Answer :
Sure, let's simplify each of the given fractions step by step and reduce them to their lowest terms where necessary.
1. [tex]\(\frac{2}{3} + \frac{2}{3}\)[/tex]
- Adding the fractions: [tex]\(\frac{2}{3} + \frac{2}{3} = \frac{4}{3}\)[/tex]
- This fraction is already in its simplest form.
- Result: [tex]\(\frac{4}{3}\)[/tex]
2. [tex]\(\frac{8}{12} + \frac{2}{12} + \frac{2}{12}\)[/tex]
- Adding the fractions: [tex]\(\frac{8}{12} + \frac{2}{12} + \frac{2}{12} = \frac{12}{12}\)[/tex]
- Simplify [tex]\(\frac{12}{12}\)[/tex] to [tex]\(1\)[/tex].
- Result: [tex]\(1\)[/tex]
3. [tex]\(\frac{5}{10} + \frac{7}{10}\)[/tex]
- Adding the fractions: [tex]\(\frac{5}{10} + \frac{7}{10} = \frac{12}{10}\)[/tex]
- Simplify [tex]\(\frac{12}{10} = \frac{6}{5}\)[/tex]
- Result: [tex]\(\frac{6}{5}\)[/tex]
4. [tex]\(\frac{9}{30} + \frac{1}{30} + \frac{5}{30}\)[/tex]
- Adding the fractions: [tex]\(\frac{9}{30} + \frac{1}{30} + \frac{5}{30} = \frac{15}{30}\)[/tex]
- Simplify [tex]\(\frac{15}{30} = \frac{1}{2}\)[/tex]
- Result: [tex]\(\frac{1}{2}\)[/tex]
5. [tex]\(\frac{8}{12} + \frac{5}{12}\)[/tex]
- Adding the fractions: [tex]\(\frac{8}{12} + \frac{5}{12} = \frac{13}{12}\)[/tex]
- This fraction is already in its simplest form.
- Result: [tex]\(\frac{13}{12}\)[/tex]
6. [tex]\(\frac{5}{25} + \frac{575}{25}\)[/tex]
- Adding the fractions: [tex]\(\frac{5}{25} + \frac{575}{25} = \frac{580}{25}\)[/tex]
- Simplify [tex]\(\frac{580}{25} = \frac{116}{5}\)[/tex]
- Result: [tex]\(\frac{116}{5}\)[/tex]
7. [tex]\(\frac{1}{20} + \frac{7}{20}\)[/tex]
- Adding the fractions: [tex]\(\frac{1}{20} + \frac{7}{20} = \frac{8}{20}\)[/tex]
- Simplify [tex]\(\frac{8}{20} = \frac{2}{5}\)[/tex]
- Result: [tex]\(\frac{2}{5}\)[/tex]
8. [tex]\(\frac{8}{100} + \frac{52}{100}\)[/tex]
- Adding the fractions: [tex]\(\frac{8}{100} + \frac{52}{100} = \frac{60}{100}\)[/tex]
- Simplify [tex]\(\frac{60}{100} = \frac{3}{5}\)[/tex]
- Result: [tex]\(\frac{3}{5}\)[/tex]
9. [tex]\(\frac{5}{10} + \frac{2}{10} + \frac{5}{10}\)[/tex]
- Adding the fractions: [tex]\(\frac{5}{10} + \frac{2}{10} + \frac{5}{10} = \frac{12}{10}\)[/tex]
- Simplify [tex]\(\frac{12}{10} = \frac{6}{5}\)[/tex]
- Result: [tex]\(\frac{6}{5}\)[/tex]
10. [tex]\(\frac{9}{5} + \frac{9}{15} + \frac{5}{15}\)[/tex]
- Converting to a common denominator (15):
- [tex]\(\frac{9}{5} = \frac{27}{15}\)[/tex]
- [tex]\(\frac{9}{15} = \frac{9}{15}\)[/tex]
- [tex]\(\frac{5}{15} = \frac{5}{15}\)[/tex]
- Adding the fractions: [tex]\(\frac{27}{15} + \frac{9}{15} + \frac{5}{15} = \frac{41}{15}\)[/tex]
- This fraction is already in its simplest form.
- Result: [tex]\(\frac{41}{15}\)[/tex]
So, the final answers are:
[tex]\[ \left( \frac{4}{3}, 1, \frac{6}{5}, \frac{1}{2}, \frac{13}{12}, \frac{116}{5}, \frac{2}{5}, \frac{3}{5}, \frac{6}{5}, \frac{41}{15} \right) \][/tex]
1. [tex]\(\frac{2}{3} + \frac{2}{3}\)[/tex]
- Adding the fractions: [tex]\(\frac{2}{3} + \frac{2}{3} = \frac{4}{3}\)[/tex]
- This fraction is already in its simplest form.
