次の計算をしなさい。 (1) $4ab \times 3b \div 6a$ (2) $9x^2 \div (-3x) \div x$ (3) $3ab^2 \div 2ab \times (-4a^2)$ (4) $(-2a)^3 \times 3a \div (-6a^2)$ (5) $12ab \div (-4a) \times \frac{1}{3}b$ (6) $2x^2y \times y \div \frac{2}{3}xy^2$ (7) $(-6x) \times \frac{3}{2}xy \div (-3x)^2$ (8) $(-2x)^2 \div \frac{4}{5}xy \times (-3y)$

はい、承知いたしました。問題の計算を解いていきます。

1. 問題の内容

次の計算をしなさい。

(1) $4ab \times 3b \div 6a$

(2) $9x^2 \div (-3x) \div x$

(3) $3ab^2 \div 2ab \times (-4a^2)$

(4) $(-2a)^3 \times 3a \div (-6a^2)$

(5) $12ab \div (-4a) \times \frac{1}{3}b$

(6) $2x^2y \times y \div \frac{2}{3}xy^2$

(7) $(-6x) \times \frac{3}{2}xy \div (-3x)^2$

(8) $(-2x)^2 \div \frac{4}{5}xy \times (-3y)$

2. 解き方の手順

(1)

$4ab \times 3b \div 6a = \frac{4ab \times 3b}{6a} = \frac{12ab^2}{6a} = 2b^2$

(2)

$9x^2 \div (-3x) \div x = \frac{9x^2}{(-3x) \times x} = \frac{9x^2}{-3x^2} = -3$

(3)

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

(4)

$(-2a)^3 \times 3a \div (-6a^2) = (-8a^3) \times 3a \div (-6a^2) = \frac{-8a^3 \times 3a}{-6a^2} = \frac{-24a^4}{-6a^2} = 4a^2$

(5)

$12ab \div (-4a) \times \frac{1}{3}b = \frac{12ab}{-4a} \times \frac{1}{3}b = -3b \times \frac{1}{3}b = -b^2$

(6)

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

(7)

$(-6x) \times \frac{3}{2}xy \div (-3x)^2 = (-6x) \times \frac{3}{2}xy \div 9x^2 = \frac{(-6x) \times \frac{3}{2}xy}{9x^2} = \frac{-9x^2y}{9x^2} = -y$

(8)

$(-2x)^2 \div \frac{4}{5}xy \times (-3y) = 4x^2 \div \frac{4}{5}xy \times (-3y) = \frac{4x^2}{\frac{4}{5}xy} \times (-3y) = \frac{4x^2 \times 5}{4xy} \times (-3y) = \frac{5x}{y} \times (-3y) = 5x/y *(-3y)= -15x$

3. 最終的な答え

(1) $2b^2$

(2) $-3$

(3) $-6a^2b$

(4) $4a^2$

(5) $-b^2$

(6) $3x$

(7) $-y$

(8) $-15x$