Sure, let's solve each of these calculations step-by-step:
1. [tex]\(\frac{3}{4} \times \frac{4}{6}\)[/tex]:
- We multiply the numerators: [tex]\(3 \times 4 = 12\)[/tex].
- We multiply the denominators: [tex]\(4 \times 6 = 24\)[/tex].
- Thus, [tex]\(\frac{3}{4} \times \frac{4}{6} = \frac{12}{24}\)[/tex].
- We simplify [tex]\(\frac{12}{24}\)[/tex] to [tex]\(\frac{1}{2} = 0.5\)[/tex].
2. [tex]\(\frac{5}{7} \times \frac{3}{8}\)[/tex]:
- We multiply the numerators: [tex]\(5 \times 3 = 15\)[/tex].
- We multiply the denominators: [tex]\(7 \times 8 = 56\)[/tex].
- Thus, [tex]\(\frac{5}{7} \times \frac{3}{8} = \frac{15}{56}\)[/tex].
- In decimal form, [tex]\(\frac{15}{56} \approx 0.26785714285714285\)[/tex].
3. [tex]\(3 \cdot \frac{7}{9} \times \frac{4}{10}\)[/tex]:
- First, calculate [tex]\(3 \cdot \frac{7}{9}\)[/tex]:
- Convert 3 to a fraction: [tex]\(3 = \frac{3}{1}\)[/tex].
- Multiply the numerators: [tex]\(3 \times 7 = 21\)[/tex].
- Multiply the denominators: [tex]\(1 \times 9 = 9\)[/tex].
- Thus, [tex]\(3 \cdot \frac{7}{9} = \frac{21}{9}\)[/tex].
- Next, multiply this result by [tex]\(\frac{4}{10}\)[/tex]:
- Multiply the numerators: [tex]\(21 \times 4 = 84\)[/tex].
- Multiply the denominators: [tex]\(9 \times 10 = 90\)[/tex].
- Thus, [tex]\(\frac{21}{9} \times \frac{4}{10} = \frac{84}{90}\)[/tex].
- In decimal form, after simplifying [tex]\(\frac{84}{90}\)[/tex]: [tex]\(0.9333333333333335\)[/tex].
4. [tex]\(4 \cdot \frac{4}{5} \times \frac{4}{7}\)[/tex]:
- First, calculate [tex]\(4 \cdot \frac{4}{5}\)[/tex]:
- Convert 4 to a fraction: [tex]\(4 = \frac{4}{1}\)[/tex].
- Multiply the numerators: [tex]\(4 \times 4 = 16\)[/tex].
- Multiply the denominators: [tex]\(1 \times 5 = 5\)[/tex].
- Thus, [tex]\(4 \cdot \frac{4}{5} = \frac{16}{5}\)[/tex].
- Next, multiply this result by [tex]\(\frac{4}{7}\)[/tex]:
- Multiply the numerators: [tex]\(16 \times 4 = 64\)[/tex].
- Multiply the denominators: [tex]\(5 \times 7 = 35\)[/tex].
- Thus, [tex]\(\frac{16}{5} \times \frac{4}{7} = \frac{64}{35}\)[/tex].
- In decimal form, after simplifying [tex]\(\frac{64}{35}\)[/tex]: [tex]\(1.8285714285714285\)[/tex].
5. [tex]\(\frac{5.2}{6} \times \frac{2}{9}\)[/tex]:
- We multiply the numerators: [tex]\(5.2 \times 2 = 10.4\)[/tex].
- We multiply the denominators: [tex]\(6 \times 9 = 54\)[/tex].
- Thus, [tex]\(\frac{5.2}{6} \times \frac{2}{9} = \frac{10.4}{54}\)[/tex].
- In decimal form, after simplifying [tex]\(\frac{10.4}{54}\)[/tex]: [tex]\(0.1925925925925926\)[/tex].
So, the results for the given calculations are:
1. [tex]\(0.5\)[/tex]
2. [tex]\(0.26785714285714285\)[/tex]
3. [tex]\(0.9333333333333335\)[/tex]
4. [tex]\(1.8285714285714285\)[/tex]
5. [tex]\(0.1925925925925926\)[/tex]
