Question

Решить уровнения 1) (у+5/7)×1/3=2целых 4/9 2)(5/12-x)÷1/2=2/9 3) (1целая 16/25+х)-4/5=4целых2/25 4) 4/15-(у+3/25)=1/25 5)(8целых 3/14-у)÷3/7=17целых 6) 3целых1/16÷( х-5/16)=7/8

Answer 1

1) 
$(y + \frac{5}{7} ) * \frac{1}{3} =2 \frac{4}{9} \\ \\ \frac{1}{3}y + \frac{5*1}{7*3} = 2 \frac{4}{9} \\ \\ \frac{1}{3} y = 2 \frac{4}{9} - \frac{5}{21} \\ \\ \frac{1}{3} y = 2 \frac{28}{63} - \frac{15}{63} \\ \\ \frac{1}{3} y = 2 \frac{13}{63} \\ \\ y= 2 \frac{13}{63} : \frac{1}{3} = \frac{2*63 + 13}{63} * \frac{3}{1} = \frac{139*3}{63*1} = \frac{139}{21} \\ \\ y= 6 \frac{13}{21} \\ \\$

2)
$( \frac{5}{12} -x): \frac{1}{2} = \frac{2}{9} \\ \\ \frac{5}{12} -x= \frac{2}{9} * \frac{1}{2} \\ \\ \frac{5}{12} -x= \frac{1}{9} \\ \\ x = \frac{5}{12} - \frac{1}{9} = \frac{15}{36} - \frac{4}{36} \\ \\ x= \frac{11}{36}$

3) 
$(1 \frac{16}{25} +x) - \frac{4}{5} = 4 \frac{2}{25} \\ \\ 1 \frac{16}{25} +x= 4 \frac{2}{25} + \frac{4}{5} \\ \\ x=4 \frac{2}{25} + \frac{20}{25} -1 \frac{16}{25}= 4 \frac{22}{25} -1 \frac{16}{25} = (4-1) + \frac{22-16}{25} \\ \\ x=3 \frac{6}{25}$

4) 
$\frac{4}{15} - (y+ \frac{3}{25} ) = \frac{1}{25} \\ \\ \frac{4}{15} - y - \frac{3}{25} = \frac{1}{25} \\ \\ -y = \frac{1}{25}+ \frac{3}{25} - \frac{4}{15} \\ \\ -y= \frac{4}{25} - \frac{4}{15} \\ \\ -y = -( \frac{20}{75} - \frac{12}{75} ) \\ \\ -y= - \frac{8}{75} \\ \\ y= \frac{8}{75}$

5)
$(8 \frac{3}{14} -y): \frac{3}{7} = 17 \\ \\ 8 \frac{3}{14} -y = 17* \frac{3}{7} \\ \\ 8 \frac{3}{14} -y = 7\frac{2}{7} \\ \\ -y= 7 \frac{2}{7} -8 \frac{3}{14} \\ \\ -y= -(8 \frac{3}{14} -7 \frac{4}{14} ) \\ \\ -y= - \frac{13}{14} \\ \\ y= \frac{13}{14}$

6)
$3 \frac{1}{16} : (x - \frac{5}{16} ) = \frac{7}{8} \\ \\ x - \frac{5}{16} = 3 \frac{1}{16} : \frac{7}{8} \\ \\ x- \frac{5}{16} = \frac{49}{16} * \frac{8}{7} \\ \\ x- \frac{5}{16} = \frac{7}{2} \\ \\ x- \frac{5}{16} =3 \frac{1}{2} \\ \\ x= 3 \frac{1}{2} + \frac{5}{16} = 3 \frac{8}{16} + \frac{5}{16} \\ \\ x=3 \frac{13}{16}$