与えられた6つの数式をそれぞれ計算し、簡略化します。

1. 問題の内容

与えられた6つの数式をそれぞれ計算し、簡略化します。

2. 解き方の手順

(1) $6ab \div 3a = \frac{6ab}{3a} = \frac{6}{3} \cdot \frac{a}{a} \cdot b = 2 \cdot 1 \cdot b = 2b$

(2) $(-10xy) \div \frac{5}{2}x = -10xy \cdot \frac{2}{5x} = \frac{-10xy \cdot 2}{5x} = \frac{-20xy}{5x} = \frac{-20}{5} \cdot \frac{x}{x} \cdot y = -4 \cdot 1 \cdot y = -4y$

(3) $8x^2 \div (-6x) = \frac{8x^2}{-6x} = \frac{8}{-6} \cdot \frac{x^2}{x} = -\frac{4}{3} \cdot x = -\frac{4}{3}x$

(4) $(-4xy^2) \div \frac{1}{2}xy = -4xy^2 \cdot \frac{2}{xy} = \frac{-4xy^2 \cdot 2}{xy} = \frac{-8xy^2}{xy} = -8 \cdot \frac{x}{x} \cdot \frac{y^2}{y} = -8 \cdot 1 \cdot y = -8y$

(5) $\frac{2}{3}b^2c \div \frac{5}{6}bc^2 = \frac{2}{3}b^2c \cdot \frac{6}{5bc^2} = \frac{2 \cdot 6}{3 \cdot 5} \cdot \frac{b^2}{b} \cdot \frac{c}{c^2} = \frac{12}{15} \cdot b \cdot \frac{1}{c} = \frac{4}{5} \cdot \frac{b}{c} = \frac{4b}{5c}$

(6) $(-9xy) \div (-3xy) = \frac{-9xy}{-3xy} = \frac{-9}{-3} \cdot \frac{x}{x} \cdot \frac{y}{y} = 3 \cdot 1 \cdot 1 = 3$

3. 最終的な答え

(1) $2b$

(2) $-4y$

(3) $-\frac{4}{3}x$

(4) $-8y$

(5) $\frac{4b}{5c}$

(6) $3$