Calculate the values of the expressions: a) 3 7/9 + 1.95 + 6 2/9 + 5.45; б) 5.1 + 5/7 + 1 2/7 + 2.9; в) 7 17/20 + 6.625 + 18 15/40; г) 2.25 + 7 3/4 - 6 11/28; д) 4.2 + 3 5/26 - (7 - 3.8); e) 33 - (4 5/7 + 2.87 + 7.1); ж) 64 - 7 11/25 + 23.44; 3) 3 4/9 - 1.8 - 1 1/3.

Решение:

1. а)\[ 3\frac{7}{9} + 1.95 + 6\frac{2}{9} + 5.45 = \left( 3\frac{7}{9} + 6\frac{2}{9} \right) + (1.95 + 5.45) = \left( 3+6 + \frac{7}{9}+\frac{2}{9} \right) + 7.40 = \left( 9 + \frac{9}{9} \right) + 7.40 = (9+1) + 7.40 = 10 + 7.40 = 17.40 \]
2. б)\[ 5.1 + \frac{5}{7} + 1\frac{2}{7} + 2.9 = (5.1+2.9) + \left( \frac{5}{7} + 1\frac{2}{7} \right) = 8.0 + \left( \frac{5}{7} + \frac{9}{7} \right) = 8.0 + \frac{14}{7} = 8.0 + 2 = 10 \]
3. в)\[ 7\frac{17}{20} + 6.625 + 18\frac{15}{40} = 7\frac{34}{40} + 6.625 + 18\frac{15}{40} = \left( 7\frac{34}{40} + 18\frac{15}{40} \right) + 6.625 = 25\frac{49}{40} + 6.625 = 26\frac{9}{40} + 6.625 = 26.225 + 6.625 = 32.85 \]
4. г)\[ 2.25 + 7\frac{3}{4} - 6\frac{11}{28} = 2.25 + 7.75 - \left( 6 + \frac{11}{28} \right) = 10 - \left( 6 + \frac{11}{28} \right) = 10 - 6 - \frac{11}{28} = 4 - \frac{11}{28} = \frac{112-11}{28} = \frac{101}{28} \]
5. д)\[ 4.2 + 3\frac{5}{26} - (7 - 3.8) = 4.2 + 3\frac{5}{26} - 3.2 = (4.2 - 3.2) + 3\frac{5}{26} = 1 + 3\frac{5}{26} = 4\frac{5}{26} \]
6. е)\[ 33 - \left( 4\frac{5}{7} + 2.87 + 7.1 \right) = 33 - \left( \frac{33}{7} + 9.97 \right) \approx 33 - (4.714 + 9.97) \approx 33 - 14.684 \approx 18.316 \]
7. ж)\[ 64 - 7\frac{11}{25} + 23.44 = 64 - 7.44 + 23.44 = 64 + (23.44 - 7.44) = 64 + 16 = 80 \]
8. 3)\[ 3\frac{4}{9} - 1.8 - 1\frac{1}{3} = \left( 3 + \frac{4}{9} \right) - 1.8 - \left( 1 + \frac{1}{3} \right) = \left( 3\frac{4}{9} - 1\frac{1}{3} \right) - 1.8 = \left( 3\frac{4}{9} - 1\frac{3}{9} \right) - 1.8 = 2\frac{1}{9} - 1.8 = \frac{19}{9} - \frac{18}{10} = \frac{190 - 162}{90} = \frac{28}{90} = \frac{14}{45} \]