Упр.660 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

Задача

1) 7/8 · 10/21; 3) 8 · 3/4; 5) (1 2/3)^3;
2) 12/5 · 9/16 · 35/27; 4) 3 3/5 · 1 1/9; 6) a/5b · 10/a^2 (a,b не равно 0).
1) 7/8•10/21=(7•10)/(8•21)=(7•2•5)/(2•4•3•7)=5/12
2) 12/5•9/16•35/27=(12•9•35)/(5•16•27)=(3•4•9•5•7)/(5•4•4•3•9)=7/4=1 3/4
3) 8•3/4=(8•3)/4=(2•4•3)/4=6/1=6
4) 3 3/5•1 1/9=(3•5+3)/5•(1•9+1)/9=18/5•10/9=(18•10)/(5•9)=(2•9•2•5)/(5•9)=4/1=4
5) (1 2/3)^3=((1•3+2)/3)^3=(5/3)^3=5/3•5/3•5/3=(5•5•5)/(3•3•3)=(25•5)/(9•3)=125/27=4 17/27
6) a/5b•10/a^2 =(a•10)/(5b•a^2 )=(a•2•5)/(5•b•a•a)=2/ab

Подробный ответ

1) $$\frac{7}{8}\cdot\frac{10}{21}=\frac{7\cdot10}{8\cdot21}=\frac{7\cdot2\cdot5}{2\cdot4\cdot3\cdot7}=\frac{5}{12}$$

2) $$\frac{12}{5}\cdot\frac{9}{16}\cdot\frac{35}{27}=\frac{12\cdot9\cdot35}{5\cdot16\cdot27}=\frac{3\cdot4\cdot9\cdot5\cdot7}{5\cdot4\cdot4\cdot3\cdot9}=\frac{7}{4}=1\frac{3}{4}$$

3) $$8\cdot\frac{3}{4}=\frac{8\cdot3}{4}=\frac{2\cdot4\cdot3}{4}=6$$

4) $$3\frac{3}{5}\cdot1\frac{1}{9}=\frac{18}{5}\cdot\frac{10}{9}=\frac{18\cdot10}{5\cdot9}=\frac{2\cdot9\cdot2\cdot5}{5\cdot9}=4$$

5) $$\left(1\frac{2}{3}\right)^3=\left(\frac{5}{3}\right)^3=\frac{5}{3}\cdot\frac{5}{3}\cdot\frac{5}{3}=\frac{125}{27}=4\frac{17}{27}$$

6) $$\frac{a}{5b}\cdot\frac{10}{a^2}=\frac{a\cdot10}{5b\cdot a^2}=\frac{a\cdot2\cdot5}{5\cdot b\cdot a\cdot a}=\frac{2}{ab}$$