ГДЗ по Математике 6 Класс Вариант 3 Номер 51 Мерзляк, Полонский — Подробные Ответы

Найдите разность:

1. 
   $\frac{71}{9} — \frac{8}{3}$
2. 
   $\frac{89}{18} — \frac{31}{12}$
3. 
   $\frac{323}{21} — \frac{89}{14}$
4. 
   $\frac{307}{48} — \frac{171}{32}$

1)

$7\frac{8}{9} — 2\frac{2}{3}$$= \frac{71}{9} — \frac{8}{3} = \frac{71}{9} — \frac{24}{9} = \frac{47}{9} = 5\frac{2}{9}$

2)

$4\frac{17}{18} — 2\frac{7}{12}$$= \frac{89}{18} — \frac{31}{12} = \frac{178}{36} — \frac{93}{36} = \frac{85}{36} = 2\frac{13}{36}$

3)

$15\frac{8}{21} — 6\frac{5}{14}$$= \frac{323}{21} — \frac{89}{14} = \frac{646}{42} — \frac{267}{42} = \frac{379}{42} = 9\frac{1}{42}$

4)

$6\frac{19}{48} — 5\frac{11}{32}$$= \frac{307}{48} — \frac{171}{32} = \frac{307}{48} — \frac{513}{96} = \frac{614}{96} — \frac{513}{96} = \frac{101}{96} = 1\frac{5}{96}$

Ответ:

1. 
   $5\frac{2}{9}$
2. 
   $2\frac{13}{36}$
3. 
   $9\frac{1}{42}$
4. 
   $1\frac{5}{96}$

1)

$7\frac{8}{9} — 2\frac{2}{3}$

Переведём в неправильные дроби:

$$7\frac{8}{9} = \frac{7 \cdot 9 + 8}{9} = \frac{63 + 8}{9} = \frac{71}{9}$$

$$2\frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$$

Приводим к общему знаменателю $9$:

$$\frac{8}{3} = \frac{8 \cdot 3}{3 \cdot 3} = \frac{24}{9}$$

Вычитаем:$$\frac{71}{9} — \frac{24}{9} = \frac{47}{9} = 5\frac{2}{9}$$2)

$4\frac{17}{18} — 2\frac{7}{12}$

Переводим:$$4\frac{17}{18} = \frac{4 \cdot 18 + 17}{18} = \frac{72 + 17}{18} = \frac{89}{18}$$

$$2\frac{7}{12} = \frac{2 \cdot 12 + 7}{12} = \frac{24 + 7}{12} = \frac{31}{12}$$

Общий знаменатель — $36$:

$$\frac{89}{18} = \frac{89 \cdot 2}{36} = \frac{178}{36}, \quad \frac{31}{12} = \frac{31 \cdot 3}{36} = \frac{93}{36}$$

Вычитаем:$$\frac{178}{36} — \frac{93}{36} = \frac{85}{36} = 2\frac{13}{36}$$

3)

$15\frac{8}{21} — 6\frac{5}{14}$

Переводим:

$$15\frac{8}{21} = \frac{15 \cdot 21 + 8}{21} = \frac{315 + 8}{21} = \frac{323}{21}$$

$$6\frac{5}{14} = \frac{6 \cdot 14 + 5}{14} = \frac{84 + 5}{14} = \frac{89}{14}$$

Общий знаменатель — $42$:

$$\frac{323}{21} = \frac{323 \cdot 2}{42} = \frac{646}{42}, \quad \frac{89}{14} = \frac{89 \cdot 3}{42} = \frac{267}{42}$$

Вычитаем:$$\frac{646}{42} — \frac{267}{42} = \frac{379}{42} = 9\frac{1}{42}$$4)

$6\frac{19}{48} — 5\frac{11}{32}$

Переводим:$$6\frac{19}{48} = \frac{6 \cdot 48 + 19}{48} = \frac{288 + 19}{48} = \frac{307}{48}$$

$$5\frac{11}{32} = \frac{5 \cdot 32 + 11}{32} = \frac{160 + 11}{32} = \frac{171}{32}$$

Общий знаменатель —$96$:

$$\frac{307}{48} = \frac{307 \cdot 2}{96} = \frac{614}{96}, \quad \frac{171}{32} = \frac{171 \cdot 3}{96} = \frac{513}{96}$$

Вычитаем:$$\frac{614}{96} — \frac{513}{96} = \frac{101}{96} = 1\frac{5}{96}$$

1. 
   $5\frac{2}{9}$
2. 
   $2\frac{13}{36}$
3. 
   $9\frac{1}{42}$
4. 
   $1\frac{5}{96}$