Упражнения 269 (1-9)

Упражнение 269

1. \(\dfrac{3}{7}+\dfrac{4}{9} =\dfrac{27}{63}+\dfrac{28}{63} =\boxed{\dfrac{55}{63}}\)

2. \(\dfrac{8}{9}-\dfrac{7}{8} =\dfrac{64}{72}-\dfrac{63}{72} =\boxed{\dfrac{1}{72}}\)

3. \(\dfrac{13}{15}-\dfrac{2}{3} =\dfrac{13}{15}-\dfrac{10}{15} =\boxed{\dfrac{1}{5}}\)

4. \(\dfrac{20}{21}+\dfrac{3}{7} =\dfrac{20}{21}+\dfrac{9}{21} =\dfrac{29}{21} =\boxed{1\dfrac{8}{21}}\)

5. \(\dfrac{17}{18}-\dfrac{11}{12} =\dfrac{34}{36}-\dfrac{33}{36} =\boxed{\dfrac{1}{36}}\)

6. \(\dfrac{7}{16}+\dfrac{1}{6} =\dfrac{21}{48}+\dfrac{8}{48} =\boxed{\dfrac{29}{48}}\)

7. \(\dfrac{2}{9}+\dfrac{5}{6} =\dfrac{4}{18}+\dfrac{15}{18} =\dfrac{19}{18} =\boxed{1\dfrac{1}{18}}\)

8. \(\dfrac{10}{21}+\dfrac{9}{14} =\dfrac{20}{42}+\dfrac{27}{42} =\dfrac{47}{42} =\boxed{1\dfrac{5}{42}}\)

9. \(\dfrac{7}{9}-\dfrac{4}{15} =\dfrac{35}{45}-\dfrac{12}{45} =\boxed{\dfrac{23}{45}}\)

Упражнение 269, № 9–12

9. \[ \frac79-\frac4{15} =\frac{35}{45}-\frac{12}{45} =\boxed{\frac{23}{45}} \]

10. \[ \frac9{14}-\frac37+\frac{15}{28} =\frac{18}{28}-\frac{12}{28}+\frac{15}{28} =\frac{21}{28} =\boxed{\frac34} \]

11. \[ \frac16+\frac14-\frac18 =\frac4{24}+\frac6{24}-\frac3{24} =\boxed{\frac7{24}} \]

12. \[ \frac{13}{18}-\frac{29}{45}+\frac8{15} =\frac{65}{90}-\frac{58}{90}+\frac{48}{90} =\frac{55}{90} =\boxed{\frac{11}{18}} \]

Упражнение 269 (9–12)

9)
\[ \frac79-\frac4{15} =\frac{35}{45}-\frac{12}{45} =\boxed{\frac{23}{45}} \]

10)
\[ \frac9{14}-\frac37+\frac{15}{28} =\frac{18}{28}-\frac{12}{28}+\frac{15}{28} =\frac{21}{28} =\boxed{\frac34} \]

11)
\[ \frac16+\frac14-\frac18 =\frac4{24}+\frac6{24}-\frac3{24} =\boxed{\frac7{24}} \]

12)
\[ \frac{13}{18}-\frac{29}{45}+\frac8{15} =\frac{65}{90}-\frac{58}{90}+\frac{48}{90} =\frac{55}{90} =\boxed{\frac{11}{18}} \]

Упражнение 274

Золушка убирала комнаты \(\frac{11}{20}\) ч, что на \(\frac{2}{15}\) ч больше времени мытья посуды.

Время мытья посуды:

\[ \frac{11}{20}-\frac{2}{15} =\frac{33}{60}-\frac{8}{60} =\frac{25}{60} =\frac{5}{12}\text{ ч}. \]

Общее время:

\[ \frac{11}{20}+\frac{5}{12} =\frac{33}{60}+\frac{25}{60} =\frac{58}{60} =\boxed{\frac{29}{30}\text{ ч}}. \]

\[ \frac{29}{30}\text{ ч}=58\text{ мин}. \]

Ответ: \(\boxed{58\text{ минут}}\).

Упражнение 274

Золушка убирала комнаты \(\frac{11}{20}\) ч, что на \(\frac{2}{15}\) ч больше времени, чем мыла посуду.

1. Найдём время мытья посуды:

\[ \frac{11}{20}-\frac{2}{15} =\frac{33}{60}-\frac{8}{60} =\frac{25}{60} =\frac{5}{12}\text{ ч}. \]

2. Найдём общее время:

\[ \frac{11}{20}+\frac{5}{12} =\frac{33}{60}+\frac{25}{60} =\frac{58}{60} =\boxed{\frac{29}{30}\text{ ч}}. \]

\[ \frac{29}{30}\cdot 60=58\text{ мин}. \]

Ответ: \(\boxed{\frac{29}{30}\) ч, или 58 минут.}