Question

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Answer 1

3. A

$\frac{4}{5} \times (5 \frac{1}{4} - 7 \frac{1}{3} ) - \frac{5}{6} = - 2 \frac{1}{2}$

1) $5 \frac{1}{4} - 7\frac{1}{3} = \frac{5 \times 4 + 1}{4} - \frac{7 \times 3 + 1}{3} = \frac{21}{4} - \frac{22}{3} = \frac{21 \times 3}{12} - \frac{22 \times 4}{12} = \frac{63}{12} - \frac{88}{12} = \frac{63 - 88}{12} = \frac{ - 25}{12} = - \frac{25}{12}$

2) $\frac{4}{5} \times ( - \frac{25}{12} ) = - \frac{4 \times 25}{5 \times 12} = - \frac{4 \times 5 \times 5}{5 \times 4 \times 3} = - \frac{5}{3}$

3) $- \frac{5}{3} - \frac{5}{6} = - \frac{5 \times 2}{3 \times 2} - \frac{5}{6} = - \frac{10}{6} - \frac{5}{6} = - ( \frac{10}{6} + \frac{5}{6} ) = - \frac{10 + 5}{6} = - \frac{15}{6} = - \frac{5}{2} = - \frac{4 + 1}{2} = - 2 \frac{1}{2}$

4. B

$(2 + \frac{1}{3} ) \times (188 \frac{3}{5} - 185 \frac{3}{5} ) = 7$

1) $2 + \frac{1}{3} = 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

2) $188 \frac{3}{5} - 185 \frac{3}{5} = (188 + \frac{3}{5} ) - (185 + \frac{3}{5} ) = (188 - 185) + ( \frac{3}{5} - \frac{3}{5} ) = 3 + 0 = 3$

3) $\frac{7}{3} \times 3 = \frac{7 \times 3}{3} = \frac{7}{1} = 7$

5. A

$(15 \frac{4}{5} - 9 \frac{3}{10} ) - (12 \frac{9}{10} - 8 \frac{3}{5} ) = 2.2$

1) $15 \frac{4}{5} - 9 \frac{3}{10} = (15 + \frac{4}{5} ) - (9 + \frac{3}{10} ) = (15 - 9) + ( \frac{4}{5} - \frac{3}{10} ) = 6 + ( \frac{8}{10} - \frac{3}{10} ) = 6 + \frac{8 - 3}{10} = 6 + \frac{5}{10} = 6 + 0.5 = 6.5$

2) $12 \frac{9}{10} - 8 \frac{3}{5} = (12 + \frac{9}{10} ) - (8 + \frac{3}{5} ) = (12 - 8) + ( \frac{9}{10} - \frac{3}{5} ) = 4 + ( \frac{9}{10} - \frac{6}{10} ) = 4 + \frac{9 - 6}{10} = 4 + \frac{3}{10} = 4 + 0.3 = 4.3$

3) $6.5 - 4.3 = 2.2$

6. C

$(13 \frac{7}{12} - 8 \frac{1}{3} ) \times ( - \frac{3}{7} ) = - 2.25$

1) $13 \frac{7}{12} - 8 \frac{1}{3} = (13 + \frac{7}{12} ) - (8 + \frac{1}{3} ) = (13 - 8) + ( \frac{7}{12} - \frac{1}{3} ) = 5 + (\frac{7}{12} - \frac{4}{12} ) = 5 + \frac{7 - 4}{12} = 5 + \frac{3}{12} = 5 + \frac{1}{4} = 5 \frac{1}{4}$

2) $5 \frac{1}{4} \times ( - \frac{3}{7} ) = \frac{21}{4} \times ( - \frac{3}{7} ) = - \frac{21 \times 3}{4 \times 7} = - \frac{7 \times 3 \times 3}{4 \times 7} = - \frac{9}{4} = - 2 \frac{1}{4} = - 2.25$