33. Simplify: (a) \( \cdot \frac{1}{9} \cdot\left(-\frac{7}{3}\right) \) (b) \( \frac{16}{13}-\left(-\frac{4}{65}\right) \) 34. How many times a whect of radius 7 cm mase nuate to po 352 m ? 35. Simplify and then find the value if \( \mathrm{a}=-1 \) and \( \mathrm{b}=2 \) \[ 3 a b-2 b-5 a-2(5 a-7 a b)-30 \] 36. The number of illterate persons in a cinuntry decreased from is0 lakhs ta 100 lakhs in 10 years. What is the pecoentage of decrease? 38. Simplify. \[ \frac{\left(2^{4} 5^{2} \times 9^{3} \times 4 \times 1^{3}\right.}{2^{1} \times 8^{2} \times 27 \times 1^{3}} \] 39. What cross-section do you get when you give a ii) settical cut. (ii) horizonal cut to the following solids? (a) A brick (b) A round apple (c) A die. 40. Kamal buys a book firr Rs 275 and sells it at a loss of \( 154 \% \). How much dues he sell at lor ?

Calculate the value by following steps: - step0: Calculate: \(\frac{\left(150-100\right)}{150}\times 100\) - step1: Remove the parentheses: \(\frac{150-100}{150}\times 100\) - step2: Subtract the numbers: \(\frac{50}{150}\times 100\) - step3: Reduce the fraction: \(\frac{1}{3}\times 100\) - step4: Multiply: \(\frac{100}{3}\) Solve the equation \( 275 - x = 275 * (154/100) \). Solve the equation by following steps: - step0: Solve for \(x\): \(275-x=275\left(\frac{154}{100}\right)\) - step1: Simplify: \(275-x=\frac{847}{2}\) - step2: Move the constant to the right side: \(-x=\frac{847}{2}-275\) - step3: Subtract the numbers: \(-x=\frac{297}{2}\) - step4: Change the signs: \(x=-\frac{297}{2}\) Calculate or simplify the expression \( 3*(-1)*2 - 2*2 - 5*(-1) - 2*(5*(-1) - 7*(-1)*2) - 30 \). Calculate the value by following steps: - step0: Calculate: \(3\left(-1\right)\times 2-2\times 2-5\left(-1\right)-2\left(5\left(-1\right)-7\left(-1\right)\times 2\right)-30\) - step1: Simplify: \(3\left(-1\right)\times 2-2\times 2-5\left(-1\right)-2\left(-5-7\left(-1\right)\times 2\right)-30\) - step2: Multiply: \(3\left(-1\right)\times 2-2\times 2-5\left(-1\right)-2\left(-5+14\right)-30\) - step3: Add the numbers: \(3\left(-1\right)\times 2-2\times 2-5\left(-1\right)-2\times 9-30\) - step4: Multiply: \(-6-2\times 2-5\left(-1\right)-2\times 9-30\) - step5: Multiply the numbers: \(-6-4-5\left(-1\right)-2\times 9-30\) - step6: Simplify: \(-6-4+5-2\times 9-30\) - step7: Multiply the numbers: \(-6-4+5-18-30\) - step8: Calculate: \(-53\) Calculate or simplify the expression \( (2^4 * 5^2 * 9^3 * 4 * 1^3)/(2^1 * 8^2 * 27 * 1^3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(2^{4}\times 5^{2}\times 9^{3}\times 4\times 1^{3}\right)}{\left(2^{1}\times 8^{2}\times 27\times 1^{3}\right)}\) - step1: Remove the parentheses: \(\frac{2^{4}\times 5^{2}\times 9^{3}\times 4\times 1^{3}}{2^{1}\times 8^{2}\times 27\times 1^{3}}\) - step2: Multiply by \(a^{-n}:\) \(\frac{2^{4}\times 5^{2}\times 9^{3}\times 4\times 2^{-1}}{8^{2}\times 27}\) - step3: Multiply: \(\frac{2^{5}\times 5^{2}\times 9^{3}}{8^{2}\times 27}\) - step4: Factor the expression: \(\frac{2^{5}\times 5^{2}\times 9^{3}}{2^{6}\times 27}\) - step5: Reduce the fraction: \(\frac{5^{2}\times 9^{3}}{2\times 27}\) - step6: Factor the expression: \(\frac{5^{2}\times 3^{6}}{2\times 3^{3}}\) - step7: Reduce the fraction: \(\frac{5^{2}\times 3^{3}}{2}\) - step8: Calculate: \(\frac{675}{2}\) Calculate or simplify the expression \( 16/13 - (-4/65) \). Calculate the value by following steps: - step0: Calculate: \(\frac{16}{13}-\left(\frac{-4}{65}\right)\) - step1: Rewrite the fraction: \(\frac{16}{13}-\left(-\frac{4}{65}\right)\) - step2: Remove the