Let's solve these step-by-step:
1. [tex]\(\frac{1}{5} \times 5\)[/tex]:
- When you multiply a fraction by its denominator, the result is just the numerator.
- [tex]\(\frac{1}{5} \times 5 = 1 \times 1 = 1.0\)[/tex]
2. [tex]\(5 \times \frac{4}{5}\)[/tex]:
- When multiplying a whole number by a fraction, you multiply the whole number by the numerator of the fraction and then divide by the denominator.
- [tex]\(5 \times \frac{4}{5} = \frac{5 \times 4}{5} = \frac{20}{5} = 4.0\)[/tex]
3. [tex]\(\frac{5}{10} \times 4\)[/tex]:
- Simplify the fraction first, [tex]\(\frac{5}{10} = \frac{1}{2}\)[/tex].
- Then multiply the simplified fraction by 4.
- [tex]\(\frac{1}{2} \times 4 = 2.0\)[/tex]
4. [tex]\(3 \frac{2}{5} \times 3\)[/tex]:
- Convert the mixed number to an improper fraction.
- [tex]\(3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}\)[/tex]
- Now, multiply the improper fraction by 3.
- [tex]\(\frac{17}{5} \times 3 = \frac{17 \times 3}{5} = \frac{51}{5} = 10.2\)[/tex]
5. [tex]\(5 \frac{7}{10} \times 8\)[/tex]:
- Convert the mixed number to an improper fraction.
- [tex]\(5 \frac{7}{10} = 5 + \frac{7}{10} = \frac{50}{10} + \frac{7}{10} = \frac{57}{10}\)[/tex]
- Now, multiply the improper fraction by 8.
- [tex]\(\frac{57}{10} \times 8 = \frac{57 \times 8}{10} = \frac{456}{10} = 45.6\)[/tex]
To summarize, the answers are:
1. [tex]\(1.0\)[/tex]
2. [tex]\(4.0\)[/tex]
3. [tex]\(2.0\)[/tex]
4. [tex]\(10.2\)[/tex]
5. [tex]\(45.6\)[/tex]
