33. Simplify: (a) \( -\frac{1}{9} \cdot\left(-\frac{7}{3}\right) \) (b) \( \frac{16}{13}+\left(-\frac{4}{65}\right) \) 34. How many times a wheel of radius \( ? \mathrm{~cm} \) must ratate 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 illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease? 38. Simplify: \[ \frac{\left(2^{4}\right)^{2} \times 9^{3} \times 4 \times 1^{9}}{2^{3} \times 8^{2} \times 27 \times 1^{5}} \] 39. What cross-section do you get when you give a (i) vertical cut (ii) herizontal cut to the following solids ? (a) A brick (b) A round apple (c) A die. 40. Kamal buys a book far Rx 275 and sells it at a loss of \( 15 \% \). How much does he sell if for ?

Calculate the value by following steps: - step0: Calculate: \(275-\left(0.15\times 275\right)\) - step1: Multiply the numbers: \(275-41.25\) - step2: Subtract the numbers: \(233.75\) Calculate or simplify the expression \( -\frac{1}{9} \cdot \left(-\frac{7}{3}\right) \). Calculate the value by following steps: - step0: Calculate: \(-\frac{1}{9}\left(-\frac{7}{3}\right)\) - step1: Use the rules for multiplication and division: \(\frac{1}{9}\times \frac{7}{3}\) - step2: Multiply the fractions: \(\frac{7}{9\times 3}\) - step3: Multiply: \(\frac{7}{27}\) Calculate or simplify the expression \( \frac{352}{2\pi} \). Calculate the value by following steps: - step0: Calculate: \(\frac{352}{2\pi }\) - step1: Reduce the fraction: \(\frac{176}{\pi }\) Calculate or simplify the expression \( \frac{16}{13}+\left(-\frac{4}{65}\right) \). Calculate the value by following steps: - step0: Calculate: \(\frac{16}{13}+\left(-\frac{4}{65}\right)\) - step1: Remove the parentheses: \(\frac{16}{13}-\frac{4}{65}\) - step2: Reduce fractions to a common denominator: \(\frac{16\times 5}{13\times 5}-\frac{4}{65}\) - step3: Multiply the numbers: \(\frac{16\times 5}{65}-\frac{4}{65}\) - step4: Transform the expression: \(\frac{16\times 5-4}{65}\) - step5: Multiply the numbers: \(\frac{80-4}{65}\) - step6: Subtract the numbers: \(\frac{76}{65}\) Calculate or simplify the expression \( \frac{150-100}{150} \times 100 \). Calculate the value by following steps: - step0: Calculate: \(\frac{150-100}{150}\times 100\) - step1: Subtract the numbers: \(\frac{50}{150}\times 100\) - step2: Reduce the fraction: \(\frac{1}{3}\times 100\) - step3: Multiply: \(\frac{100}{3}\) 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 \( \frac{\left(2^{4}\right)^{2} \times 9^{3} \times 4 \times 1^{9}}{2^{3} \times 8^{2} \times 27 \times 1^{5}} \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(2^{4}\right)^{2}\times 9^{3}\times 4\times 1^{9}}{2^{3}\times 8^{2}\times 27\times 1^{5}}\) - step1: Multiply by \(a^{-n}:\) \(\frac{\left(2^{4}\right)^{2}\times 9^{3}\times 4}{2^{3}\times 8^{2}\times 27}\) - step2: Multiply the exponents: \(\frac{2^{4\times 2}\times 9^{3}\times 4}{2^{3}\times 8^{2}\times 27}\) - step3: Multiply by \(a^{-n}:\) \(\frac{2^{4\times 2}\times 9^{3}\times 4\times 2^{-3}}{8^{2}\times 27}\) - step4: Multiply the numbers: \(\frac{2^{8}\times 9^{3}\times 4\times 