1. 5/6*9/15-5/12*4/15= 7/18*9/14+1/3*6/7= 9/20*2/3+5/14*7/25= 3целых 3/4*2/5-3целых 6/25*5/27= 2целых 2/5*5/6-3/4*1целая 2/3= 1 целая 17/28*7/9+14/25*5/7= 2. 8*4/11+8*7/11= 5*1/7+5*6/7= 2/5*6/13+1/4*6/13= 5/8*5/6-1/4*5/6= 3/5-3/5*2/7= 1/7*1/8+1/7*1/6= зарание .
1.
1)![\frac{5}{6} * \frac{9}{15} - \frac{5}{12} * \frac{4}{15} = \frac{7}{18}](/tpl/images/0961/7497/9da04.png)
Для начала вспомним что первое действие - всегда умножение, исключение скобки.
1.![\frac{5}{6} * \frac{9}{15} = \frac{3}{6}](/tpl/images/0961/7497/37246.png)
2.![\frac{5}{12} * \frac{4}{15} = \frac{1}{9}](/tpl/images/0961/7497/eadf0.png)
3.![\frac{3}{6} - \frac{1}{9} = \frac{9}{18} - \frac{2}{18} = \frac{7}{18}](/tpl/images/0961/7497/8587e.png)
НОЗ: 18.
2)![\frac{7}{18} * \frac{9}{14} + \frac{1}{3} * \frac{6}{7} = \frac{15}{28}](/tpl/images/0961/7497/7136e.png)
1.![\frac{7}{18} * \frac{9}{14} = \frac{1}{4}](/tpl/images/0961/7497/76094.png)
2.![\frac{1}{3} * \frac{6}{7} = \frac{2}{7}](/tpl/images/0961/7497/a2f3f.png)
3.![\frac{1}{4} + \frac{2}{7} = \frac{7}{28} + \frac{8}{28} = \frac{15}{28}](/tpl/images/0961/7497/dd5e6.png)
НОЗ: 28.
3)![\frac{9}{20} * \frac{2}{3} + \frac{5}{14} * \frac{7}{25} = 0,4](/tpl/images/0961/7497/23d7b.png)
1.![\frac{9}{20} * \frac{2}{3} = \frac{3}{10}](/tpl/images/0961/7497/0db6b.png)
2.![\frac{5}{14} * \frac{7}{25} = \frac{1}{10}](/tpl/images/0961/7497/928de.png)
3.![\frac{3}{10} + \frac{1}{10} = \frac{4}{10} = 0,4](/tpl/images/0961/7497/f5b60.png)
Теперь переводим смешанные дроби в неправильные:
4)![\frac{15}{4} * \frac{2}{5} - \frac{81}{25} * \frac{5}{27} = 0,9](/tpl/images/0961/7497/ea9f4.png)
1.![\frac{15}{4} * \frac{2}{5} = \frac{3}{2}](/tpl/images/0961/7497/70f6c.png)
2.![\frac{81}{25} * \frac{5}{27} = \frac{3}{5}](/tpl/images/0961/7497/f9f2c.png)
3.![\frac{3}{2} - \frac{3}{5} = \frac{15}{10} - \frac{6}{10} = \frac{9}{10} = 0,9](/tpl/images/0961/7497/8a457.png)
НОЗ: 10.
5)![\frac{12}{5} * \frac{5}{6} - \frac{3}{4} * \frac{5}{3} = 0,75](/tpl/images/0961/7497/46b9f.png)
1.![\frac{12}{5} * \frac{5}{6} = 2](/tpl/images/0961/7497/e2c62.png)
2.![\frac{3}{4} * \frac{5}{3} = \frac{5}{4} = 1\frac{1}{4} = 1,25](/tpl/images/0961/7497/63544.png)
3. 2-1,25=0,75
6)![\frac{45}{28} * \frac{7}{9} + \frac{14}{25} * \frac{5}{7} = 1,65](/tpl/images/0961/7497/74a32.png)
1.![\frac{45}{28} * \frac{7}{9} = \frac{5}{4} = 1\frac{1}{4} = 1,25](/tpl/images/0961/7497/c4984.png)
2.![\frac{14}{25} * \frac{5}{7} = \frac{2}{5} = 0,4](/tpl/images/0961/7497/f3320.png)
3. 1,25+0,40 = 1,65
2.
