a) (-124) + 24 = -100
b) 37. 78 + 37. 22
=  37 . ( 78 + 22 )
=  37 . 100
= 3700

\(a) (-124) + 24 = -100 b) 37. 78 + 37. 22 = 37 . ( 78 + 22 ) = 37 . 100 = 3700\)

a) (- 124) + 24                                          b) 37 . 78 + 37 . 22

= - ( 124 - 24)                                              =37 . ( 78 + 22)

= - 100                                                        =37 . 100 

                                                                    3700

b: \(\dfrac{3}{4}-\dfrac{7}{15}+\dfrac{1}{4}+\dfrac{1}{2022}-\dfrac{8}{15}\)

\(=\left(\dfrac{3}{4}+\dfrac{1}{4}\right)-\left(\dfrac{7}{15}+\dfrac{8}{15}\right)+\dfrac{1}{2022}\)

\(=1-1+\dfrac{1}{2022}=\dfrac{1}{2022}\)

c: \(\dfrac{3}{5}\cdot\dfrac{4}{7}+\dfrac{3}{7}\cdot\dfrac{9}{5}+\dfrac{13}{7}\cdot\dfrac{2}{5}\)

\(=\dfrac{3}{5}\cdot\dfrac{4}{7}+\dfrac{3}{5}\cdot\dfrac{9}{7}+\dfrac{13}{7}\cdot\dfrac{2}{5}\)

\(=\dfrac{3}{5}\left(\dfrac{4}{7}+\dfrac{9}{7}\right)+\dfrac{13}{7}\cdot\dfrac{2}{5}\)

\(=\dfrac{3}{5}\cdot\dfrac{13}{7}+\dfrac{13}{7}\cdot\dfrac{2}{5}\)

\(=\dfrac{13}{7}\left(\dfrac{3}{5}+\dfrac{2}{5}\right)=\dfrac{13}{7}\)

= 3/7 + 15/26 - 2/13 + 3/7

=3/7 + (15/26 - 2/13)

=3/7 + 4/26

=.......

\(=\dfrac{2^{32}\cdot5^{16}\cdot5^9\cdot2^9\cdot5^6\cdot7^6}{2^{36}\cdot5^{28}\cdot2^5\cdot7^5}=\dfrac{2^{41}\cdot5^{31}\cdot7^6}{2^{41}\cdot5^{28}\cdot7^5}=5^3\cdot7=875\)

\(=\dfrac{2^{32}\cdot5^{16}\cdot2^9\cdot5^9\cdot5^6\cdot7^6}{2^{36}\cdot5^{28}\cdot2^5\cdot7^5}=5^3\cdot7=875\)

\(A=-\dfrac{1}{6}-\left[\dfrac{9}{16}-\dfrac{9}{8}+\dfrac{3}{4}\right]\)

\(=\dfrac{-1}{6}-\dfrac{9-18+12}{16}=\dfrac{-1}{6}-\dfrac{3}{16}\)

\(=\dfrac{-8}{48}-\dfrac{9}{48}=-\dfrac{17}{48}\)

\(B=\left(-\dfrac{3}{4}+\dfrac{3}{4}\right)^2+\dfrac{3}{4}\cdot\dfrac{-5}{9}+7^3\)

=-15/36+343

=343-5/12=4111/12

\(=64\cdot\dfrac{-1}{8}+100\cdot\dfrac{1}{100}\)

=-8+1

=-7

\(\dfrac{\dfrac{5}{3}-\dfrac{5}{7}+\dfrac{5}{9}}{\dfrac{10}{3}-\dfrac{10}{7}+\dfrac{10}{9}}=\dfrac{5\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{9}\right)}{10\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{9}\right)}=\dfrac{1}{2}\)

17² - 17 + 17.84

= 17.(17 - 1 + 84)

= 17.100

= 1700