与えられた数式を計算しなさい。 (1) $8xy^2 \div \frac{1}{4}y$ (2) $\frac{9}{14}a^2b \div (-\frac{6}{7}ab)$ (3) $5x^2y \div \frac{x}{3}$ (4) $(-4xy^2) \div \frac{1}{2}xy$ (5) $\frac{2}{3}b^2c \div \frac{5}{6}bc^2$

1. 問題の内容

与えられた数式を計算しなさい。

(1) $8xy^2 \div \frac{1}{4}y$

(2) $\frac{9}{14}a^2b \div (-\frac{6}{7}ab)$

(3) $5x^2y \div \frac{x}{3}$

(4) $(-4xy^2) \div \frac{1}{2}xy$

(5) $\frac{2}{3}b^2c \div \frac{5}{6}bc^2$

2. 解き方の手順

(1)

$8xy^2 \div \frac{1}{4}y = 8xy^2 \times \frac{4}{y} = 32x \frac{y^2}{y} = 32xy$

(2)

$\frac{9}{14}a^2b \div (-\frac{6}{7}ab) = \frac{9}{14}a^2b \times (-\frac{7}{6ab}) = -\frac{9 \times 7}{14 \times 6} \times \frac{a^2b}{ab} = -\frac{3 \times 1}{2 \times 2} a = -\frac{3}{4}a$

(3)

$5x^2y \div \frac{x}{3} = 5x^2y \times \frac{3}{x} = 15 \times \frac{x^2}{x}y = 15xy$

(4)

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

(5)

$\frac{2}{3}b^2c \div \frac{5}{6}bc^2 = \frac{2}{3}b^2c \times \frac{6}{5bc^2} = \frac{2 \times 6}{3 \times 5} \times \frac{b^2c}{bc^2} = \frac{2 \times 2}{1 \times 5} \frac{b}{c} = \frac{4b}{5c}$

3. 最終的な答え

(1) $32xy$

(2) $-\frac{3}{4}a$

(3) $15xy$

(4) $-8y$

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