11.18. Divide:a) 10 ÷b)3423÷ 36Ans. a) 15b)48c)c) 3x÷d)74y12x77-y575/2d)За2bf)11.19. Divide:(6.1)abb2rs²e)g)÷4616t822f)*2301.ax62x10yh)y3x3x²g)2sh)5y²(6.2)3x5x2x² + 2y²x² + y²a)g)÷x+2x + 2x²-4y2x + 2y2(y+3)8(y+3)s²+sts² - fb)763h)÷rs - st2-2​

Answer:Let's tackle each division problem one by one. ### 11.18a) \( \frac{10}{15} \) To divide 10 by 15, simplify the fraction: \[ \frac{10}{15} = \frac{2}{3} \]b) \( \frac{\frac{34}{23}}{36} \) To divide a fraction by a number, multiply by the reciprocal: \[ \frac{34}{23} \times \frac{1}{36} = \frac{34}{23 \times 36} = \frac{34}{828} \] Simplify if possible: \[ \frac{34}{828} = \frac{17}{414} \] (after dividing the numerator and denominator by 2)c) \( \frac{3x}{12x} \) Simplify by canceling common factors: \[ \frac{3x}{12x} = \frac{3}{12} = \frac{1}{4} \]d) \( \frac{74}{7-y} \div \frac{57}{5/2} \) To divide by a fraction, multiply by its reciprocal: \[ \frac{74}{7-y} \times \frac{5/2}{57} = \frac{74 \times 5/2}{57 \times (7-y)} = \frac{370}{114(7-y)} \] Simplify if possible: \[ \frac{370}{114} = \frac{185}{57} \]e) \( \frac{2b}{a} \) This is already in its simplest form: \[ \frac{2b}{a} \]f) \( \frac{11}{x} \div \frac{2}{30} \) To divide by a fraction, multiply by its reciprocal: \[ \frac{11}{x} \times \frac{30}{2} = \frac{11 \times 30}{2x} = \frac{330}{2x} = \frac{165}{x} \]g) \( \frac{3x}{5x} \) Simplify by canceling common factors: \[ \frac{3x}{5x} = \frac{3}{5} \]h) \( \frac{5y^2}{2x} \) This is already in its simplest form: \[ \frac{5y^2}{2x} \]### 11.19a) \( \frac{ab}{b^2} \) Simplify by canceling common factors: \[ \frac{ab}{b^2} = \frac{a}{b} \]b) \( \frac{rs^2}{4} \div \frac{6}{16t} \) To divide by a fraction, multiply by its reciprocal: \[ \frac{rs^2}{4} \times \frac{16t}{6} = \frac{rs^2 \times 16t}{4 \times 6} = \frac{16trs^2}{24} \] Simplify: \[ \frac{16trs^2}{24} = \frac{2trs^2}{3} \]c) \( \frac{30}{1} \div \frac{ax}{6} \) To divide by a fraction, multiply by its reciprocal: \[ 30 \times \frac{6}{ax} = \frac{180}{ax} \]d) \( \frac{2x}{x + 2} \div \frac{x^2 - 4y^2}{x + 2y} \) To divide by a fraction, multiply by its reciprocal: \[ \frac{2x}{x + 2} \times \frac{x + 2y}{x^2 - 4y^2} = \frac{2x \times (x + 2y)}{(x + 2) \times (x^2 - 4y^2)} \] Factor \( x^2 - 4y^2 \) as \( (x - 2y)(x + 2y) \): \[ \frac{2x \times (x + 2y)}{(x + 2) \times (x - 2y) \times (x + 2y)} = \frac{2x}{(x + 2) \times (x - 2y)} \]e) \( \frac{s^2 + st}{s^2 - st} \) This is already in its simplest form: \[ \frac{s^2 + st}{s^2 - st} \]f) \( \frac{7}{63} \div \frac{2 - 2}{rs - st} \) Since \( 2 - 2 = 0 \), dividing by zero is undefined. So, this problem has no valid solution.g) \( \frac{x + 2}{x^2 - 4y^2} \) Factor \( x^2 - 4y^2 \) as \( (x - 2y)(x + 2y) \): \[ \frac{x + 2}{(x - 2y)(x + 2y)} \]h) \( \frac{8(y + 3)}{s^2 + st} \) This is already in its simplest form: \[ \frac{8(y + 3)}{s^2 + st} \]

Answered by lycapatricio149 | 2024-09-08