- Result: [tex]\(\frac{4}{3}\)[/tex]
2. [tex]\(\frac{8}{12} + \frac{2}{12} + \frac{2}{12}\)[/tex]
- Adding the fractions: [tex]\(\frac{8}{12} + \frac{2}{12} + \frac{2}{12} = \frac{12}{12}\)[/tex]
- Simplify [tex]\(\frac{12}{12}\)[/tex] to [tex]\(1\)[/tex].
- Result: [tex]\(1\)[/tex]
3. [tex]\(\frac{5}{10} + \frac{7}{10}\)[/tex]
- Adding the fractions: [tex]\(\frac{5}{10} + \frac{7}{10} = \frac{12}{10}\)[/tex]
- Simplify [tex]\(\frac{12}{10} = \frac{6}{5}\)[/tex]
- Result: [tex]\(\frac{6}{5}\)[/tex]
4. [tex]\(\frac{9}{30} + \frac{1}{30} + \frac{5}{30}\)[/tex]
- Adding the fractions: [tex]\(\frac{9}{30} + \frac{1}{30} + \frac{5}{30} = \frac{15}{30}\)[/tex]
- Simplify [tex]\(\frac{15}{30} = \frac{1}{2}\)[/tex]
- Result: [tex]\(\frac{1}{2}\)[/tex]
5. [tex]\(\frac{8}{12} + \frac{5}{12}\)[/tex]
- Adding the fractions: [tex]\(\frac{8}{12} + \frac{5}{12} = \frac{13}{12}\)[/tex]
- This fraction is already in its simplest form.
- Result: [tex]\(\frac{13}{12}\)[/tex]
6. [tex]\(\frac{5}{25} + \frac{575}{25}\)[/tex]
- Adding the fractions: [tex]\(\frac{5}{25} + \frac{575}{25} = \frac{580}{25}\)[/tex]
- Simplify [tex]\(\frac{580}{25} = \frac{116}{5}\)[/tex]
- Result: [tex]\(\frac{116}{5}\)[/tex]
7. [tex]\(\frac{1}{20} + \frac{7}{20}\)[/tex]
- Adding the fractions: [tex]\(\frac{1}{20} + \frac{7}{20} = \frac{8}{20}\)[/tex]
- Simplify [tex]\(\frac{8}{20} = \frac{2}{5}\)[/tex]
- Result: [tex]\(\frac{2}{5}\)[/tex]
8. [tex]\(\frac{8}{100} + \frac{52}{100}\)[/tex]
- Adding the fractions: [tex]\(\frac{8}{100} + \frac{52}{100} = \frac{60}{100}\)[/tex]
- Simplify [tex]\(\frac{60}{100} = \frac{3}{5}\)[/tex]
- Result: [tex]\(\frac{3}{5}\)[/tex]
9. [tex]\(\frac{5}{10} + \frac{2}{10} + \frac{5}{10}\)[/tex]
- Adding the fractions: [tex]\(\frac{5}{10} + \frac{2}{10} + \frac{5}{10} = \frac{12}{10}\)[/tex]
- Simplify [tex]\(\frac{12}{10} = \frac{6}{5}\)[/tex]
- Result: [tex]\(\frac{6}{5}\)[/tex]
10. [tex]\(\frac{9}{5} + \frac{9}{15} + \frac{5}{15}\)[/tex]
- Converting to a common denominator (15):
- [tex]\(\frac{9}{5} = \frac{27}{15}\)[/tex]
- [tex]\(\frac{9}{15} = \frac{9}{15}\)[/tex]
- [tex]\(\frac{5}{15} = \frac{5}{15}\)[/tex]
- Adding the fractions: [tex]\(\frac{27}{15} + \frac{9}{15} + \frac{5}{15} = \frac{41}{15}\)[/tex]
- This fraction is already in its simplest form.
- Result: [tex]\(\frac{41}{15}\)[/tex]
So, the final answers are:
[tex]\[ \left( \frac{4}{3}, 1, \frac{6}{5}, \frac{1}{2}, \frac{13}{12}, \frac{116}{5}, \frac{2}{5}, \frac{3}{5}, \frac{6}{5}, \frac{41}{15} \right) \][/tex]
