Упр.446 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)
Решение #1
Решение #2
Рассмотрим вариант решения задания из учебника Дорофеев, Петерсон 5 класс, Бином:
446. Составь программу действий и вычисли:
1) 1+2/(1-1/2);
1+2/(1-1/2)=1+2/(2/2-1/2)=1+2/((2-1)/2)=1+2/(1/2)=1+2:1/2=1+2•2/1=
=1+2•2=1+4=5
2) (3/(1/3+1)-2)/(1-3/4);
(3/(1/3+1)-2)/(1-3/4)=(3/(1 1/3)-2)/(4/4-3/4)=(3:1 1/3-2)/((4-3)/4)=(3:(1•3+1)/3-2)/(1/4)=(3:4/3-2)/(1/4)=(3•3/4-2)/(1/4)=((3•3)/4-2)/(1/4)=
=(9/4-2)/(1/4)=(2 1/4-2)/(1/4)=(1/4)/(1/4)=1/4 :1/4=1
3) (1+(1/3-1/5)/2)/(1-(1/3+1/5)/2);
(1+(1/3-1/5)/2)/(1-(1/3+1/5)/2)=(1+((1•5)/(3•5)-(1•3)/(5•3))/2)/(1-((1•5)/(3•5)+(1•3)/(5•3))/2)=(1+(5/15-3/15)/2)/(1-(5/15+3/15)/2)=(1+((5-3)/15)/2)/(1-((5+3)/15)/2)=(1+(2/15)/2)/(1-(8/15)/2)=(1+2/15 :2)/(1-8/15 :2)=(1+2/(15•2))/(1-8/(15•2))=
=(1+1/15)/(1-(2•4)/(15•2))=(1 1/15)/(1-4/15)=(1 1/15)/(15/15-4/15)=(1 1/15)/((15-4)/15)=((1•15+1)/15)/(11/15)=(16/15)/(11/15)=16/15 :11/15=16/15•15/11=
=(16•15)/(15•11)=16/11=1 5/11
4) (4/(1/2+1/6)-1 1/2)/(4/(1/2-1/6)+1 1/2);
(4/(1/2+1/6)-1 1/2)/(4/(1/2-1/6)+1 1/2)=(4/((1•3)/(2•3)+1/6)-1 1/2)/(4/((1•3)/(2•3)-1/6)+1 1/2)=(4/(3/6+1/6)-1 1/2)/(4/(3/6-1/6)+1 1/2)=(4/((3+1)/6)-1 1/2)/(4/((3-1)/6)+1 1/2)=(4/(4/6)-1 1/2)/(4/(2/6)+1 1/2)=(4/((2•2)/(2•3))-1 1/2)/(4/(2/(2•3))+1 1/2)=(4/(2/3)-1 1/2)/(4/(1/3)+1 1/2)=
=(4:2/3-1 1/2)/(4:1/3+1 1/2)=(4•3/2-1 1/2)/(4•3/1+1 1/2)=((4•3)/2-1 1/2)/((4•3)/1+1 1/2)=((2•2•3)/2-1 1/2)/(12/1+1 1/2)=(6-1 1/2)/(12+1 1/2)=(5 2/2-1 1/2)/(13 1/2)=(5-1+2/2-1/2)/(13 1/2)=
=(4+(2-1)/2)/(13 1/2)=(4 1/2)/(13 1/2)=4 1/2 :13 1/2=(4•2+1)/2 :(13•2+1)/2=9/2 :27/2=9/2•2/27=(9•2)/(2•27)=
=9/(3•9)=1/3
5) 1+1/(1+1/(1+1/(1+1/2)));
1+1/(1+1/(1+1/(1+1/2)))=1+1/(1+1/(1+1/(1 1/2)))=1+1/(1+1/(1+1/((1•2+1)/2)))=1+1/(1+1/(1+1/(3/2)))=
=1+1/(1+1/(1+1:3/2))=1+1/(1+1/(1+1•2/3))=1+1/(1+1/(1+2/3))=1+1/(1+1/(1 2/3))=1+1/(1+1/((1•3+2)/3))=
=1+1/(1+1/(5/3))=1+1/(1+1:5/3)=1+1/(1+1•3/5)=1+1/(1+3/5)=1+1/(1 3/5)=1+1/((1•5+3)/5)=
=1+1/(8/5)=1+1:8/5=1+1•5/8=1+5/8=1 5/8
6) 2-1/(2-1/(2-1/(2-1/2))).
2-1/(2-1/(2-1/(2-1/2)))=2-1/(2-1/(2-1/(1 2/2-1/2)))=2-1/(2-1/(2-1/(1+(2-1)/2)))=2-1/(2-1/(2-1/(1+1/2)))=
=2-1/(2-1/(2-1/(1 1/2)))=2-1/(2-1/(2-1/((1•2+1)/2)))=2-1/(2-1/(2-1/(3/2)))=2-1/(2-1/(2-1:3/2))=
=2-1/(2-1/(2-1•2/3))=2-1/(2-1/(2-2/3))=2-1/(2-1/(1 3/3-2/3))=2-1/(2-1/(1+(3-2)/3))=2-1/(2-1/(1+1/3))=
=2-1/(2-1/(1 1/3))=2-1/(2-1/((1•3+1)/3))=2-1/(2-1/(4/3))=2-1/(2-1:4/3)=2-1/(2-1•3/4)=
=2-1/(2-3/4)=2-1/(1 4/4-3/4)=2-1/(1+4/4-3/4)=2-1/(1+(4-3)/4)=2-1/(1+1/4)=2-1/(1 1/4)=
=2-1/((1•4+1)/4)=2-1/(5/4)=2-1:5/4=2-1•4/5=2-4/5=1 5/5-4/5=
=1+5/5-4/5=1+(5-4)/5=1+1/5=1 1/5
Популярные решебники 5 класс Все решебники
*К сожалению, временные проблемы с публикацией комментариев с мобильных устройств.