15. Представьте в виде неправильных дробей смешанные числа: 2 \frac{7}{12} = 31 4 \frac{4}{11} = 3 \frac{4}{10} = 5 \frac{2}{9} = 4 \frac{5}{8} = 1 \frac{19}{25} = 1 \frac{51}{53} = 2 \frac{6}{13} = 7 \frac{1}{5} = 5 \frac{5}{11} = 6 \frac{2}{7} = 1 \frac{3}{9} = 6 \frac{2}{5} = 3 \frac{3}{4} = 24 2 \frac{1}{4} = 2 \frac{8}{9} = 10 \frac{2}{3} = 7 \frac{4}{5} = 3 \frac{5}{6} = 13 \frac{4}{9} = 5 \frac{7}{8} = 5 \frac{4}{7} = 7 \frac{3}{7} = 17 \frac{2}{3} = 5 \frac{2}{5} = 3 \frac{5}{12} = 29 \frac{1}{2} = 9 \frac{3}{4} = 11 \frac{3}{5} = 13 \frac{1}{2} =

Решим примеры, представленные в задании.

Для того чтобы представить смешанное число в виде неправильной дроби, нужно целую часть умножить на знаменатель дробной части и прибавить числитель дробной части. Полученное число будет числителем неправильной дроби, а знаменатель останется тем же.

1. $$2 \frac{7}{12} = \frac{2 \cdot 12 + 7}{12} = \frac{24 + 7}{12} = \frac{31}{12}$$
2. $$4 \frac{4}{11} = \frac{4 \cdot 11 + 4}{11} = \frac{44 + 4}{11} = \frac{48}{11}$$
3. $$3 \frac{4}{10} = \frac{3 \cdot 10 + 4}{10} = \frac{30 + 4}{10} = \frac{34}{10} = \frac{17}{5}$$
4. $$5 \frac{2}{9} = \frac{5 \cdot 9 + 2}{9} = \frac{45 + 2}{9} = \frac{47}{9}$$
5. $$4 \frac{5}{8} = \frac{4 \cdot 8 + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}$$
6. $$1 \frac{19}{25} = \frac{1 \cdot 25 + 19}{25} = \frac{25 + 19}{25} = \frac{44}{25}$$
7. $$1 \frac{51}{53} = \frac{1 \cdot 53 + 51}{53} = \frac{53 + 51}{53} = \frac{104}{53}$$
8. $$2 \frac{6}{13} = \frac{2 \cdot 13 + 6}{13} = \frac{26 + 6}{13} = \frac{32}{13}$$
9. $$7 \frac{1}{5} = \frac{7 \cdot 5 + 1}{5} = \frac{35 + 1}{5} = \frac{36}{5}$$
10. $$5 \frac{5}{11} = \frac{5 \cdot 11 + 5}{11} = \frac{55 + 5}{11} = \frac{60}{11}$$
11. $$6 \frac{2}{7} = \frac{6 \cdot 7 + 2}{7} = \frac{42 + 2}{7} = \frac{44}{7}$$
12. $$1 \frac{3}{9} = \frac{1 \cdot 9 + 3}{9} = \frac{9 + 3}{9} = \frac{12}{9} = \frac{4}{3}$$
13. $$6 \frac{2}{5} = \frac{6 \cdot 5 + 2}{5} = \frac{30 + 2}{5} = \frac{32}{5}$$
14. $$3 \frac{3}{4} = \frac{3 \cdot 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$$
15. $$2 \frac{1}{4} = \frac{2 \cdot 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$$
16. $$2 \frac{8}{9} = \frac{2 \cdot 9 + 8}{9} = \frac{18 + 8}{9} = \frac{26}{9}$$
17. $$10 \frac{2}{3} = \frac{10 \cdot 3 + 2}{3} = \frac{30 + 2}{3} = \frac{32}{3}$$
18. $$7 \frac{4}{5} = \frac{7 \cdot 5 + 4}{5} = \frac{35 + 4}{5} = \frac{39}{5}$$
19. $$3 \frac{5}{6} = \frac{3 \cdot 6 + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6}$$
20. $$13 \frac{4}{9} = \frac{13 \cdot 9 + 4}{9} = \frac{117 + 4}{9} = \frac{121}{9}$$
21. $$5 \frac{7}{8} = \frac{5 \cdot 8 + 7}{8} = \frac{40 + 7}{8} = \frac{47}{8}$$
22. $$5 \frac{4}{7} = \frac{5 \cdot 7 + 4}{7} = \frac{35 + 4}{7} = \frac{39}{7}$$
23. $$7 \frac{3}{7} = \frac{7 \cdot 7 + 3}{7} = \frac{49 + 3}{7} = \frac{52}{7}$$
24. $$17 \frac{2}{3} = \frac{17 \cdot 3 + 2}{3} = \frac{51 + 2}{3} = \frac{53}{3}$$
25. $$5 \frac{2}{5} = \frac{5 \cdot 5 + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5}$$
26. $$3 \frac{5}{12} = \frac{3 \cdot 12 + 5}{12} = \frac{36 + 5}{12} = \frac{41}{12}$$
27. $$29 \frac{1}{2} = \frac{29 \cdot 2 + 1}{2} = \frac{58 + 1}{2} = \frac{59}{2}$$
28. $$9 \frac{3}{4} = \frac{9 \cdot 4 + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4}$$
29. $$11 \frac{3}{5} = \frac{11 \cdot 5 + 3}{5} = \frac{55 + 3}{5} = \frac{58}{5}$$
30. $$13 \frac{1}{2} = \frac{13 \cdot 2 + 1}{2} = \frac{26 + 1}{2} = \frac{27}{2}$$

Ответ: $$\frac{31}{12}; \frac{48}{11}; \frac{17}{5}; \frac{47}{9}; \frac{37}{8}; \frac{44}{25}; \frac{104}{53}; \frac{32}{13}; \frac{36}{5}; \frac{60}{11}; \frac{44}{7}; \frac{4}{3}; \frac{32}{5}; \frac{15}{4}; \frac{9}{4}; \frac{26}{9}; \frac{32}{3}; \frac{39}{5}; \frac{23}{6}; \frac{121}{9}; \frac{47}{8}; \frac{39}{7}; \frac{52}{7}; \frac{53}{3}; \frac{27}{5}; \frac{41}{12}; \frac{59}{2}; \frac{39}{4}; \frac{58}{5}; \frac{27}{2}.$$