A)
[tex] \frac{4}{19} \times ( \frac{1}{3} + \frac{1}{4} ) = \frac{4}{19} \times \frac{4 + 3}{12} \\ = \frac{4}{19} \times \frac{7}{12} = \frac{1}{19} \times \frac{7}{3} = [/tex]
[tex] = \frac{7}{57} [/tex]
B)
[tex] \frac{1 \times 5 + 4}{5} \times ( \frac{1}{12} - \frac{1}{18} ) = \frac{9}{5} \times \frac{18 - 12}{216} [/tex]
[tex] = \frac{9}{5} \times \frac{6}{216} = \frac{1}{5} \times \frac{6}{24} = \frac{6}{120} \div 6 \\ = \frac{1}{20} [/tex]
C)
[tex]( \frac{2}{5} \times \frac{3 \times 3 + 1}{3} - 1) \times \frac{1 \times 5 + 4}{5} + \frac{1}{10} = [/tex]
[tex]( \frac{2}{5} \times \frac{10}{3} - 1) \times \frac{9}{5} + \frac{1}{10} = [/tex]
[tex]( \frac{2}{1} \times \frac{2}{3} - 1) \times \frac{9}{5} + \frac{1}{10} = \\ ( \frac{4}{3} - 1) \times \frac{9}{5} + \frac{1}{10} = [/tex]
[tex] \frac{4 - 3}{3} \times \frac{9}{5} + \frac{1}{10} = \frac{1}{3} \times \frac{9}{5} + \frac{1}{10} \\ = \frac{1}{1} \times \frac{3}{5} + \frac{1}{10} = \frac{3}{5} + \frac{1}{10} = [/tex]
[tex] = \frac{2 \times 3 + 1}{10} = \frac{6 + 1}{10} = \frac{7}{10} [/tex]
D)
[tex]10 \times ( \frac{1}{2} + \frac{1}{7} - ( \frac{2 \times 3 + 1}{3} \times \frac{3}{10} - \frac{3}{5} ))[/tex]
[tex] = 10 \times ( \frac{1}{2} + \frac{1}{7} - ( \frac{7}{3} \times \frac{3}{10} - \frac{3}{2} )) = [/tex]
[tex] = 10 \times ( \frac{1}{2} + \frac{1}{7} - ( \frac{7}{10} - \frac{3}{5} )) = \\ 10 \times ( \frac{1}{2} + \frac{1}{7} - \frac{7 - 2 \times 3}{10} ) = [/tex]
[tex] = 10 \times ( \frac{1}{2} + \frac{1}{7} - \frac{1}{10} )) = \\ 10 \times ( \frac{35 + 10 - 7}{70} ) = 10 \times \frac{38}{70} = [/tex]
[tex] = \frac{38}{7} [/tex]
E)
[tex]( \frac{10}{63} - \frac{1}{9} ) \times 21 + \frac{5}{2} = \frac{10 - 7}{63} \times \\ 21 + \frac{5}{2} = \frac{3}{63} \times 21 + \frac{5}{2} = [/tex]
[tex] = \frac{3}{3} + \frac{5}{2} = \frac{2 \times 3 + 3 \times 5}{6} = \\ \frac{6 + 15}{6} = \frac{21}{6} \div 3 = \frac{7}{2} [/tex]
F)
[tex]( \frac{1}{15} + \frac{5}{64} \times \frac{1 \times 25 + 7}{25} - 2 \times \\ ( \frac{1}{8} - \frac{1}{12} )) \times 10 = [/tex]
[tex]( \frac{1}{15} + \frac{5}{64} \times \frac{32}{25} - 2 \times \frac{12 - 8}{96} ) \times 10 = [/tex]
[tex]( \frac{1}{15} + \frac{5}{2 \times 25} - 2 \times \frac{4}{96} ) \times 10 \\ = ( \frac{1}{15} + \frac{5}{50} - \frac{4}{48} ) \times 10 = [/tex]
[tex] = ( \frac{160 + 48 \times 5 - 50 \times 4}{2400} ) \times 10 = \\ \frac{160 + 240 - 200}{2400} \times 10 = [/tex]
[tex] \frac{200}{2400} \times 10 = \frac{200}{240} = \frac{20}{24} \div 4 = \\ \frac{5}{6} [/tex]
G)
[tex] \frac{1}{17} \times ( \frac{5}{28} + \frac{1}{42} ) \times \frac{21}{2} = \\ \frac{1}{17} \times \frac{42 \times 5 + 28}{1176} \times \frac{21}{2} = [/tex]
[tex] = \frac{1}{17} \times \frac{210 + 28}{1176} \times \frac{21}{2} = \\ \frac{1}{17} \times \frac{238}{1176} \times \frac{21}{2} = \frac{14}{1176} \times \frac{21}{2} [/tex]
[tex] = \frac{7}{56} \div 7 = \frac{1}{8} [/tex]
H)
[tex](1 - ( \frac{8}{35} - \frac{2}{15} ) \times \frac{1 \times 12 + 2}{12}) \\ \times \frac{18}{40} - \frac{4 \times 5 + 4}{5} \times ( \frac{1}{3} - \frac{1}{4} ) = [/tex]
[tex](1 - \frac{15 \times 8 -35 \times 2 }{525} \times \frac{14}{12} ) \times \frac{18}{40} \\ - \frac{24}{5} [/tex]x 1/12=
(1-(120-70)/525x14/12)x18/40-2/5=
(1-50/525x14/12)x18/40-2/5=(1-700/6300)x18/40-2/5=((6300-700)/6300)x18/14-2/5=5600/6300x18/40-2/5=140/350-2/5=(140-2x70)/350=0
I) (3/7x (2x9+3)/9+2/5x(4x6+1)/6-1/4)x24/29=(3/7x21/9+2/5x25/6-1/4)x24/29=(3/3+5/3-1/4)x24/29=(4x3+4x5-3)/12x24/29=(12+20-3)/12x24/29=29/12x24/29=2
J)[(3x11+3)/11x(1/18+5/12+7/24) - 7/4]x10/15=[36/11x((24+5x36+7x18)/432)-7/4]x10/15=
[36/11x((24+180+126)/432)-7/4]x10/15=36/11x330/432-7/4)x10/15=(5/2-7/4)x10/15=(5x2-7)/4x10/15=3/4x10/15=1/2
