IDNLearn.com is the perfect place to get detailed and accurate answers to your questions. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.
Sagot :
Sure! Let's solve each fraction addition problem step-by-step.
1. [tex]\(\frac{1}{3} + \frac{1}{5}\)[/tex]
- Find a common denominator, which is 15.
- Convert each fraction: [tex]\(\frac{1}{3} = \frac{5}{15}\)[/tex] and [tex]\(\frac{1}{5} = \frac{3}{15}\)[/tex].
- Add the fractions: [tex]\(\frac{5}{15} + \frac{3}{15} = \frac{8}{15}\)[/tex].
2. [tex]\(\frac{1}{8} + \frac{2}{6}\)[/tex]
- Find a common denominator, which is 24.
- Convert each fraction: [tex]\(\frac{1}{8} = \frac{3}{24}\)[/tex] and [tex]\(\frac{2}{6} = \frac{8}{24}\)[/tex].
- Add the fractions: [tex]\(\frac{3}{24} + \frac{8}{24} = \frac{11}{24}\)[/tex].
3. [tex]\(\frac{8}{9} + \frac{11}{12}\)[/tex]
- Find a common denominator, which is 36.
- Convert each fraction: [tex]\(\frac{8}{9} = \frac{32}{36}\)[/tex] and [tex]\(\frac{11}{12} = \frac{33}{36}\)[/tex].
- Add the fractions: [tex]\(\frac{32}{36} + \frac{33}{36} = \frac{65}{36}\)[/tex].
4. [tex]\(\frac{1}{7} + \frac{5}{8}\)[/tex]
- Find a common denominator, which is 56.
- Convert each fraction: [tex]\(\frac{1}{7} = \frac{8}{56}\)[/tex] and [tex]\(\frac{5}{8} = \frac{35}{56}\)[/tex].
- Add the fractions: [tex]\(\frac{8}{56} + \frac{35}{56} = \frac{43}{56}\)[/tex].
5. [tex]\(\frac{1}{4} + \frac{2}{4}\)[/tex]
- The denominators are the same, so just add the numerators: [tex]\(\frac{1}{4} + \frac{2}{4} = \frac{3}{4}\)[/tex].
6. [tex]\(\frac{1}{2} + \frac{3}{9}\)[/tex]
- Find a common denominator, which is 18.
- Convert each fraction: [tex]\(\frac{1}{2} = \frac{9}{18}\)[/tex] and [tex]\(\frac{3}{9} = \frac{6}{18}\)[/tex].
- Add the fractions: [tex]\(\frac{9}{18} + \frac{6}{18} = \frac{15}{18} = \frac{5}{6}\)[/tex].
7. [tex]\(\frac{1}{10} + \frac{1}{4}\)[/tex]
- Find a common denominator, which is 20.
- Convert each fraction: [tex]\(\frac{1}{10} = \frac{2}{20}\)[/tex] and [tex]\(\frac{1}{4} = \frac{5}{20}\)[/tex].
- Add the fractions: [tex]\(\frac{2}{20} + \frac{5}{20} = \frac{7}{20}\)[/tex].
8. [tex]\(\frac{3}{11} + \frac{11}{12}\)[/tex]
- Find a common denominator, which is 132.
- Convert each fraction: [tex]\(\frac{3}{11} = \frac{36}{132}\)[/tex] and [tex]\(\frac{11}{12} = \frac{121}{132}\)[/tex].
- Add the fractions: [tex]\(\frac{36}{132} + \frac{121}{132} = \frac{157}{132}\)[/tex].
9. [tex]\(\frac{2}{7} + \frac{1}{3}\)[/tex]
- Find a common denominator, which is 21.
- Convert each fraction: [tex]\(\frac{2}{7} = \frac{6}{21}\)[/tex] and [tex]\(\frac{1}{3} = \frac{7}{21}\)[/tex].
- Add the fractions: [tex]\(\frac{6}{21} + \frac{7}{21} = \frac{13}{21}\)[/tex].
10. [tex]\(\frac{1}{8} + \frac{3}{5}\)[/tex]
- Find a common denominator, which is 40.
- Convert each fraction: [tex]\(\frac{1}{8} = \frac{5}{40}\)[/tex] and [tex]\(\frac{3}{5} = \frac{24}{40}\)[/tex].
- Add the fractions: [tex]\(\frac{5}{40} + \frac{24}{40} = \frac{29}{40}\)[/tex].
11. [tex]\(\frac{2}{3} + \frac{1}{2}\)[/tex]
- Find a common denominator, which is 6.
- Convert each fraction: [tex]\(\frac{2}{3} = \frac{4}{6}\)[/tex] and [tex]\(\frac{1}{2} = \frac{3}{6}\)[/tex].
