Answer :
Sure, let's go through each problem step by step to multiply the fractions and then simplify them. Remember that multiplying fractions involves multiplying the numerators together and the denominators together, and simplifying involves finding the greatest common divisor (GCD) to reduce the fraction.
1. [tex]\(\frac{2}{1} \times \frac{3}{10}\)[/tex]:
- Multiply the numerators: [tex]\(2 \times 3 = 6\)[/tex]
- Multiply the denominators: [tex]\(1 \times 10 = 10\)[/tex]
- Resulting fraction: [tex]\(\frac{6}{10}\)[/tex]
- Simplify: GCD of 6 and 10 is 2, so [tex]\(\frac{6 \div 2}{10 \div 2} = \frac{3}{5}\)[/tex]
2. [tex]\(\frac{8}{1} \times \frac{4}{8}\)[/tex]:
- Multiply the numerators: [tex]\(8 \times 4 = 32\)[/tex]
- Multiply the denominators: [tex]\(1 \times 8 = 8\)[/tex]
- Resulting fraction: [tex]\(\frac{32}{8}\)[/tex]
- Simplify: [tex]\(\frac{32}{8} = 4\)[/tex]
3. [tex]\(9 \times \frac{3}{9}\)[/tex]:
- Multiply the numerators: [tex]\(9 \times 3 = 27\)[/tex]
- The denominator remains 9.
- Resulting fraction: [tex]\(\frac{27}{9}\)[/tex]
- Simplify: [tex]\(\frac{27}{9} = 3\)[/tex]
4. [tex]\(12 \times \frac{2}{11}\)[/tex]:
- Multiply the numerators: [tex]\(12 \times 2 = 24\)[/tex]
- The denominator remains 11.
- Resulting fraction: [tex]\(\frac{24}{11}\)[/tex]
- Since 24 and 11 have no common factors besides 1, [tex]\(\frac{24}{11}\)[/tex] is already in its simplest form.
5. [tex]\(3 \times \frac{5}{7}\)[/tex]:
- Multiply the numerators: [tex]\(3 \times 5 = 15\)[/tex]
- The denominator remains 7.
- Resulting fraction: [tex]\(\frac{15}{7}\)[/tex]
- Since 15 and 7 have no common factors besides 1, [tex]\(\frac{15}{7}\)[/tex] is already in its simplest form.
6. [tex]\(2 \times \frac{3}{5}\)[/tex]:
- Multiply the numerators: [tex]\(2 \times 3 = 6\)[/tex]
- The denominator remains 5.
- Resulting fraction: [tex]\(\frac{6}{5}\)[/tex]
- Since 6 and 5 have no common factors besides 1, [tex]\(\frac{6}{5}\)[/tex] is already in its simplest form.
7. [tex]\(11 \times \frac{4}{8}\)[/tex]:
- Multiply the numerators: [tex]\(11 \times 4 = 44\)[/tex]
- The denominator remains 8.
- Resulting fraction: [tex]\(\frac{44}{8}\)[/tex]
- Simplify: GCD of 44 and 8 is 4, so [tex]\(\frac{44 \div 4}{8 \div 4} = \frac{11}{2}\)[/tex]
8. [tex]\(10 \times \frac{1}{4}\)[/tex]:
- Multiply the numerators: [tex]\(10 \times 1 = 10\)[/tex]
- The denominator remains 4.
- Resulting fraction: [tex]\(\frac{10}{4}\)[/tex]
- Simplify: GCD of 10 and 4 is 2, so [tex]\(\frac{10 \div 2}{4 \div 2} = \frac{5}{2}\)[/tex]
9. [tex]\(5 \times \frac{1}{4}\)[/tex]:
- Multiply the numerators: [tex]\(5 \times 1 = 5\)[/tex]
- The denominator remains 4.
- Resulting fraction: [tex]\(\frac{5}{4}\)[/tex]
- Since 5 and 4 have no common factors besides 1, [tex]\(\frac{5}{4}\)[/tex] is already in its simplest form.
10. [tex]\(11 \times \frac{2}{7}\)[/tex]:
- Multiply the numerators: [tex]\(11 \times 2 = 22\)[/tex]
- The denominator remains 7.
- Resulting fraction: [tex]\(\frac{22}{7}\)[/tex]
- Since 22 and 7 have no common factors besides 1, [tex]\(\frac{22}{7}\)[/tex] is already in its simplest form.
