与えられた数式をそれぞれ計算し、最も簡単な形で表す。具体的には以下の9つの問題を解く。 (1) $3x \times (-2x)^2 \div x^3$ (2) $2a \times (3b)^2 \div 6a^2b$ (3) $(-3a)^2 \div (-3a) \times 5a$ (4) $(-6x) \div (-2x)^2 \times 3y$ (5) $8y^2 \div (-4y)^2 \div 2y$ (6) $10a^2b \div 5a \div (-a)^2$ (7) $18a^2 \div (-3a) \div a$ (8) $12xy^2 \div y \div 3x^2$ (9) $(-6a^2b) \div 4a \div (-3ab)$ (10) $18x \times \frac{1}{2}xy \div (-3y)$ (11) $(-\frac{2}{3}ab) \div (-2b) \times \frac{1}{4}b$ (12) $-18x \div \frac{3}{5}x \times (-\frac{2}{3}y)$

1. 問題の内容

与えられた数式をそれぞれ計算し、最も簡単な形で表す。具体的には以下の9つの問題を解く。

(1) $3x \times (-2x)^2 \div x^3$

(2) $2a \times (3b)^2 \div 6a^2b$

(3) $(-3a)^2 \div (-3a) \times 5a$

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

(5) $8y^2 \div (-4y)^2 \div 2y$

(6) $10a^2b \div 5a \div (-a)^2$

(7) $18a^2 \div (-3a) \div a$

(8) $12xy^2 \div y \div 3x^2$

(9) $(-6a^2b) \div 4a \div (-3ab)$

(10) $18x \times \frac{1}{2}xy \div (-3y)$

(11) $(-\frac{2}{3}ab) \div (-2b) \times \frac{1}{4}b$

(12) $-18x \div \frac{3}{5}x \times (-\frac{2}{3}y)$

2. 解き方の手順

(1) $3x \times (-2x)^2 \div x^3 = 3x \times 4x^2 \div x^3 = 12x^3 \div x^3 = 12$

(2) $2a \times (3b)^2 \div 6a^2b = 2a \times 9b^2 \div 6a^2b = 18ab^2 \div 6a^2b = \frac{3b}{a}$

(3) $(-3a)^2 \div (-3a) \times 5a = 9a^2 \div (-3a) \times 5a = -3a \times 5a = -15a^2$

(4) $(-6x) \div (-2x)^2 \times 3y = -6x \div 4x^2 \times 3y = \frac{-6x}{4x^2} \times 3y = \frac{-3}{2x} \times 3y = -\frac{9y}{2x}$

(5) $8y^2 \div (-4y)^2 \div 2y = 8y^2 \div 16y^2 \div 2y = \frac{8y^2}{16y^2} \div 2y = \frac{1}{2} \div 2y = \frac{1}{4y}$

(6) $10a^2b \div 5a \div (-a)^2 = 10a^2b \div 5a \div a^2 = \frac{10a^2b}{5a} \div a^2 = 2ab \div a^2 = \frac{2b}{a}$

(7) $18a^2 \div (-3a) \div a = \frac{18a^2}{-3a} \div a = -6a \div a = -6$

(8) $12xy^2 \div y \div 3x^2 = \frac{12xy^2}{y} \div 3x^2 = 12xy \div 3x^2 = \frac{4y}{x}$

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

(10) $18x \times \frac{1}{2}xy \div (-3y) = 9x^2y \div (-3y) = \frac{9x^2y}{-3y} = -3x^2$

(11) $(-\frac{2}{3}ab) \div (-2b) \times \frac{1}{4}b = \frac{-2ab}{3} \times \frac{1}{-2b} \times \frac{1}{4}b = \frac{2ab}{6b} \times \frac{1}{4}b = \frac{a}{3} \times \frac{b}{4} = \frac{ab}{12}$

(12) $-18x \div \frac{3}{5}x \times (-\frac{2}{3}y) = -18x \times \frac{5}{3x} \times (-\frac{2}{3}y) = -30 \times (-\frac{2}{3}y) = 20y$

3. 最終的な答え

(1) 12

(2) $\frac{3b}{a}$

(3) $-15a^2$

(4) $-\frac{9y}{2x}$

(5) $\frac{1}{4y}$

(6) $\frac{2b}{a}$

(7) -6

(8) $\frac{4y}{x}$

(9) $\frac{1}{2}$

(10) $-3x^2$

(11) $\frac{ab}{12}$

(12) $20y$