Question

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Answer 1

1)

$12 \frac{5}{6} + 2 \frac{7}{9} \times (15 \frac{9}{10} - 12 \frac{9}{10} ) =21 \frac{1}{6} \\ 1) \: 15 \frac{9}{10} - 12 \frac{9}{10} = 3 \\ 2) \: 2 \frac{7}{9} \times 3 = \frac{25 \times 3}{9} = \frac{25}{3} = 8 \frac{1}{3} \\ 3) \: 1 2\frac{5}{6} + 8 \frac{1}{3} = 12 \frac{5}{6} + 8 \frac{2}{6} = 20 \frac{7}{6} = 21 \frac{1}{6}$

2)

$5 \frac{7}{16} \times 1 \frac{3}{29} + 2 \frac{5}{16} \times 2 \frac{2}{7} = \frac{87 \times 32}{16 \times 29} + \frac{37 \times 16}{16 \times 7} = 6 + \frac{37}{7} = \\ = 6 + 5 \frac{2}{7} = 11 \frac{2}{7}$

3)

$(2022 \frac{3}{5} - 2021 \frac{1}{6} ) \times 1 \frac{1}{29} = (2022 \frac{18}{30} - 2021 \frac{5}{30} ) \times 1 \frac{1}{29} = \\ = 1 \frac{13}{30} \times 1 \frac{1}{29} = \frac{43 \times 30}{30 \times 29} = \frac{43}{29} = 1 \frac{14}{29}$

4)

$\frac{7}{10} + (1 \frac{1}{3} - \frac{2}{9} ) \div 1 \frac{2}{9} + 2 \frac{1}{2} \times ( \frac{1}{3} + \frac{1}{6} ) = 2 \frac{189}{220} \\ 1) \: 1 \frac{1}{3} - \frac{2}{9} = 1 \frac{3}{9} - \frac{2}{9} = 1 \frac{1}{9} \\ 2) \: 1 \frac{1}{9} \div 1 \frac{2}{9} = \frac{10 \times 9}{9 \times 11} = \frac{10}{11} \\ 3) \: \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \\ 4) \: 2 \frac{1}{2} \times \frac{1}{2} = \frac{5}{2 \times 2} = \frac{5}{4} = 1 \frac{1}{4} \\ 5) \: \frac{7}{10 } + \frac{10}{11} + 1 \frac{1}{4} = \frac{154}{220} + \frac{200}{220} + 1 \frac{55}{220} = \\ = 1 \frac{409}{220} = 2 \frac{189}{220}$