Answer :
Sure, let's break these down step by step:
### 1. [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex]:
- The least common denominator (LCD) of 5 and 7 is 35.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{4}{5} = \frac{4 \times 7}{5 \times 7} = \frac{28}{35}\)[/tex]
- [tex]\(\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}\)[/tex]
- Add the fractions:
- [tex]\(\frac{28}{35} + \frac{30}{35} = \frac{58}{35}\)[/tex]
### 2. [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{9}{11}\)[/tex]:
- The least common denominator (LCD) of 3 and 11 is 33.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{2}{3} = \frac{2 \times 11}{3 \times 11} = \frac{22}{33}\)[/tex]
- [tex]\(\frac{9}{11} = \frac{9 \times 3}{11 \times 3} = \frac{27}{33}\)[/tex]
- Add the fractions:
- [tex]\(\frac{22}{33} + \frac{27}{33} = \frac{49}{33}\)[/tex]
### 3. [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- The least common denominator (LCD) of 7 and 3 is 21.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}\)[/tex]
- [tex]\(\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}\)[/tex]
- Add the fractions:
- [tex]\(\frac{12}{21} + \frac{7}{21} = \frac{19}{21}\)[/tex]
### 4. [tex]\(\frac{2}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- The least common denominator (LCD) of 10 and 5 is 10.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}\)[/tex]
- Add the fractions:
- [tex]\(\frac{2}{10} + \frac{6}{10} = \frac{8}{10} = \frac{4}{5}\)[/tex]
### 5. [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- The least common denominator (LCD) of 8 and 3 is 24.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{2}{8} = \frac{2 \times 3}{8 \times 3} = \frac{6}{24}\)[/tex]
- [tex]\(\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}\)[/tex]
- Add the fractions:
- [tex]\(\frac{6}{24} + \frac{8}{24} = \frac{14}{24} = \frac{7}{12}\)[/tex]
For the final results, we have:
1. [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex]: LCD = 35; [tex]\(\frac{28}{35} + \frac{30}{35} = \frac{58}{35}\)[/tex]
2. [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{9}{11}\)[/tex]: LCD = 33; [tex]\(\frac{22}{33} + \frac{27}{33} = \frac{49}{33}\)[/tex]
3. [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]: LCD = 21; [tex]\(\frac{12}{21} + \frac{7}{21} = \frac{19}{21}\)[/tex]
4. [tex]\(\frac{2}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]: LCD = 10; [tex]\(\frac{2}{10} + \frac{6}{10} = \frac{8}{10} = \frac{4}{5}\)[/tex]
5. [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]: LCD = 24; [tex]\(\frac{6}{24} + \frac{8}{24} = \frac{14}{24} = \frac{7}{12}\)[/tex]
Please revisit fractions addition results for verification.
### 1. [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex]:
- The least common denominator (LCD) of 5 and 7 is 35.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{4}{5} = \frac{4 \times 7}{5 \times 7} = \frac{28}{35}\)[/tex]
- [tex]\(\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}\)[/tex]
- Add the fractions:
- [tex]\(\frac{28}{35} + \frac{30}{35} = \frac{58}{35}\)[/tex]
### 2. [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{9}{11}\)[/tex]:
- The least common denominator (LCD) of 3 and 11 is 33.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{2}{3} = \frac{2 \times 11}{3 \times 11} = \frac{22}{33}\)[/tex]
- [tex]\(\frac{9}{11} = \frac{9 \times 3}{11 \times 3} = \frac{27}{33}\)[/tex]
- Add the fractions:
- [tex]\(\frac{22}{33} + \frac{27}{33} = \frac{49}{33}\)[/tex]
### 3. [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- The least common denominator (LCD) of 7 and 3 is 21.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}\)[/tex]
- [tex]\(\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}\)[/tex]
- Add the fractions:
- [tex]\(\frac{12}{21} + \frac{7}{21} = \frac{19}{21}\)[/tex]
### 4. [tex]\(\frac{2}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- The least common denominator (LCD) of 10 and 5 is 10.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}\)[/tex]
- Add the fractions:
- [tex]\(\frac{2}{10} + \frac{6}{10} = \frac{8}{10} = \frac{4}{5}\)[/tex]
### 5. [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- The least common denominator (LCD) of 8 and 3 is 24.
- Convert each fraction to have this common denominator:
- [tex]\(\frac{2}{8} = \frac{2 \times 3}{8 \times 3} = \frac{6}{24}\)[/tex]
- [tex]\(\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}\)[/tex]
- Add the fractions:
- [tex]\(\frac{6}{24} + \frac{8}{24} = \frac{14}{24} = \frac{7}{12}\)[/tex]
For the final results, we have:
1. [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex]: LCD = 35; [tex]\(\frac{28}{35} + \frac{30}{35} = \frac{58}{35}\)[/tex]
2. [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{9}{11}\)[/tex]: LCD = 33; [tex]\(\frac{22}{33} + \frac{27}{33} = \frac{49}{33}\)[/tex]
3. [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]: LCD = 21; [tex]\(\frac{12}{21} + \frac{7}{21} = \frac{19}{21}\)[/tex]
4. [tex]\(\frac{2}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]: LCD = 10; [tex]\(\frac{2}{10} + \frac{6}{10} = \frac{8}{10} = \frac{4}{5}\)[/tex]
5. [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]: LCD = 24; [tex]\(\frac{6}{24} + \frac{8}{24} = \frac{14}{24} = \frac{7}{12}\)[/tex]
Please revisit fractions addition results for verification.
