Упр.444 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

Задача

а) 30/(5/12 + 1/4); в) (4 — 1 3/5)/(7 1/2 · 9/25); д) ((7 1/3 : 1 1/6) : (8 : 7))/(9 : (1 3/11 + 2));
б) (1 3/8 · 2)/11; г) (8 1/3 : 2)/(1 9/10 + 4 7/20); е) (3 4/7 : (6 1/28 — 3 3/4))/((1 5/6 · 1 5/22) : 18 · 5).
а) 30/(5/12+1/4)=30/(5/12+(1•3)/(4•3))=30/(5/12+3/12)=30/((5+3)/12)=30/(8/12)=30/((2•4)/(3•4))=30/(2/3)=30:2/3=30•3/2=
=(30•3)/2=(2•15•3)/2=45/1=45
б) (1 3/8•2)/11=((1•8+3)/8•2)/11=((8+3)/8•2)/11=(11/8•2)/11=((11•2)/8)/11=((11•2)/(2•4))/11=(11/4)/11=11/4 :11=11/(4•11)=1/4
в) (4-1 3/5)/(7 1/2•9/25)=(3+1-1 3/5)/((7•2+1)/2•9/25)=(3+5/5-1 3/5)/((14+1)/2•9/25)=(3-1+5/5-3/5)/(15/2•9/25)=(2+(5-3)/5)/((15•9)/(2•25))=(2+2/5)/((3•5•9)/(2•5•5))=(2 2/5)/(27/10)=
=2 2/5 :27/10=(2•5+2)/5 :27/10=12/5•10/27=(12•10)/(5•27)=(3•4•2•5)/(5•3•9)=8/9
г) (8 1/3 :2)/(1 9/10+4 7/20)=((8+1/3) :2)/(1 (9•2)/(10•2)+4 7/20)=(8:2+1/3 :2)/(1 18/20+4 7/20)=(4+1/(3•2))/(1+4+18/20+7/20)=(4+1/6)/(5+(18+7)/20)=(4 1/6)/(5+25/20)=(4 1/6)/(5+(5•5)/(4•5))=
=(4 1/6)/(5+5/4)=(4 1/6)/(5+1 1/4)=(4 1/6)/(6 1/4)=4 1/6 :6 1/4=(4•6+1)/6 :(6•4+1)/4=25/6 :25/4=25/6•4/25=
=(25•4)/(6•25)=(2•2)/(2•3)=2/3
д) ((7 1/3 :1 1/6) :(8:7))/(9:(1 3/11+2) )=(((7•3+1)/3 :(1•6+1)/6) :8/7)/(9:3 3/11)=((22/3 :7/6)•7/8)/(9:(3•11+3)/11)=(22/3•6/7•7/8)/(9:36/11)=((22•6•7)/(3•7•8))/(9•11/36)=((2•11•2•3)/(3•2•4))/((9•11)/36)=
=((2•11)/(2•2))/((9•11)/(9•4))=(11/2)/(11/4)=11/2 :11/4=11/2•4/11=(11•4)/(2•11)=4/2=2
е) (3 4/7 :(6 1/28-3 3/4))/((1 5/6•1 5/22) :18•5)=((3•7+4)/7 :(6 1/28-3 (3•7)/(4•7)))/(((1•6+5)/6•(1•22+5)/22) :18•5)=(25/7 :(6 1/28-3 21/28))/((11/6•27/22)•1/18•5)=(25/7 :(5 1/28+1-3 21/28))/(11/6•27/22•5/18)=
=(25/7 :(5 1/28+28/28-3 21/28))/((11•27•5)/(6•22•18))=(25/7 :(5-3+(1+28-21)/28))/((11•3•9•5)/(2•3•2•11•2•9))=(25/7 :(2+8/28))/(5/8)=(25/7 :(2+(2•4)/(4•7)))/(5/8)=(25/7 :2 2/7)/(5/8)=
=(25/7 :(2•7+2)/7)/(5/8)=(25/7 :16/7)/(5/8)=(25/7•7/16)/(5/8)=((25•7)/(7•16))/(5/8)=25/16 :5/8=25/16•8/5=(5•5•8)/(2•8•5)=5/2=2 1/2

Подробный ответ

а) $$30:\left(\frac{5}{12}+\frac{1}{4}\right)=30:\left(\frac{5}{12}+\frac{3}{12}\right)=30:\frac{8}{12}=30:\frac{2}{3}=30\cdot\frac{3}{2}=45$$

б) $$\left(1\frac{3}{8}\cdot 2\right):11=\left(\frac{11}{8}\cdot 2\right):11=\frac{11}{4}:11=\frac{11}{4}\cdot\frac{1}{11}=\frac{1}{4}$$

в) $$\left(4-1\frac{3}{5}\right):\left(7\frac{1}{2}\cdot\frac{9}{25}\right)=\frac{12}{5}:\frac{27}{10}=\frac{12}{5}\cdot\frac{10}{27}=\frac{8}{9}$$

г) $$\left(8\frac{1}{3}:2\right):\left(1\frac{9}{10}+4\frac{7}{20}\right)=\left(\frac{25}{3}:2\right):\left(\frac{19}{10}+\frac{87}{20}\right)$$

$$=\frac{25}{6}:\frac{25}{4}=\frac{25}{6}\cdot\frac{4}{25}=\frac{2}{3}$$

д) $$\left(\left(7\frac{1}{3}:1\frac{1}{6}\right):(8:7)\right):\left(9:\left(1\frac{3}{11}+2\right)\right)$$

$$=\left(\frac{22}{3}:\frac{7}{6}\right):\frac{8}{7}:\left(9:\frac{36}{11}\right)=\frac{22}{3}\cdot\frac{6}{7}\cdot\frac{7}{8}:\frac{9\cdot 11}{36}$$

$$=\frac{11}{2}:\frac{11}{4}=\frac{11}{2}\cdot\frac{4}{11}=2$$

е) $$\left(3\frac{4}{7}:\left(6\frac{1}{28}-3\frac{3}{4}\right)\right):\left(\left(1\frac{5}{6}\cdot 1\frac{5}{22}\right):18\cdot 5\right)$$

$$=\left(\frac{25}{7}:\frac{15}{28}\right):\left(\frac{11}{6}\cdot\frac{27}{22}:18\cdot 5\right)=\frac{25}{7}:\frac{15}{28}:\frac{5}{8}$$

$$=\frac{25}{7}\cdot\frac{28}{15}\cdot\frac{8}{5}=\frac{5}{2}=2\frac{1}{2}$$