Упр.8 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) 1/3 + 5/6;
2) 3/7-2/9;
3) 7/16*8/35;
4) 4/9* 18;
5) 46/75:23/45;
6) 2/3:4;
7) 10:5/11;
8) 2*3/8 + 4*1/6;
9) 6-1*3/5;
10) 4*2/7 — 1*4/9;
11) 8*3/4 * 1*3/14;
12) 1*3/5 : 5*1/3?
Найдите значение выражения:
1) 2х — 3 при х = 4; 0; -3;
2) 1/3*а + 1/4*b при а = -6, b = 16;
3) 3m — 5n + 3k при m = -7, n = 1,4, k = -0,1.

1. $$\frac{1}{3}+\frac{5}{6}=\frac{2}{6}+\frac{5}{6}=\frac{7}{6}=1\frac{1}{6}$$
2. $$\frac{3}{7}-\frac{2}{9}=\frac{27}{63}-\frac{14}{63}=\frac{13}{63}$$
3. $$\frac{7}{16}\cdot\frac{8}{35}=\frac{1}{2}\cdot\frac{1}{5}=\frac{1}{10}$$
4. $$\frac{4}{9}\cdot 18=\frac{4\cdot 18}{9}=4\cdot 2=8$$
5. $$\frac{46}{75}:\frac{23}{45}=\frac{46}{75}\cdot\frac{45}{23}=\frac{2\cdot 3}{5\cdot 1}=\frac{6}{5}=1\frac{1}{5}$$
6. $$\frac{2}{3}:4=\frac{2}{3}\cdot\frac{1}{4}=\frac{1}{6}$$
7. $$10:\frac{5}{11}=10\cdot\frac{11}{5}=22$$
8. $$2\frac{3}{8}+4\frac{1}{6}=2\frac{9}{24}+4\frac{4}{24}=6\frac{13}{24}$$
9. $$6-1\frac{3}{5}=5\frac{5}{5}-1\frac{3}{5}=4\frac{2}{5}$$
10. $$4\frac{2}{7}-1\frac{4}{9}=4\frac{18}{63}-1\frac{28}{63}=3\frac{81}{63}-1\frac{28}{63}=2\frac{53}{63}$$
11. $$8\frac{3}{4}\cdot 1\frac{3}{14}=\frac{35}{4}\cdot\frac{17}{14}=\frac{5\cdot 17}{4\cdot 2}=\frac{85}{8}=10\frac{5}{8}$$
12. $$1\frac{3}{5}:5\frac{1}{3}=\frac{8}{5}:\frac{16}{3}=\frac{8}{5}\cdot\frac{3}{16}=\frac{3}{10}$$

13. При $$x=4$$:
    $$2x-3=2\cdot 4-3=8-3=5$$
    
    При $$x=0$$:
    $$2x-3=2\cdot 0-3=-3$$
    
    При $$x=-3$$:
    $$2x-3=2\cdot(-3)-3=-6-3=-9$$
14. При $$a=-6,\ b=16$$:
    $$\frac{1}{3}a+\frac{1}{4}b=\frac{1}{3}\cdot(-6)+\frac{1}{4}\cdot 16=-2+4=2$$
15. При $$m=-7,\ n=1{,}4,\ k=-0{,}1$$:
    $$3m-5n+3k=3\cdot(-7)-5\cdot 1{,}4+3\cdot(-0{,}1)=-21-7-0{,}3=-28{,}3$$

Ответ

1) $$1\frac{1}{6}$$; 2) $$\frac{13}{63}$$; 3) $$\frac{1}{10}$$; 4) $$8$$; 5) $$1\frac{1}{5}$$; 6) $$\frac{1}{6}$$; 7) $$22$$; 8) $$6\frac{13}{24}$$; 9) $$4\frac{2}{5}$$; 10) $$2\frac{53}{63}$$; 11) $$10\frac{5}{8}$$; 12) $$\frac{3}{10}$$; 13) $$5,\ -3,\ -9$$; 14) $$2$$; 15) $$-28{,}3$$.