a) \( - \frac{{15}}{8}\left( {\frac{8}{{ - 15}} + \frac{{32}}{{27}}} \right) - \frac{{15}}{7}\)

\( = - \frac{{15}}{8}.\frac{8}{{ - 15}} - \frac{{15}}{8}.\frac{{32}}{{27}} - \frac{{15}}{7}\)

\( = 1 - \frac{{20}}{9} - \frac{{15}}{7}\)

\( = - \frac{{212}}{{63}}\)

b) 41,54 + 23,17 + 8,46 – 3,17

= (41,54 + 8,46) + (23,17 – 3,17)

= 50 + 20

= 70

c) 3(32,1 – 6,32) + 7.32,1 + 3.0,32

= 3.32,1 – 3.6,32 + 7.32,1 + 3.0,32

= 32,1(3 + 7) – 3(6,32 – 0,32)

= 32,1 . 10 – 3 . 6

= 321 – 18

= 303

d) \(\frac{5}{7}.\frac{5}{{11}} + \frac{5}{7}.\frac{2}{{11}} - \frac{5}{7}.\frac{{14}}{{11}}\)

\( = \frac{5}{7}.\left( {\frac{5}{{11}} + \frac{2}{{11}} - \frac{{14}}{{11}}} \right)\)

\( = \frac{5}{7}.\frac{{ - 7}}{{11}}\)

\( = - \frac{5}{{11}}\)

e) \(\frac{2}{{11}}.\frac{{ - 5}}{4} + \frac{{ - 9}}{{11}}.\frac{5}{4} + 1\frac{3}{4}\)

\( = \frac{{ - 5}}{4}\left( {\frac{2}{{11}} + \frac{9}{{11}}} \right) + \frac{7}{4}\)

\( = \frac{{ - 5}}{4} + \frac{7}{4}\)

\( = \frac{2}{4}\)

\( = \frac{1}{2}\)

f) \(\frac{{ - 5}}{7}.\frac{3}{{13}} - \frac{5}{7}.\frac{{10}}{{13}} + 1\frac{5}{7}\)

\( = \frac{{ - 5}}{7}.\left( {\frac{3}{{13}} + \frac{{10}}{{13}}} \right) + 1 + \frac{5}{7}\)

\( = \frac{{ - 5}}{7} + 1 + \frac{5}{7}\)

= 1

g) \(\frac{7}{4}.\frac{{29}}{5} - \frac{7}{5}.\frac{9}{4} + 3\frac{2}{{13}}\)

\( = \frac{7}{5}.\frac{{29}}{4} - \frac{7}{5}.\frac{9}{4} + 3 + \frac{2}{{13}}\)

\( = \frac{7}{5}.\left( {\frac{{29}}{4} - \frac{9}{4}} \right) + 3 + \frac{2}{{13}}\)

\( = \frac{7}{5}.5 + 3 + \frac{2}{{13}}\)

\( = 10 + \frac{2}{{13}}\)

\( = \frac{{132}}{{13}}\)

Tìm số tự nhiên biết rằng nếu số đó cộng thêm 15 đơn vị ta thu được số tự nhiên là 83.