1)![\frac{8}{1} * \frac{4}{11} + \frac{8}{1} * \frac{7}{11} = 8](/tpl/images/0961/7497/a9c66.png)
1.![\frac{8}{1} * \frac{4}{11} = \frac{32}{11}](/tpl/images/0961/7497/4e4ce.png)
2.![\frac{8}{1} * \frac{7}{11} = \frac{56}{11}](/tpl/images/0961/7497/1ed24.png)
3.
(Также тут работает распределительный закон, но я решу по-обычному)
2)![\frac{5}{1} * \frac{1}{7} + \frac{5}{1} * \frac{6}{7} = 5](/tpl/images/0961/7497/5280e.png)
1.![\frac{5}{1} * \frac{1}{7} = \frac{5}{7}](/tpl/images/0961/7497/83754.png)
2.![\frac{5}{1} * \frac{6}{7} = \frac{30}{7}](/tpl/images/0961/7497/5e7f3.png)
3.![\frac{5}{7} + \frac{30}{7} = \frac{35}{7} = 5](/tpl/images/0961/7497/32b8a.png)
3)![\frac{2}{5} * \frac{6}{13} + \frac{1}{4} * \frac{6}{13} = \frac{78}{260}](/tpl/images/0961/7497/c8fd6.png)
1.![\frac{2}{5} * \frac{6}{13} = \frac{12}{65}](/tpl/images/0961/7497/a796b.png)
2.![\frac{1}{4} * \frac{6}{13} = \frac{6}{52}](/tpl/images/0961/7497/1db46.png)
3.![\frac{12}{65} + \frac{6}{52} = \frac{48}{260} + \frac{30}{260} = \frac{78}{260}](/tpl/images/0961/7497/e2cc1.png)
НОЗ: 260.
4)![\frac{5}{8} * \frac{5}{6} - \frac{1}{4} * \frac{5}{6} = 0,3125](/tpl/images/0961/7497/3e16e.png)
1.![\frac{5}{8} * \frac{5}{6} = \frac{25}{48}](/tpl/images/0961/7497/3ba0d.png)
2.![\frac{1}{4} * \frac{5}{6} = \frac{5}{24}](/tpl/images/0961/7497/3a6d4.png)
3.![\frac{25}{48} - \frac{5}{24} = \frac{25}{48} - \frac{10}{48} = \frac{15}{48} = 0,3125](/tpl/images/0961/7497/2d661.png)
НОЗ: 48.
5)![\frac{3}{5} - \frac{3}{5} * \frac{2}{7} = \frac{15}{35}](/tpl/images/0961/7497/905b4.png)
1.![\frac{3}{5} * \frac{2}{7} = \frac{6}{35}](/tpl/images/0961/7497/e74d9.png)
2.![\frac{3}{5} - \frac{6}{35} = \frac{21}{35} - \frac{6}{35} = \frac{15}{35}](/tpl/images/0961/7497/848f8.png)
НОЗ: 35.
6)![\frac{1}{7} * \frac{1}{8} + \frac{1}{7} * \frac{1}{6} = \frac{7}{168}](/tpl/images/0961/7497/5f59e.png)
1.![\frac{1}{7} * \frac{1}{8} = \frac{1}{56}](/tpl/images/0961/7497/163e0.png)
2.![\frac{1}{7} * \frac{1}{6} = \frac{1}{42}](/tpl/images/0961/7497/80adc.png)
3.![\frac{1}{56} + \frac{1}{42} = \frac{3}{168} + \frac{4}{168} = \frac{7}{168}](/tpl/images/0961/7497/2950d.png)
НОЗ: 168.
1.1. 7/18
1.2. 11/14
1.3. 4/10=2/5(не дописала на фото)
1.4. 23/30
1.5. 157/180
2.
2.1. 8
2.2. 5
2.3. 3/10
2.4. 5/16
2.5. 3/7
2.6. 1/24