2^{-3}}{8^{2}\times 27}\) - step5: Multiply: \(\frac{2^{7}\times 9^{3}}{8^{2}\times 27}\) - step6: Factor the expression: \(\frac{2^{7}\times 9^{3}}{2^{6}\times 27}\) - step7: Reduce the fraction: \(\frac{2\times 9^{3}}{27}\) - step8: Factor the expression: \(\frac{2\times 3^{6}}{3^{3}}\) - step9: Reduce the fraction: \(2\times 3^{3}\) - step10: Evaluate the power: \(2\times 27\) - step11: Multiply: \(54\) Let's solve each part step by step. ### 33. Simplify: (a) \( -\frac{1}{9} \cdot\left(-\frac{7}{3}\right) \) To simplify this expression: 1. Multiply the fractions: \[ -\frac{1}{9} \cdot -\frac{7}{3} = \frac{1 \cdot 7}{9 \cdot 3} = \frac{7}{27} \] So, the simplified result is \( \frac{7}{27} \). (b) \( \frac{16}{13}+\left(-\frac{4}{65}\right) \) To simplify this expression: 1. Convert \( -\frac{4}{65} \) to a common denominator with \( \frac{16}{13} \): \[ \frac{16}{13} = \frac{16 \cdot 5}{13 \cdot 5} = \frac{80}{65} \] 2. Now add: \[ \frac{80}{65} - \frac{4}{65} = \frac{80 - 4}{65} = \frac{76}{65} \] So, the simplified result is \( \frac{76}{65} \). ### 34. How many times must a wheel of radius \( r \) cm rotate to cover 352 m? 1. First, convert 352 m to cm: \[ 352 \text{ m} = 352 \times 100 = 35200 \text{ cm} \] 2. The circumference \( C \) of the wheel is given by: \[ C = 2\pi r \] 3. The number of rotations \( N \) is: \[ N = \frac{35200}{2\pi r} \] So, the number of rotations is \( \frac{17600}{\pi r} \). ### 35. Simplify and find the value if \( a=-1 \) and \( b=2 \): \[ 3 a b - 2 b - 5 a - 2(5 a - 7 a b) - 30 \] 1. Substitute \( a \) and \( b \): \[ 3(-1)(2) - 2(2) - 5(-1) - 2(5(-1) - 7(-1)(2)) - 30 \] 2. Calculate each term: \[ = -6 - 4 + 5 - 2(-5 + 14) - 30 \] \[ = -6 - 4 + 5 - 2(9) - 30 \] \[ = -6 - 4 + 5 - 18 - 30 \] \[ = -53 \] So, the final value is \( -53 \). ### 36. Percentage of decrease in illiterate persons: 1. Initial number: 150 lakhs, Final number: 100 lakhs. 2. Percentage decrease: \[ \text{Percentage Decrease} = \frac{150 - 100}{150} \times 100 = \frac{50}{150} \times 100 = \frac{100}{3} \approx 33.33\% \] So, the percentage of decrease is \( \frac{100}{3} \) or approximately \( 33.33\% \). ### 38. Simplify: \[ \frac{\left(2^{4}\right)^{2} \times 9^{3} \times 4 \times 1^{9}}{2^{3} \times 8^{2} \times 27 \times 1^{5}} \] 1. Simplify the numerator: \[ (2^4)^2 = 2^8, \quad 9^3 = (3^2)^3 = 3^6, \quad 4 = 2^2, \quad 1^9 = 1 \] So, the numerator becomes: \[ 2^8 \times 3^6 \times 2^2 = 2^{10} \times 3^6 \] 2. Simplify the denominator: \[ 2^3 \times 8^2 = 2^3 \times (2^3)^2 = 2^3 \times 2^6 = 2^9, \quad 27 = 3^3, \quad 1^5 = 1 \] So, the denominator becomes: \[ 2^9 \times 3^3 \] 3. Now, simplify the entire fraction: \[ \frac{2^{10} \times 3^6}{2^9 \times 3^3} = 2^{10-9} \times 3^{6-3} = 2^1 \times 3^3 = 2 \times 27 = 54 \] So, the simplified result is \( 54 \). ### 40. Kamal's selling price after a loss of \( 15\% \): 1. Calculate the loss: \[ \text{Loss} = 0.15 \times 275 = 41.25 \] 2. Selling price: \[ \text{Selling Price} = 275 - 41.25 = 233.75 \] So, Kamal sells the book for \( 233.75 \).