Answer :
Sure, let's work through each addition problem step by step:
1. Add [tex]\( \frac{2}{5} + \frac{3}{8} \)[/tex]:
- First, find a common denominator. The least common multiple of 5 and 8 is 40.
- Convert each fraction:
- [tex]\( \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \)[/tex]
- [tex]\( \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \)[/tex]
- Add the two fractions:
- [tex]\( \frac{16}{40} + \frac{15}{40} = \frac{31}{40} \)[/tex]
2. Add [tex]\( \frac{1}{3} + \frac{4}{7} \)[/tex]:
- Common denominator is 21.
- Convert each fraction:
- [tex]\( \frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21} \)[/tex]
- [tex]\( \frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21} \)[/tex]
- Add the fractions:
- [tex]\( \frac{7}{21} + \frac{12}{21} = \frac{19}{21} \)[/tex]
3. Add [tex]\( \frac{3}{5} + \frac{7}{40} \)[/tex]:
- Common denominator is 40.
- Convert each fraction:
- [tex]\( \frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40} \)[/tex]
- [tex]\( \frac{7}{40} = \frac{7}{40} \)[/tex] (already common denominator)
- Add the fractions:
- [tex]\( \frac{24}{40} + \frac{7}{40} = \frac{31}{40} \)[/tex]
4. Add the mixed numbers [tex]\( 1 \frac{1}{2} + 2 \frac{1}{15} \)[/tex]:
- Convert the mixed numbers to improper fractions:
- [tex]\( 1 \frac{1}{2} = \frac{3}{2} \)[/tex]
- [tex]\( 2 \frac{1}{15} = \frac{31}{15} \)[/tex]
- Find a common denominator, which is 30.
- Convert:
- [tex]\( \frac{3}{2} = \frac{3 \times 15}{2 \times 15} = \frac{45}{30} \)[/tex]
- [tex]\( \frac{31}{15} = \frac{31 \times 2}{15 \times 2} = \frac{62}{30} \)[/tex]
- Add the fractions:
- [tex]\( \frac{45}{30} + \frac{62}{30} = \frac{107}{30} \)[/tex]
Now, you match these fractions with their respective letters in the table:
- For [tex]\( \frac{31}{40} \)[/tex], the matching letter is [tex]\( A \)[/tex] or [tex]\( M \)[/tex].
- For [tex]\( \frac{19}{21} \)[/tex], the corresponding letter is [tex]\( G \)[/tex].
- For [tex]\( \frac{107}{30} \)[/tex], it doesn't directly correspond to a single straightforward letter based on the given fractions in the dictionary but appears as a result of calculation.
Each calculation aligns with the results provided, ensuring accuracy in your understanding and verification.
1. Add [tex]\( \frac{2}{5} + \frac{3}{8} \)[/tex]:
- First, find a common denominator. The least common multiple of 5 and 8 is 40.
- Convert each fraction:
- [tex]\( \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \)[/tex]
- [tex]\( \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \)[/tex]
- Add the two fractions:
- [tex]\( \frac{16}{40} + \frac{15}{40} = \frac{31}{40} \)[/tex]
2. Add [tex]\( \frac{1}{3} + \frac{4}{7} \)[/tex]:
- Common denominator is 21.
- Convert each fraction:
- [tex]\( \frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21} \)[/tex]
- [tex]\( \frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21} \)[/tex]
- Add the fractions:
- [tex]\( \frac{7}{21} + \frac{12}{21} = \frac{19}{21} \)[/tex]
3. Add [tex]\( \frac{3}{5} + \frac{7}{40} \)[/tex]:
- Common denominator is 40.
- Convert each fraction:
- [tex]\( \frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40} \)[/tex]
- [tex]\( \frac{7}{40} = \frac{7}{40} \)[/tex] (already common denominator)
- Add the fractions:
- [tex]\( \frac{24}{40} + \frac{7}{40} = \frac{31}{40} \)[/tex]
4. Add the mixed numbers [tex]\( 1 \frac{1}{2} + 2 \frac{1}{15} \)[/tex]:
- Convert the mixed numbers to improper fractions:
- [tex]\( 1 \frac{1}{2} = \frac{3}{2} \)[/tex]
- [tex]\( 2 \frac{1}{15} = \frac{31}{15} \)[/tex]
- Find a common denominator, which is 30.
- Convert:
- [tex]\( \frac{3}{2} = \frac{3 \times 15}{2 \times 15} = \frac{45}{30} \)[/tex]
- [tex]\( \frac{31}{15} = \frac{31 \times 2}{15 \times 2} = \frac{62}{30} \)[/tex]
- Add the fractions:
- [tex]\( \frac{45}{30} + \frac{62}{30} = \frac{107}{30} \)[/tex]
Now, you match these fractions with their respective letters in the table:
- For [tex]\( \frac{31}{40} \)[/tex], the matching letter is [tex]\( A \)[/tex] or [tex]\( M \)[/tex].
- For [tex]\( \frac{19}{21} \)[/tex], the corresponding letter is [tex]\( G \)[/tex].
- For [tex]\( \frac{107}{30} \)[/tex], it doesn't directly correspond to a single straightforward letter based on the given fractions in the dictionary but appears as a result of calculation.
Each calculation aligns with the results provided, ensuring accuracy in your understanding and verification.
