1. Выполните сложение чисел: a) 5+3/10; 23/8+4; 37/18+5/18; 3/7+54/7; 32/15+24/15, 97/10+13/10; 48/15+53/25; б) 2/9+7; 3+14/7; 25/16+7/16; 8/11+43/11; 55/12+15/12; 75/8+23/8; 37/18+34/45.

Решение:

а)

• $$5+\frac{3}{10} = \frac{5 \cdot 10}{10} + \frac{3}{10} = \frac{50}{10} + \frac{3}{10} = \frac{50+3}{10} = \frac{53}{10} = 5\frac{3}{10}$$
• $$2\frac{3}{8}+4 = 6\frac{3}{8}$$
• $$3\frac{7}{18}+\frac{5}{18} = 3\frac{7+5}{18} = 3\frac{12}{18} = 3\frac{2}{3}$$
• $$\frac{3}{7}+5\frac{4}{7} = 5\frac{3}{7} + \frac{4}{7} = 5\frac{3+4}{7} = 5\frac{7}{7} = 5+1 = 6$$
• $$3\frac{2}{15}+2\frac{4}{15} = 5\frac{2}{15} + \frac{4}{15} = 5\frac{2+4}{15} = 5\frac{6}{15} = 5\frac{2}{5}$$
• $$9\frac{7}{10}+1\frac{3}{10} = 10\frac{7}{10} + \frac{3}{10} = 10\frac{7+3}{10} = 10\frac{10}{10} = 10+1 = 11$$
• $$4\frac{8}{15}+5\frac{3}{25} = 4\frac{8 \cdot 5}{15 \cdot 5}+5\frac{3 \cdot 3}{25 \cdot 3} = 4\frac{40}{75}+5\frac{9}{75} = 9\frac{40+9}{75} = 9\frac{49}{75}$$

б)

• $$\frac{2}{9}+7 = 7\frac{2}{9}$$
• $$3+1\frac{4}{7} = 4\frac{4}{7}$$
• $$2\frac{5}{16}+\frac{7}{16} = 2\frac{5+7}{16} = 2\frac{12}{16} = 2\frac{3}{4}$$
• $$\frac{8}{11}+4\frac{3}{11} = 4\frac{8}{11} + \frac{3}{11} = 4\frac{8+3}{11} = 4\frac{11}{11} = 4+1 = 5$$
• $$5\frac{5}{12}+1\frac{5}{12} = 6\frac{5}{12} + \frac{5}{12} = 6\frac{5+5}{12} = 6\frac{10}{12} = 6\frac{5}{6}$$
• $$7\frac{5}{8}+2\frac{3}{8} = 9\frac{5}{8} + \frac{3}{8} = 9\frac{5+3}{8} = 9\frac{8}{8} = 9+1 = 10$$
• $$3\frac{7}{18}+3\frac{4}{45} = 3\frac{7 \cdot 5}{18 \cdot 5}+3\frac{4 \cdot 2}{45 \cdot 2} = 3\frac{35}{90}+3\frac{8}{90} = 6\frac{35+8}{90} = 6\frac{43}{90}$$

Ответ: a) $$5\frac{3}{10}$$, $$6\frac{3}{8}$$, $$3\frac{2}{3}$$, $$6$$, $$5\frac{2}{5}$$, $$11$$, $$9\frac{49}{75}$$; б) $$7\frac{2}{9}$$, $$4\frac{4}{7}$$, $$2\frac{3}{4}$$, $$5$$, $$6\frac{5}{6}$$, $$10$$, $$6\frac{43}{90}$$