Упр.361 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 1/2a+ 1/3a? 1/4a, если a = 1*5/7 ;
2) 4/7b+ 5/21b? 2/3b, если b = 2*1/3 ;
3) 1*5/12m+2*7/18m?1*2/9m, если m = 1*17/31.

1) При $$a=1\frac{5}{7}=\frac{12}{7}$$:

$$ \frac{1}{2}a+\frac{1}{3}a-\frac{1}{4}a = \frac{6}{12}a+\frac{4}{12}a-\frac{3}{12}a = \frac{7}{12}a $$
$$ \frac{7}{12}\cdot \frac{12}{7}=1 $$

2) При $$b=2\frac{1}{3}=\frac{7}{3}$$:

$$ \frac{4}{7}b+\frac{5}{21}b-\frac{2}{3}b = \frac{12}{21}b+\frac{5}{21}b-\frac{14}{21}b = \frac{3}{21}b = \frac{1}{7}b $$
$$ \frac{1}{7}\cdot \frac{7}{3}=\frac{1}{3} $$

3) При $$m=1\frac{17}{31}=\frac{48}{31}$$:

$$ 1\frac{5}{12}m+2\frac{7}{18}m-1\frac{2}{9}m = 1\frac{15}{36}m+2\frac{14}{36}m-1\frac{8}{36}m $$
$$ = 3\frac{29}{36}m-1\frac{8}{36}m = 2\frac{21}{36}m = 2\frac{7}{12}m = \frac{31}{12}m $$
$$ \frac{31}{12}\cdot \frac{48}{31}=4 $$

Ответ

1) $$1$$; 2) $$\frac{1}{3}$$; 3) $$4$$.