- Add the fractions: [tex]\(\frac{4}{6} + \frac{3}{6} = \frac{7}{6}\)[/tex].
12. [tex]\(\frac{7}{8} + \frac{5}{6}\)[/tex]
- Find a common denominator, which is 24.
- Convert each fraction: [tex]\(\frac{7}{8} = \frac{21}{24}\)[/tex] and [tex]\(\frac{5}{6} = \frac{20}{24}\)[/tex].
- Add the fractions: [tex]\(\frac{21}{24} + \frac{20}{24} = \frac{41}{24}\)[/tex].
13. [tex]\(\frac{1}{2} + \frac{2}{12}\)[/tex]
- Find a common denominator, which is 12.
- Convert each fraction: [tex]\(\frac{1}{2} = \frac{6}{12}\)[/tex] and [tex]\(\frac{2}{12} = \frac{2}{12}\)[/tex].
- Add the fractions: [tex]\(\frac{6}{12} + \frac{2}{12} = \frac{8}{12} = \frac{2}{3}\)[/tex].
14. [tex]\(\frac{5}{6} + \frac{1}{9}\)[/tex]
- Find a common denominator, which is 18.
- Convert each fraction: [tex]\(\frac{5}{6} = \frac{15}{18}\)[/tex] and [tex]\(\frac{1}{9} = \frac{2}{18}\)[/tex].
- Add the fractions: [tex]\(\frac{15}{18} + \frac{2}{18} = \frac{17}{18}\)[/tex].
So the sums are:
1. [tex]\(\frac{8}{15}\)[/tex]
2. [tex]\(\frac{11}{24}\)[/tex]
3. [tex]\(\frac{65}{36}\)[/tex]
4. [tex]\(\frac{43}{56}\)[/tex]
5. [tex]\(\frac{3}{4}\)[/tex]
6. [tex]\(\frac{5}{6}\)[/tex]
7. [tex]\(\frac{7}{20}\)[/tex]
8. [tex]\(\frac{157}{132}\)[/tex]
9. [tex]\(\frac{13}{21}\)[/tex]
10. [tex]\(\frac{29}{40}\)[/tex]
11. [tex]\(\frac{7}{6}\)[/tex]
12. [tex]\(\frac{41}{24}\)[/tex]
13. [tex]\(\frac{2}{3}\)[/tex]
14. [tex]\(\frac{17}{18}\)[/tex]
1. [tex]\(\frac{1}{3} + \frac{1}{5}\)[/tex]
- Find a common denominator, which is 15.
- Convert each fraction: [tex]\(\frac{1}{3} = \frac{5}{15}\)[/tex] and [tex]\(\frac{1}{5} = \frac{3}{15}\)[/tex].
- Add the fractions: [tex]\(\frac{5}{15} + \frac{3}{15} = \frac{8}{15}\)[/tex].
2. [tex]\(\frac{1}{8} + \frac{2}{6}\)[/tex]
- Find a common denominator, which is 24.
- Convert each fraction: [tex]\(\frac{1}{8} = \frac{3}{24}\)[/tex] and [tex]\(\frac{2}{6} = \frac{8}{24}\)[/tex].
- Add the fractions: [tex]\(\frac{3}{24} + \frac{8}{24} = \frac{11}{24}\)[/tex].
3. [tex]\(\frac{8}{9} + \frac{11}{12}\)[/tex]
- Find a common denominator, which is 36.
- Convert each fraction: [tex]\(\frac{8}{9} = \frac{32}{36}\)[/tex] and [tex]\(\frac{11}{12} = \frac{33}{36}\)[/tex].
- Add the fractions: [tex]\(\frac{32}{36} + \frac{33}{36} = \frac{65}{36}\)[/tex].
4. [tex]\(\frac{1}{7} + \frac{5}{8}\)[/tex]
- Find a common denominator, which is 56.
- Convert each fraction: [tex]\(\frac{1}{7} = \frac{8}{56}\)[/tex] and [tex]\(\frac{5}{8} = \frac{35}{56}\)[/tex].
- Add the fractions: [tex]\(\frac{8}{56} + \frac{35}{56} = \frac{43}{56}\)[/tex].
5. [tex]\(\frac{1}{4} + \frac{2}{4}\)[/tex]
- The denominators are the same, so just add the numerators: [tex]\(\frac{1}{4} + \frac{2}{4} = \frac{3}{4}\)[/tex].
6. [tex]\(\frac{1}{2} + \frac{3}{9}\)[/tex]
- Find a common denominator, which is 18.
- Convert each fraction: [tex]\(\frac{1}{2} = \frac{9}{18}\)[/tex] and [tex]\(\frac{3}{9} = \frac{6}{18}\)[/tex].
