frac{3}{8} \times 2 \frac{2}{5} \)[/tex]
- Convert the mixed numbers to improper fractions:
- [tex]\(4 \frac{3}{8} = 4 + \frac{3}{8} = \frac{32}{8} + \frac{3}{8} = \frac{35}{8}\)[/tex]
- [tex]\(2 \frac{2}{5} = 2 + \frac{2}{5} = \frac{10}{5} + \frac{2}{5} = \frac{12}{5}\)[/tex]
- We multiply the fractions:
- Numerators: [tex]\(35 \times 12 = 420\)[/tex]
- Denominators: [tex]\(8 \times 5 = 40\)[/tex]
- So, [tex]\(\frac{35}{8} \times \frac{12}{5} = \frac{420}{40} = 10.5\)[/tex].
4. [tex]\(10 \frac{1}{2} \times 13 \times 9 \frac{2}{5}\)[/tex]
- Convert the mixed numbers to improper fractions where needed:
- [tex]\(10 \frac{1}{2} = 10 + \frac{1}{2} = \frac{20}{2} + \frac{1}{2} = \frac{21}{2}\)[/tex]
- [tex]\(9 \frac{2}{5} = 9 + \frac{2}{5} = \frac{45}{5} + \frac{2}{5} = \frac{47}{5}\)[/tex]
- Multiplying the numbers step-by-step:
- [tex]\(10 \frac{1}{2} \times 13 = \frac{21}{2} \times 13 = \frac{21 \times 13}{2} = \frac{273}{2}\)[/tex]
- Then [tex]\(\frac{273}{2} \times 9 \frac{2}{5} = \frac{273}{2} \times \frac{47}{5}= \frac{273 \times 47}{2 \times 5}= \frac{12831}{10} = 1283.1000000000001 \)[/tex]
5. [tex]\(\frac{6}{15} \times 2 \frac{5}{8} \times \frac{21}{17}\)[/tex]
- Simplify [tex]\(\frac{6}{15} = \frac{2}{5}\)[/tex].
- Convert mixed numbers to improper fractions where needed:
- [tex]\(2 \frac{5}{8} = 2 + \frac{5}{8} = \frac{16}{8} + \frac{5}{8} = \frac{21}{8}\)[/tex]
- Multiplying all the fractions step-by-step:
- [tex]\(\frac{2}{5} \times 2 \frac{5}{8} = \frac{2}{5} \times \frac{21}{8} = \frac{2 \times 21}{5 \times 8} = \frac{42}{40}\)[/tex]
- Then [tex]\(\frac{42}{40} \times \frac{21}{17} = \frac{42 \times 21}{40 \times 17} = \frac{882}{680} = 1.2159926470588236\)[/tex]
These detailed steps show the full work for each part, confirming the numerical results given.
