1. Write in words 1101001. 1101001 in words is "one million, one hundred and one thousand, and one". 2. Write in figures one million, one hundred thousand and eleven. One million, one hundred thousand and eleven in figures is 1100011. 3. What is the place value of 8 in the number: 83641400? The digit 8 is in the ten millions place. So, place value of 8 = $8 \times 10^7 = 80000000$. 4. Work out 54) 74136 (i.e., 74136 ÷ 54). Divide 74136 by 54: $54 \times 1373 = 74142$, which is too high. Checking $54 \times 1372 = 74136$ exactly. So, quotient = 1372. 5. What is the total value of the underlined digit? 848637. Assuming digit "8" in tens place is underlined (the second digit from left), the value is: $8 \times 10000 = 80000$. 6. Round off 919 to the nearest 1000. 919 is closer to 1000 than 0, so rounded value is 1000. 7. Which is the number just before 49000? The number just before 49000 is 48999. 8. Eight wildlife club members planted 5 trees each per day. How many trees did they plant in 4 days? Total trees = number of members × trees per member per day × days = $8 \times 5 \times 4 = 160$ trees. 9. Find the square root of 1296 using prime factorization method. Prime factorization of 1296: $1296 = 2^4 \times 3^4$ Square root = $2^{4/2} \times 3^{4/2} = 2^2 \times 3^2 = 4 \times 9 = 36$. 10. Round off 9919 to the nearest 100. 9919 rounded to nearest 100 is 9900. 11. Work out 700000 - 111. $700000 - 111 = 699889$. 12. Work out 3019 × 23. Multiplying: $3019 \times 23 = 3019 \times (20 + 3) = 3019 \times 20 + 3019 \times 3 = 60380 + 9057 = 69437$. 13. Work out 8233 ÷ 26. Divide 8233 by 26: $26 \times 316 = 8216$, remainder 17. So, quotient = 316 remainder 17, or 316.65 approx. 14. Find the G.C.D. of 28, 42 and 56. Prime factors: 28 = $2^2 \times 7$, 42 = $2 \times 3 \times 7$, 56 = $2^3 \times 7$. Common factors under minimum powers: $2^1 \times 7 = 14$. So, G.C.D. = 14. 15. Arrange the following fractions from the smallest to the largest: 4/6, 3/5, 7/12. Convert to decimals: 4/6 = 0.6667, 3/5 = 0.6, 7/12 = 0.5833. Order: 7/12 < 3/5 < 4/6. 16. Work out 8 1/3 - 1 5/10. Convert mixed numbers to improper fractions: $8 \frac{1}{3} = \frac{25}{3}$, $1 \frac{5}{10} = 1 \frac{1}{2} = \frac{3}{2}$. Find common denominator 6: $\frac{25}{3} = \frac{50}{6}$, $\frac{3}{2} = \frac{9}{6}$. Subtract: $\frac{50}{6} - \frac{9}{6} = \frac{41}{6} = 6 \frac{5}{6}$. 17. Work out 8 - 2 4/9. Convert mixed number: $2 \frac{4}{9} = \frac{22}{9}$. Convert 8 to fraction: $8 = \frac{72}{9}$. Subtract: $\frac{72}{9} - \frac{22}{9} = \frac{50}{9} = 5 \frac{5}{9}$. 18. Change 2565 cm into metres. $2565 \text{ cm} = \frac{2565}{100} = 25.65$ metres. 19. Change ½ m into cm. $\frac{1}{2} \text{ m} = 0.5 \times 100 = 50$ cm. 20. Work out (22 km 520 m 49 cm) - (19 km 849 m 66 cm). Convert all to cm: 22 km = 2,200,000 cm, 520 m = 52,000 cm, Total = 2,200,000 + 52,000 + 49 = 2,252,049 cm. Similarly, 19 km = 1,900,000 cm, 849 m = 84,900 cm, Total = 1,900,000 + 84,900 + 66 = 1,984,966 cm. Subtract: $2,252,049 - 1,984,966 = 267,083$ cm. Convert back: $267,083 \text{ cm} = 2 \text{ km } 670 \text{ m } 83 \text{ cm}$. 21. Find the area of the right-angled triangle with base 8m and height 3m. Area = $\frac{1}{2} \times base \times height = \frac{1}{2} \times 8 \times 3 = 12$ sqm. 22. Find the length of the side marked x in a rectangle with area 91 cm2 and length 7 cm. Area = length × width, So width = area ÷ length = $\frac{91}{7} = 13$ cm. 22 (second). Write 3.125 as a mixed number. 