- Add the fractions: [tex]\(\frac{9}{18} + \frac{6}{18} = \frac{15}{18} = \frac{5}{6}\)[/tex].
7. [tex]\(\frac{1}{10} + \frac{1}{4}\)[/tex]
- Find a common denominator, which is 20.
- Convert each fraction: [tex]\(\frac{1}{10} = \frac{2}{20}\)[/tex] and [tex]\(\frac{1}{4} = \frac{5}{20}\)[/tex].
- Add the fractions: [tex]\(\frac{2}{20} + \frac{5}{20} = \frac{7}{20}\)[/tex].
8. [tex]\(\frac{3}{11} + \frac{11}{12}\)[/tex]
- Find a common denominator, which is 132.
- Convert each fraction: [tex]\(\frac{3}{11} = \frac{36}{132}\)[/tex] and [tex]\(\frac{11}{12} = \frac{121}{132}\)[/tex].
- Add the fractions: [tex]\(\frac{36}{132} + \frac{121}{132} = \frac{157}{132}\)[/tex].
9. [tex]\(\frac{2}{7} + \frac{1}{3}\)[/tex]
- Find a common denominator, which is 21.
- Convert each fraction: [tex]\(\frac{2}{7} = \frac{6}{21}\)[/tex] and [tex]\(\frac{1}{3} = \frac{7}{21}\)[/tex].
- Add the fractions: [tex]\(\frac{6}{21} + \frac{7}{21} = \frac{13}{21}\)[/tex].
10. [tex]\(\frac{1}{8} + \frac{3}{5}\)[/tex]
- Find a common denominator, which is 40.
- Convert each fraction: [tex]\(\frac{1}{8} = \frac{5}{40}\)[/tex] and [tex]\(\frac{3}{5} = \frac{24}{40}\)[/tex].
- Add the fractions: [tex]\(\frac{5}{40} + \frac{24}{40} = \frac{29}{40}\)[/tex].
11. [tex]\(\frac{2}{3} + \frac{1}{2}\)[/tex]
- Find a common denominator, which is 6.
- Convert each fraction: [tex]\(\frac{2}{3} = \frac{4}{6}\)[/tex] and [tex]\(\frac{1}{2} = \frac{3}{6}\)[/tex].
- Add the fractions: [tex]\(\frac{4}{6} + \frac{3}{6} = \frac{7}{6}\)[/tex].
12. [tex]\(\frac{7}{8} + \frac{5}{6}\)[/tex]
- Find a common denominator, which is 24.
- Convert each fraction: [tex]\(\frac{7}{8} = \frac{21}{24}\)[/tex] and [tex]\(\frac{5}{6} = \frac{20}{24}\)[/tex].
- Add the fractions: [tex]\(\frac{21}{24} + \frac{20}{24} = \frac{41}{24}\)[/tex].
13. [tex]\(\frac{1}{2} + \frac{2}{12}\)[/tex]
- Find a common denominator, which is 12.
- Convert each fraction: [tex]\(\frac{1}{2} = \frac{6}{12}\)[/tex] and [tex]\(\frac{2}{12} = \frac{2}{12}\)[/tex].
- Add the fractions: [tex]\(\frac{6}{12} + \frac{2}{12} = \frac{8}{12} = \frac{2}{3}\)[/tex].
14. [tex]\(\frac{5}{6} + \frac{1}{9}\)[/tex]
- Find a common denominator, which is 18.
- Convert each fraction: [tex]\(\frac{5}{6} = \frac{15}{18}\)[/tex] and [tex]\(\frac{1}{9} = \frac{2}{18}\)[/tex].
- Add the fractions: [tex]\(\frac{15}{18} + \frac{2}{18} = \frac{17}{18}\)[/tex].
So the sums are:
1. [tex]\(\frac{8}{15}\)[/tex]
2. [tex]\(\frac{11}{24}\)[/tex]
3. [tex]\(\frac{65}{36}\)[/tex]
4. [tex]\(\frac{43}{56}\)[/tex]
5. [tex]\(\frac{3}{4}\)[/tex]
6. [tex]\(\frac{5}{6}\)[/tex]
7. [tex]\(\frac{7}{20}\)[/tex]
8. [tex]\(\frac{157}{132}\)[/tex]
9. [tex]\(\frac{13}{21}\)[/tex]
10. [tex]\(\frac{29}{40}\)[/tex]
11. [tex]\(\frac{7}{6}\)[/tex]
12. [tex]\(\frac{41}{24}\)[/tex]
13. [tex]\(\frac{2}{3}\)[/tex]
14. [tex]\(\frac{17}{18}\)[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.
