画像にある以下の問題を解きます。 * (30) $54ab \div 6b$ * (31) $(-8x^2) \div 12a^2$ * (32) $(-20xy) \div (-\frac{5}{4}x)$ * (33) $\frac{5}{6}a^2 \div (-\frac{5}{12}a)$ * (34) $(-4x) \times 6xy \div (-3y)$ * (35) $16a^2b^2 \div 2ab \times (-4a)$ * (36) $32xy^2 \div (-8y) \div 2y$ * (37) $(-18xy^2) \times 2x \div (-3x)^2$ * (38) $2x+y = 5$ (y について解く) * (39) $5a-2b = 12$ (b について解く) * (40) $a = \frac{3b+c}{2}$ (c について解く) * (25) $9a \times (-7b)$ * (26) $\frac{2}{3}ab \times (-12b)$ * (27) $-(-4a)^2$ * (28) $(-5x)^2 \times (-2y)$ * (29) $6a \times (-b)^3$

1. 問題の内容

画像にある以下の問題を解きます。

* (30) $54ab \div 6b$

* (31) $(-8x^2) \div 12a^2$

* (32) $(-20xy) \div (-\frac{5}{4}x)$

* (33) $\frac{5}{6}a^2 \div (-\frac{5}{12}a)$

* (34) $(-4x) \times 6xy \div (-3y)$

* (35) $16a^2b^2 \div 2ab \times (-4a)$

* (36) $32xy^2 \div (-8y) \div 2y$

* (37) $(-18xy^2) \times 2x \div (-3x)^2$

* (38) $2x+y = 5$ (y について解く)

* (39) $5a-2b = 12$ (b について解く)

* (40) $a = \frac{3b+c}{2}$ (c について解く)

* (25) $9a \times (-7b)$

* (26) $\frac{2}{3}ab \times (-12b)$

* (27) $-(-4a)^2$

* (28) $(-5x)^2 \times (-2y)$

* (29) $6a \times (-b)^3$

2. 解き方の手順

それぞれの問題に対して以下の手順で計算します。

* (30) $54ab \div 6b = \frac{54ab}{6b} = 9a$

* (31) $(-8x^2) \div 12a^2 = \frac{-8x^2}{12a^2} = -\frac{2x^2}{3a^2}$

* (32) $(-20xy) \div (-\frac{5}{4}x) = -20xy \times (-\frac{4}{5x}) = \frac{80xy}{5x} = 16y$

* (33) $\frac{5}{6}a^2 \div (-\frac{5}{12}a) = \frac{5}{6}a^2 \times (-\frac{12}{5a}) = -\frac{60a^2}{30a} = -2a$

* (34) $(-4x) \times 6xy \div (-3y) = \frac{(-4x) \times 6xy}{-3y} = \frac{-24x^2y}{-3y} = 8x^2$

* (35) $16a^2b^2 \div 2ab \times (-4a) = \frac{16a^2b^2}{2ab} \times (-4a) = 8ab \times (-4a) = -32a^2b$

* (36) $32xy^2 \div (-8y) \div 2y = \frac{32xy^2}{-8y} \div 2y = -4xy \div 2y = \frac{-4xy}{2y} = -2x$

* (37) $(-18xy^2) \times 2x \div (-3x)^2 = \frac{(-18xy^2) \times 2x}{(-3x)^2} = \frac{-36x^2y^2}{9x^2} = -4y^2$

* (38) $2x+y = 5$ より $y = 5 - 2x$

* (39) $5a-2b = 12$ より $-2b = 12 - 5a$ よって $b = \frac{5a - 12}{2}$

* (40) $a = \frac{3b+c}{2}$ より $2a = 3b + c$ よって $c = 2a - 3b$

* (25) $9a \times (-7b) = -63ab$

* (26) $\frac{2}{3}ab \times (-12b) = -8ab^2$

* (27) $-(-4a)^2 = - (16a^2) = -16a^2$

* (28) $(-5x)^2 \times (-2y) = 25x^2 \times (-2y) = -50x^2y$

* (29) $6a \times (-b)^3 = 6a \times (-b^3) = -6ab^3$

3. 最終的な答え

* (30) $9a$

* (31) $-\frac{2x^2}{3a^2}$

* (32) $16y$

* (33) $-2a$

* (34) $8x^2$

* (35) $-32a^2b$

* (36) $-2x$

* (37) $-4y^2$

* (38) $y = 5 - 2x$

* (39) $b = \frac{5a - 12}{2}$

* (40) $c = 2a - 3b$

* (25) $-63ab$

* (26) $-8ab^2$

* (27) $-16a^2$

* (28) $-50x^2y$

* (29) $-6ab^3$