Упр.1052 ГДЗ Ткачёва 5 класс (Математика)

1) 24 : 3 = 16 : x; 2) x : 7 = 12 : 3; 3) x/15 = 6/5; 4) 4/11 = 8/x;
5) 48 : x = 24 : 3; 6) 25 : 10 = x : 4; 7) 4/14 = x/35; 8) 54/x = 27/6.

Используем основное свойство пропорции: произведение крайних членов равно произведению средних.

1) $$24 : 3 = 16 : x$$

$$24x = 3 \cdot 16$$
$$x = \frac{3 \cdot 16}{24} = 2$$

2) $$x : 7 = 12 : 3$$

$$3x = 7 \cdot 12$$
$$x = \frac{7 \cdot 12}{3} = 28$$

3) $$\frac{x}{15} = \frac{6}{5}$$

$$5x = 15 \cdot 6$$
$$x = \frac{15 \cdot 6}{5} = 18$$

4) $$\frac{4}{11} = \frac{8}{x}$$

$$4x = 11 \cdot 8$$
$$x = \frac{11 \cdot 8}{4} = 22$$

5) $$48 : x = 24 : 3$$

$$24x = 48 \cdot 3$$
$$x = \frac{48 \cdot 3}{24} = 6$$

6) $$25 : 10 = x : 4$$

$$10x = 25 \cdot 4$$
$$x = \frac{25 \cdot 4}{10} = 10$$

7) $$\frac{4}{14} = \frac{x}{35}$$

$$14x = 4 \cdot 35$$
$$x = \frac{4 \cdot 35}{14} = 10$$

8) $$\frac{54}{x} = \frac{27}{6}$$

$$27x = 54 \cdot 6$$
$$x = \frac{54 \cdot 6}{27} = 12$$

Ответ

1) 2; 2) 28; 3) 18; 4) 22; 5) 6; 6) 10; 7) 10; 8) 12.