Given all the steps and simplifications, the final simplified results are:
1. [tex]\(\frac{2}{1} \times \frac{3}{10} = \frac{3}{5}\)[/tex]
2. [tex]\(\frac{8}{1} \times \frac{4}{8} = 4\)[/tex]
3. [tex]\(9 \times \frac{3}{9} = 3\)[/tex]
4. [tex]\(12 \times \frac{2}{11} = \frac{24}{11}\)[/tex]
5. [tex]\(3 \times \frac{5}{7} = \frac{15}{7}\)[/tex]
6. [tex]\(2 \times \frac{3}{5} = \frac{6}{5}\)[/tex]
7. [tex]\(11 \times \frac{4}{8} = \frac{11}{2}\)[/tex]
8. [tex]\(10 \times \frac{1}{4} = \frac{5}{2}\)[/tex]
9. [tex]\(5 \times \frac{1}{4} = \frac{5}{4}\)[/tex]
10. [tex]\(11 \times \frac{2}{7} = \frac{22}{7}\)[/tex]
1. [tex]\(\frac{2}{1} \times \frac{3}{10}\)[/tex]:
- Multiply the numerators: [tex]\(2 \times 3 = 6\)[/tex]
- Multiply the denominators: [tex]\(1 \times 10 = 10\)[/tex]
- Resulting fraction: [tex]\(\frac{6}{10}\)[/tex]
- Simplify: GCD of 6 and 10 is 2, so [tex]\(\frac{6 \div 2}{10 \div 2} = \frac{3}{5}\)[/tex]
2. [tex]\(\frac{8}{1} \times \frac{4}{8}\)[/tex]:
- Multiply the numerators: [tex]\(8 \times 4 = 32\)[/tex]
- Multiply the denominators: [tex]\(1 \times 8 = 8\)[/tex]
- Resulting fraction: [tex]\(\frac{32}{8}\)[/tex]
- Simplify: [tex]\(\frac{32}{8} = 4\)[/tex]
3. [tex]\(9 \times \frac{3}{9}\)[/tex]:
- Multiply the numerators: [tex]\(9 \times 3 = 27\)[/tex]
- The denominator remains 9.
- Resulting fraction: [tex]\(\frac{27}{9}\)[/tex]
- Simplify: [tex]\(\frac{27}{9} = 3\)[/tex]
4. [tex]\(12 \times \frac{2}{11}\)[/tex]:
- Multiply the numerators: [tex]\(12 \times 2 = 24\)[/tex]
- The denominator remains 11.
- Resulting fraction: [tex]\(\frac{24}{11}\)[/tex]
- Since 24 and 11 have no common factors besides 1, [tex]\(\frac{24}{11}\)[/tex] is already in its simplest form.
5. [tex]\(3 \times \frac{5}{7}\)[/tex]:
- Multiply the numerators: [tex]\(3 \times 5 = 15\)[/tex]
- The denominator remains 7.
- Resulting fraction: [tex]\(\frac{15}{7}\)[/tex]
- Since 15 and 7 have no common factors besides 1, [tex]\(\frac{15}{7}\)[/tex] is already in its simplest form.
6. [tex]\(2 \times \frac{3}{5}\)[/tex]:
- Multiply the numerators: [tex]\(2 \times 3 = 6\)[/tex]
- The denominator remains 5.
- Resulting fraction: [tex]\(\frac{6}{5}\)[/tex]
- Since 6 and 5 have no common factors besides 1, [tex]\(\frac{6}{5}\)[/tex] is already in its simplest form.
7. [tex]\(11 \times \frac{4}{8}\)[/tex]:
- Multiply the numerators: [tex]\(11 \times 4 = 44\)[/tex]
- The denominator remains 8.
- Resulting fraction: [tex]\(\frac{44}{8}\)[/tex]
- Simplify: GCD of 44 and 8 is 4, so [tex]\(\frac{44 \div 4}{8 \div 4} = \frac{11}{2}\)[/tex]
8. [tex]\(10 \times \frac{1}{4}\)[/tex]:
- Multiply the numerators: [tex]\(10 \times 1 = 10\)[/tex]
- The denominator remains 4.
- Resulting fraction: [tex]\(\frac{10}{4}\)[/tex]
- Simplify: GCD of 10 and 4 is 2, so [tex]\(\frac{10 \div 2}{4 \div 2} = \frac{5}{2}\)[/tex]
9. [tex]\(5 \times \frac{1}{4}\)[/tex]:
- Multiply the numerators: [tex]\(5 \times 1 = 5\)[/tex]
- The denominator remains 4.
- Resulting fraction: [tex]\(\frac{5}{4}\)[/tex]
- Since 5 and 4 have no common factors besides 1, [tex]\(\frac{5}{4}\)[/tex] is already in its simplest form.
10. [tex]\(11 \times \frac{2}{7}\)[/tex]:
- Multiply the numerators: [tex]\(11 \times 2 = 22\)[/tex]
- The denominator remains 7.
- Resulting fraction: [tex]\(\frac{22}{7}\)[/tex]
- Since 22 and 7 have no common factors besides 1, [tex]\(\frac{22}{7}\)[/tex] is already in its simplest form.
Given all the steps and simplifications, the final simplified results are:
1. [tex]\(\frac{2}{1} \times \frac{3}{10} = \frac{3}{5}\)[/tex]
2. [tex]\(\frac{8}{1} \times \frac{4}{8} = 4\)[/tex]
3. [tex]\(9 \times \frac{3}{9} = 3\)[/tex]
4. [tex]\(12 \times \frac{2}{11} = \frac{24}{11}\)[/tex]
5. [tex]\(3 \times \frac{5}{7} = \frac{15}{7}\)[/tex]
6. [tex]\(2 \times \frac{3}{5} = \frac{6}{5}\)[/tex]
7. [tex]\(11 \times \frac{4}{8} = \frac{11}{2}\)[/tex]
8. [tex]\(10 \times \frac{1}{4} = \frac{5}{2}\)[/tex]
9. [tex]\(5 \times \frac{1}{4} = \frac{5}{4}\)[/tex]
10. [tex]\(11 \times \frac{2}{7} = \frac{22}{7}\)[/tex]
