§5. Обыкновенные дроби — Упражнения — 5.169 — стр. 32

\( \frac{4}{18} + n \), при \( n = \frac{1}{18}, \frac{3}{18}, \frac{6}{18} \):

1. \( n = \frac{1}{18} \):

\(\frac{4}{18} + \frac{1}{18} = \frac{4 + 1}{18} = \frac{5}{18}.\)

2. \( n = \frac{3}{18} \):

\(\frac{4}{18} + \frac{3}{18} = \frac{4 + 3}{18} = \frac{7}{18}.\)

3. \( n = \frac{6}{18} \):

\(\frac{4}{18} + \frac{6}{18} = \frac{4 + 6}{18} = \frac{10}{18} = \frac{5}{9}\).

\( m - \frac{1}{9} \), при \( m = \frac{6}{9}, \frac{5}{9}, \frac{2}{9} \):

1. \( m = \frac{6}{9} \):

\(\frac{6}{9} - \frac{1}{9} = \frac{6 - 1}{9} = \frac{5}{9}.\)

2. \( m = \frac{5}{9} \):

\(\frac{5}{9} - \frac{1}{9} = \frac{5 - 1}{9} = \frac{4}{9}.\)

3. \( m = \frac{2}{9} \):

\(\frac{2}{9} - \frac{1}{9} = \frac{2 - 1}{9} = \frac{1}{9}\).

\( \frac{4}{15} + \frac{3}{15} + x \), при \( x = \frac{1}{15}, \frac{3}{15}, \frac{6}{15} \):

1. \( x = \frac{1}{15} \):

\(\frac{4}{15} + \frac{3}{15} + \frac{1}{15} = \frac{4 + 3 + 1}{15} = \frac{8}{15}.\)

2. \( x = \frac{3}{15} \):

\(\frac{4}{15} + \frac{3}{15} + \frac{3}{15} = \frac{4 + 3 + 3}{15} = \frac{10}{15} = \frac{2}{3}.\)

3. \( x = \frac{6}{15} \):

\(\frac{4}{15} + \frac{3}{15} + \frac{6}{15} = \frac{4 + 3 + 6}{15} = \frac{13}{15}\).

\( \frac{13}{19} - \frac{3}{19} - z \), при \( z = \frac{3}{19}, \frac{5}{19}, \frac{7}{19} \):

1. \( z = \frac{3}{19} \):

\(\frac{13}{19} - \frac{3}{19} - \frac{3}{19} = \frac{13 - 3 - 3}{19} = \frac{7}{19}.\)

2. \( z = \frac{5}{19} \):

\(\frac{13}{19} - \frac{3}{19} - \frac{5}{19} = \frac{13 - 3 - 5}{19} = \frac{5}{19}.\)

3. \( z = \frac{7}{19} \):

\(\frac{13}{19} - \frac{3}{19} - \frac{7}{19} = \frac{13 - 3 - 7}{19} = \frac{3}{19}\).