i) 4\frac{1}{4} + \frac{2}{9} j) \frac{3}{8}+2\frac{1}{4} k) 1\frac{1}{3} + 2\frac{1}{3}+3 l) 8\frac{3}{5} + 1\frac{9}{10} m) \frac{7}{20}+8\frac{3}{4} n) \frac{1}{4}+3\frac{1}{6} o) 1\frac{3}{5}+10\frac{1}{4}

Ответ:

Решение:

i) \(4\frac{1}{4} + \frac{2}{9} = \frac{17}{4} + \frac{2}{9} = \frac{17 \cdot 9}{4 \cdot 9} + \frac{2 \cdot 4}{9 \cdot 4} = \frac{153}{36} + \frac{8}{36} = \frac{161}{36} = 4\frac{17}{36}\)

j) \(\frac{3}{8}+2\frac{1}{4} = \frac{3}{8} + \frac{9}{4} = \frac{3}{8} + \frac{9 \cdot 2}{4 \cdot 2} = \frac{3}{8} + \frac{18}{8} = \frac{21}{8} = 2\frac{5}{8}\)

k) \(1\frac{1}{3} + 2\frac{1}{3}+3 = \frac{4}{3} + \frac{7}{3} + 3 = \frac{4}{3} + \frac{7}{3} + \frac{9}{3} = \frac{4+7+9}{3} = \frac{20}{3} = 6\frac{2}{3}\)

l) \(8\frac{3}{5} + 1\frac{9}{10} = \frac{43}{5} + \frac{19}{10} = \frac{43 \cdot 2}{5 \cdot 2} + \frac{19}{10} = \frac{86}{10} + \frac{19}{10} = \frac{86+19}{10} = \frac{105}{10} = 10\frac{5}{10} = 10\frac{1}{2}\)

m) \(\frac{7}{20}+8\frac{3}{4} = \frac{7}{20} + \frac{35}{4} = \frac{7}{20} + \frac{35 \cdot 5}{4 \cdot 5} = \frac{7}{20} + \frac{175}{20} = \frac{7+175}{20} = \frac{182}{20} = 9\frac{2}{20} = 9\frac{1}{10}\)

n) \(\frac{1}{4}+3\frac{1}{6} = \frac{1}{4} + \frac{19}{6} = \frac{1 \cdot 3}{4 \cdot 3} + \frac{19 \cdot 2}{6 \cdot 2} = \frac{3}{12} + \frac{38}{12} = \frac{3+38}{12} = \frac{41}{12} = 3\frac{5}{12}\)

o) \(1\frac{3}{5}+10\frac{1}{4} = \frac{8}{5} + \frac{41}{4} = \frac{8 \cdot 4}{5 \cdot 4} + \frac{41 \cdot 5}{4 \cdot 5} = \frac{32}{20} + \frac{205}{20} = \frac{32+205}{20} = \frac{237}{20} = 11\frac{17}{20}\)

Ответ:

i) \(4\frac{17}{36}\)

j) \(2\frac{5}{8}\)

k) \(6\frac{2}{3}\)

l) \(10\frac{1}{2}\)

m) \(9\frac{1}{10}\)

n) \(3\frac{5}{12}\)

o) \(11\frac{17}{20}\)