Solving Word Problems and Evaluating Continued Fractions NCERT CBSE

Learn how to solve word problems involving fractions and equations, and how to evaluate an infinite continued fraction. This video provides step-by-step solutions and explanations. Perfect for students learning algebra! #algebra #wordproblems #continuedfractions #equations #math #tutorial 𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Find the number which when added to its two thirds is equal to 35. 𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧: Let the number be x. According to the problem statement, the number added to its two thirds is equal to 35. We can write this as an equation: x + (2/3)x = 35 To solve for x, first find a common denominator for the terms on the left side: (3/3)x + (2/3)x = 35 (3x + 2x) / 3 = 35 5x / 3 = 35 Now, multiply both sides of the equation by 3 to isolate the term with x: 5x = 35 * 3 5x = 105 Finally, divide both sides by 5 to solve for x: x = 105 / 5 x = 21 The number is 21. Final Answer: 21 𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Solve (12x+1)/4 = (13x-1)/5 + 3 𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧: To solve this equation, first eliminate the fractions by multiplying both sides by the least common multiple (LCM) of the denominators, which is LCM(4, 5) = 20. 20 * [(12x+1)/4] = 20 * [(13x-1)/5 + 3] 5 * (12x + 1) = 4 * (13x - 1) + 20 * 3 60x + 5 = 52x - 4 + 60 60x + 5 = 52x + 56 Now, rearrange the equation to group the x terms on one side and the constant terms on the other side: 60x - 52x = 56 - 5 8x = 51 Finally, divide by 8 to solve for x: x = 51 / 8 Final Answer: x = 51/8 𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: What is the value of 4 + 1/(4 + 1/(4 + 1/(4 + ...∞) ) ) 𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧: Let the given expression be equal to y: y = 4 + 1/(4 + 1/(4 + 1/(4 + ...∞) ) ) Notice that the part after the initial '4' is the same as the original expression y. So, we can rewrite the equation as: y = 4 + 1/y Now, we need to solve this equation for y. Multiply both sides by y: y * y = 4 * y + (1/y) * y y² = 4y + 1 Rearrange the equation into a standard quadratic form: y² - 4y - 1 = 0 We can solve this quadratic equation using the quadratic formula: y = [-b ± √(b² - 4ac)] / 2a Here, a = 1, b = -4, and c = -1. y = [-(-4) ± √((-4)² - 4(1)(-1))] / 2(1) y = [4 ± √(16 + 4)] / 2 y = [4 ± √20] / 2 y = [4 ± √(4 * 5)] / 2 y = [4 ± 2√5] / 2 y = 2 ± √5 Since the expression is a sum of positive numbers, its value must be positive. √5 is approximately 2.236. So, 2 + √5 ≈ 2 + 2.236 = 4.236 (positive) And, 2 - √5 ≈ 2 - 2.236 = -0.236 (negative) Therefore, the value of the expression is 2 + √5. Final Answer: 2 + √5 𝐀𝐛𝐨𝐮𝐭 𝐌𝐚𝐭𝐡𝐬 𝐏𝐥𝐚𝐭𝐭𝐞𝐫 Are you ready to explore the world of mathematics and statistics? Our channel offers a variety of short, solved example videos that cover everything from high school and college-level math to statistics and quantitative aptitude concepts for entrance exams.