70 Сократи дроби с натуральными числителями и знаменателями: a) 15⋅3 / 7⋅10, 9⋅5 / 5⋅21, 21⋅4⋅3 / 9⋅105, 19⋅8⋅11 / 12⋅57⋅7; б) 2a / 8ab, 15mkt / 34mt, 18dcm / 45bdmk, xy / 4mnxy; в) mn²/mnh, 3a²b / 6ab, 4c / 8c²d, 15xy² / 20x²yz.

а)

• $$\frac{15 \cdot 3}{7 \cdot 10} = \frac{3 \cdot 5 \cdot 3}{7 \cdot 2 \cdot 5} = \frac{9}{14}$$
• $$\frac{9 \cdot 5}{5 \cdot 21} = \frac{9 \cdot 5}{5 \cdot 3 \cdot 7} = \frac{3}{7}$$
• $$\frac{21 \cdot 4 \cdot 3}{9 \cdot 105} = \frac{3 \cdot 7 \cdot 4 \cdot 3}{9 \cdot 3 \cdot 5 \cdot 7} = \frac{4}{5}$$
• $$\frac{19 \cdot 8 \cdot 11}{12 \cdot 57 \cdot 7} = \frac{19 \cdot 4 \cdot 2 \cdot 11}{4 \cdot 3 \cdot 3 \cdot 19 \cdot 7} = \frac{22}{63}$$

б)

• $$\frac{2a}{8ab} = \frac{2a}{2a \cdot 4b} = \frac{1}{4b}$$
• $$\frac{15mkt}{34mt} = \frac{15k}{34}$$
• $$\frac{18dcm}{45bdmk} = \frac{9dc \cdot 2}{9bd \cdot 5mk} = \frac{2c}{5bmk}$$
• $$\frac{xy}{4mnxy} = \frac{1}{4mn}$$

в)

• $$\frac{mn^2}{mnh} = \frac{mn \cdot n}{mn \cdot h} = \frac{n}{h}$$
• $$\frac{3a^2b}{6ab} = \frac{3ab \cdot a}{3ab \cdot 2} = \frac{a}{2}$$
• $$\frac{4c}{8c^2d} = \frac{4c}{4c \cdot 2cd} = \frac{1}{2cd}$$
• $$\frac{15xy^2}{20x^2yz} = \frac{5xy \cdot 3y}{5xy \cdot 4xz} = \frac{3y}{4xz}$$

Ответ: a) 9/14, 3/7, 4/5, 22/63; б) 1/4b, 15k/34, 2c/5bmk, 1/4mn; в) n/h, a/2, 1/2cd, 3y/4xz