parentheses: \(\frac{16}{13}+\frac{4}{65}\) - step3: Reduce fractions to a common denominator: \(\frac{16\times 5}{13\times 5}+\frac{4}{65}\) - step4: Multiply the numbers: \(\frac{16\times 5}{65}+\frac{4}{65}\) - step5: Transform the expression: \(\frac{16\times 5+4}{65}\) - step6: Multiply the numbers: \(\frac{80+4}{65}\) - step7: Add the numbers: \(\frac{84}{65}\) Calculate or simplify the expression \( 1/9 * (-7/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{1}{9}\left(\frac{-7}{3}\right)\) - step1: Rewrite the fraction: \(\frac{1}{9}\left(-\frac{7}{3}\right)\) - step2: Multiply the numbers: \(-\frac{1}{9}\times \frac{7}{3}\) - step3: Multiply the fractions: \(-\frac{7}{9\times 3}\) - step4: Multiply: \(-\frac{7}{27}\) Let's solve each part step by step. ### 33. Simplify: (a) \( \cdot \frac{1}{9} \cdot\left(-\frac{7}{3}\right) \) To simplify this expression: \[ \frac{1}{9} \cdot \left(-\frac{7}{3}\right) = -\frac{7}{27} \] (b) \( \frac{16}{13}-\left(-\frac{4}{65}\right) \) To simplify this expression: \[ \frac{16}{13} - \left(-\frac{4}{65}\right) = \frac{16}{13} + \frac{4}{65} \] To add these fractions, we need a common denominator. The least common multiple of 13 and 65 is 65. \[ \frac{16}{13} = \frac{16 \times 5}{13 \times 5} = \frac{80}{65} \] Now, adding: \[ \frac{80}{65} + \frac{4}{65} = \frac{84}{65} \] ### 34. How many times a wheel of radius 7 cm must rotate to cover 352 m? First, we need to find the circumference of the wheel: \[ C = 2 \pi r = 2 \pi (7) = 14 \pi \text{ cm} \] Now, convert 352 m to cm: \[ 352 \text{ m} = 352 \times 100 = 35200 \text{ cm} \] Now, we can find the number of rotations: \[ \text{Number of rotations} = \frac{35200}{14 \pi} \] ### 35. Simplify and then find the value if \( a = -1 \) and \( b = 2 \) \[ 3 a b - 2 b - 5 a - 2(5 a - 7 a b) - 30 \] Substituting \( a = -1 \) and \( b = 2 \): \[ 3(-1)(2) - 2(2) - 5(-1) - 2(5(-1) - 7(-1)(2)) - 30 \] Calculating this gives: \[ -6 - 4 + 5 - 2(-5 + 14) - 30 = -6 - 4 + 5 - 2(9) - 30 = -6 - 4 + 5 - 18 - 30 = -53 \] ### 36. The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease? The decrease in number is: \[ 150 - 100 = 50 \text{ lakhs} \] The percentage decrease is: \[ \frac{50}{150} \times 100 = \frac{100}{3} \approx 33.33\% \] ### 38. Simplify: \[ \frac{(2^{4} 5^{2} \times 9^{3} \times 4 \times 1^{3})}{(2^{1} \times 8^{2} \times 27 \times 1^{3})} \] Calculating this gives: \[ \frac{675}{2} \] ### 39. What cross-section do you get when you give: (i) A vertical cut to a brick: A rectangle. (ii) A horizontal cut to a brick: A rectangle. (iii) A vertical cut to a round apple: A circle. (iv) A horizontal cut to a round apple: A circle. (v) A vertical cut to a die: A square. (vi) A horizontal cut to a die: A square. ### 40. Kamal buys a book for Rs 275 and sells it at a loss of \( 154\% \). How much does he sell at loss? To find the selling price: \[ \text{Loss} = 275 \times \frac{154}{100} = 275 \times 1.54 = 423.5 \] The selling price is: \[ \text{Selling Price} = 275 - 423.5 = -148.5 \] This indicates a misunderstanding in the loss percentage, as a loss cannot exceed the cost price. ### Summary of Results: - (a) \( -\frac{7}{27} \) - (b) \( \frac{84}{65} \) - (c) Number of rotations: \( \frac{35200}{14 \pi} \) - (d) Simplified expression: \( -53 \) - (e) Percentage decrease: \( \frac{100}{3} \) - (f) Simplified expression: \( \frac{675}{2} \) - (g) Cross-sections: Rectangle for brick, circle for apple, square for die. - (h) Selling price: \( -148.5 \) (indicating a loss greater than the cost price).