Задание 121. Приведите дроби к данному знаменателю и найдите сумму этих дробей.

Задание 121

Приведём дроби к заданному знаменателю и найдём их сумму.

1.

\( \frac{2}{3} = \frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{12} \)

\( \frac{3}{4} = \frac{3 \cdot 3}{4 \cdot 3} = \frac{9}{12} \)

\( \frac{8}{12} + \frac{9}{12} = \frac{8+9}{12} = \frac{17}{12} = 1 \frac{5}{12} \)

2.

\( \frac{5}{6} = \frac{5 \cdot 3}{6 \cdot 3} = \frac{15}{18} \)

\( \frac{2}{9} = \frac{2 \cdot 2}{9 \cdot 2} = \frac{4}{18} \)

\( \frac{15}{18} + \frac{4}{18} = \frac{19}{18} = 1 \frac{1}{18} \)

3.

\( \frac{5}{8} = \frac{5 \cdot 3}{8 \cdot 3} = \frac{15}{24} \)

\( \frac{1}{6} = \frac{1 \cdot 4}{6 \cdot 4} = \frac{4}{24} \)

\( \frac{15}{24} + \frac{4}{24} = \frac{19}{24} \)

4.

\( \frac{3}{16} = \frac{3 \cdot 3}{16 \cdot 3} = \frac{9}{48} \)

\( \frac{11}{12} = \frac{11 \cdot 4}{12 \cdot 4} = \frac{44}{48} \)

\( \frac{9}{48} + \frac{44}{48} = \frac{53}{48} = 1 \frac{5}{48} \)

5.

\( \frac{7}{16} = \frac{7 \cdot 2}{16 \cdot 2} = \frac{14}{32} \)

\( \frac{3}{8} = \frac{3 \cdot 4}{8 \cdot 4} = \frac{12}{32} \)

\( \frac{14}{32} + \frac{12}{32} = \frac{26}{32} = \frac{13}{16} \)

6.

\( \frac{3}{7} = \frac{3 \cdot 4}{7 \cdot 4} = \frac{12}{28} \)

\( \frac{13}{14} = \frac{13 \cdot 2}{14 \cdot 2} = \frac{26}{28} \)

\( \frac{12}{28} + \frac{26}{28} = \frac{38}{28} = \frac{19}{14} = 1 \frac{5}{14} \)

7.

\( \frac{5}{6} = \frac{5 \cdot 7}{6 \cdot 7} = \frac{35}{42} \)

\( \frac{10}{21} = \frac{10 \cdot 2}{21 \cdot 2} = \frac{20}{42} \)

\( \frac{35}{42} + \frac{20}{42} = \frac{55}{42} = 1 \frac{13}{42} \)

8.

\( \frac{2}{15} = \frac{2 \cdot 2}{15 \cdot 2} = \frac{4}{30} \)

\( \frac{9}{10} = \frac{9 \cdot 3}{10 \cdot 3} = \frac{27}{30} \)

\( \frac{4}{30} + \frac{27}{30} = \frac{31}{30} = 1 \frac{1}{30} \)

9.

\( \frac{8}{17} = \frac{8 \cdot 3}{17 \cdot 3} = \frac{24}{51} \)

\( \frac{2}{3} = \frac{2 \cdot 17}{3 \cdot 17} = \frac{34}{51} \)

\( \frac{24}{51} + \frac{34}{51} = \frac{58}{51} = 1 \frac{7}{51} \)

10.

\( \frac{11}{18} = \frac{11 \cdot 2}{18 \cdot 2} = \frac{22}{36} \)

\( \frac{5}{12} = \frac{5 \cdot 3}{12 \cdot 3} = \frac{15}{36} \)

\( \frac{22}{36} + \frac{15}{36} = \frac{37}{36} = 1 \frac{1}{36} \)

Ответ: 1. \( 1 \frac{5}{12} \), 2. \( 1 \frac{1}{18} \), 3. \( \frac{19}{24} \), 4. \( 1 \frac{5}{48} \), 5. \( \frac{13}{16} \), 6. \( 1 \frac{5}{14} \), 7. \( 1 \frac{13}{42} \), 8. \( 1 \frac{1}{30} \), 9. \( 1 \frac{7}{51} \), 10. \( 1 \frac{1}{36} \).