3.125 = $3 + 0.125 = 3 + \frac{1}{8} = 3 \frac{1}{8}$. 23. Convert 0.375 into a fraction. $0.375 = \frac{375}{1000} = \frac{3}{8}$ after simplification. 24. Work out 4.3 - 2.562. Subtract: $4.3 - 2.562 = 1.738$. 25. Add 0.12 + 2.001 + 32.301. Sum = $0.12 + 2.001 + 32.301 = 34.422$. 26. Change 7/8 into a decimal. $\frac{7}{8} = 0.875$. 27. Work out 136 × 0.015. $136 \times 0.015 = 2.04$. 28. What is the am/pm time for one and quarter hours before 1:00 noon? One hour 15 minutes before 1:00 pm is 11:45 am. 28 (second). Change 3 ¼ hrs into minutes. $3 \frac{1}{4} = 3.25$ hrs = $3.25 \times 60 = 195$ minutes. 29. Divide 19h 30min by 6. Convert to minutes: $19 \times 60 + 30 = 1170$ minutes. Divide by 6: $1170 \div 6 = 195$ minutes = 3h 15min. 30. Collect the like terms 15p + 2t + p + 17t. Collect p terms: $15p + p = 16p$, Collect t terms: $2t + 17t = 19t$. Sum: $16p + 19t$. 31. Work out 15b + 3b - 12b - 2b. Sum coefficients: $15 + 3 -12 -2 = 4$. Result: $4b$. 32. Solve the equation 17n - 16n - 10 = 7. Simplify: $17n -16n = n$. So: $n -10 = 7$ $n = 17$. 33. Calculate the size angle marked y in triangle with angles 21°, y°, and 140°. Sum of angles in triangle = 180°. So: $21 + 140 + y = 180$. Calculate y: $y = 180 - 161 = 19°$. 34. How many ½ kg kilograms are there in 35 kg? Number of halves in 35 = $35 \div \frac{1}{2} = 35 \times 2 = 70$. 35. Change 4000 ml into litres. $4000 \text{ ml} = \frac{4000}{1000} = 4$ litres. 36. What number is three thousand more than four million, six hundred thousand in symbols? $4600000 + 3000 = 4603000$. 37. Round off 980931 to the nearest 1000. $980931 \approx 981000$. 38. What is the area of a square whose sides are 24 m? Area = $24^2 = 576$ sqm. 39. What is the sum of the square of 42 and 58? Calculate: $42^2 + 58 = 1764 + 58 = 1822$. 40. Collect like terms and add 14v + 3w + v + 12w. $v$ terms: $14v + v = 15v$, $w$ terms: $3w + 12w = 15w$. Sum: $15v + 15w$. 41. Three bells ring at intervals of 15 min, 20 min, and 25 min respectively. If the bells are set at the same time, how long will it take them to ring together? Find LCM of 15, 20, 25. Prime factors: 15 = 3 × 5, 20 = 2^2 × 5, 25 = 5^2. LCM = $2^2 \times 3 \times 5^2 = 4 \times 3 \times 25 = 300$ minutes = 5 hours. 42. Find the G.C.D. of 21, 63, and 84. Prime factors: 21 = 3 × 7, 63 = 3^2 × 7, 84 = 2^2 × 3 × 7. Common factors: 3 × 7 = 21. Additional problems: - Volume of rectangular prism with dimensions 5 cm, 4 cm, and 4 cm: Volume = $5 \times 4 \times 4 = 80$ cm³. - Angle X between 76° and 67°: Sum of known angles in a straight line = 180°. $X = 180 - (76 + 67) = 37°$. - Area of shaded triangle with base 30 cm and height 12 cm: Area = $\frac{1}{2} \times 30 \times 12 = 180$ cm². - Sum of XLVI + XV in Hindu Arabic numerals: XLVI = 46, XV = 15, Sum = 61. - Perimeter of Andrew's plot with length 75 m and width 68 m: Perimeter = $2 \times (75 + 68) = 2 \times 143 = 286$ m. - Adding 3 2/5 + 5 3/4: Convert to improper fractions: $3 \frac{2}{5} = \frac{17}{5}, 5 \frac{3}{4} = \frac{23}{4}$. Common denominator 20: $\frac{68}{20} + \frac{115}{20} = \frac{183}{20} = 9 \frac{3}{20}$. - Multiplying 14 × 5 2/7: Convert mixed number: $5 \frac{2}{7} = \frac{37}{7}$. Multiply: $14 \times \frac{37}{7} = 2 \times 37 = 74$. - Triangle ABC with angle ACB 90°, AB = 8 cm, AC = 5 cm: Find BC using Pythagoras: $BC = \sqrt{AB^2 - AC^2} = \sqrt{64-25} = \sqrt{39} \approx 6.24$ cm. Summary: All problems answered with complete working.