What are the answers to Questions 18, 19, and 20 regarding square tiles, number patterns, and reciprocals?

Step 1: Solve Question 18. The floor of a room was covered by 2916 square tiles. This means the area of the floor is 2916 square tiles. Since it's a square floor, the number of tiles along each side is the square root of the total number of tiles. Number of tiles per side = sqrt(2916) To find the square root of 2916: We can estimate: 50^2 = 2500 and 60^2 = 3600. So the answer is between 50 and 60. The last digit of 2916 is 6, so the square root must end in 4 or 6. Let's try 54^2: 54 × 54 = 2916 So, there were 54 square tiles along each side of the floor. The final answer is A. 54. Step 2: Solve Question 19. The given number pattern is 5, 11, 23, 47, 95, Let's find the difference between consecutive terms: 11 - 5 = 6 23 - 11 = 12 47 - 23 = 24 95 - 47 = 48 The differences are 6, 12, 24, 48. This sequence of differences is doubling each time (6 × 2 = 12, 12 × 2 = 24, 24 × 2 = 48). The next difference should be 48 × 2 = 96. To find the next number in the pattern, add this difference to the last term: 95 + 96 = 191 The next number in the pattern is 191. The final answer is D. 191. Step 3: Solve Question 20. We need to write the reciprocal of 2(2)/(5). First, convert the mixed number to an improper fraction: 2(2)/(5) = ((2 × 5) + 2)/(5) = (10 + 2)/(5) = (12)/(5) The reciprocal of a fraction is obtained by inverting the numerator and the denominator. The reciprocal of (12)/(5) is (5)/(12). The final answer is D. (5)/(12). Step 4: Solve Question 21. Hassan bought 5(5)/(7) kg of meat and Abdan bought 4(1)/(4) kg of meat. To find the total fraction of meat they bought altogether, add the two amounts: 5(5)/(7) + 4(1)/(4) Add the whole numbers and the fractions separately: 5 + 4 = 9 Now add the fractions: (5)/(7) + (1)/(4) Find a common denominator for 7 and 4, which is 28. (5)/(7) = (5 × 4)/(7 × 4) = (20)/(28) (1)/(4) = (1 × 7)/(4 × 7) = (7)/(28) Now add the converted fractions: (20)/(28) + (7)/(28) = (20 + 7)/(28) = (27)/(28) Combine the whole number and the fraction: 9 + (27)/(28) = 9(27)/(28) The total amount of meat bought is 9(27)/(28) kg. Looking at the options, none of them exactly match 9(27)/(28). Let's recheck the calculation. The options are given as improper fractions or mixed numbers with different denominators. Let's convert 9(27)/(28) to an improper fraction: 9(27)/(28) = ((9 × 28) + 27)/(28) = (252 + 27)/(28) = (279)/(28) Let's check the options provided. Option B is 9(1)/(21). This is ((9 × 21) + 1)/(21) = (189+1)/(21) = (190)/(21). Option D is 9(6)/(10). This is 9(3)/(5) = ((9 × 5) + 3)/(5) = (45+3)/(5) = (48)/(5). Option A is 10(21)/(22). Option C is 10(1)/(21). It seems there might be a slight discrepancy in the options or the question's intended answer. However, based on the calculation, 9(27)/(28) is the correct sum. Let's re-examine the options and the question. The question asks "What fraction of meat did they buy altogether?". If we assume a typo in the options and that 9(27)/(28) should be an option, then that would be the answer. Let's check if any option is close or if there's a common mistake. 9(27)/(28) is very close to 10. Let's check the options again. A. 10(21)/(22) B. 9(1)/(21) C. 10(1)/(21) D. 9(6)/(10) None of the options match 9(27)/(28). Let's re-calculate to ensure no arithmetic error. 5(5)/(7) + 4(1)/(4) = (5+4) + ((5)/(7) + (1)/(4)) = 9 + ((20)/(28) + (7)/(28)) = 9 + (27)/(28) = 9(27)/(28). The calculation is correct. Given the multiple-choice format, there might be an error in the question's options. However, if forced to choose the closest option, 9(27)/(28) is approximately 9.96. 10(21)/(22) ≈ 10.95 9(1)/(21) ≈ 9.04 10(1)/(21) ≈ 10.04 9(6)/(10) = 9.6 None of the options are particularly close to 9.96. Let's assume there was a typo in the question and one of the fractions was different. If the question was 5(5)/(7) + 4(1)/(7) = 9(6)/(7). If the question was 5(5)/(7) + 4(1)/(21) = 9 + (15)/(21) + (1)/(21) = 9(16)/(21). Given the options, it's possible there's a mistake in the question or options. However, I must provide an answer from the given options. Let's re-evaluate the problem and options. The sum is 9(27)/(28). Let's check if any option is a simplified form or an equivalent fraction. No. Let's consider if the question meant something else, e.g., multiplication, but it clearly says "altogether". Since I must choose an option, and my calculation is 9(27)/(28), which is not an option, I will state that the calculated answer is not among the options. However, as per instructions, I must select an option. This implies there's an error in the question or options. Let's assume the question intended for a result that simplifies to one of the options. If the answer was 10(1)/(21), it would mean the sum was 10 + (1)/(21) = (210+1)/(21) = (211)/(21). If the answer was 9(1)/(21), it would mean the sum was 9 + (1)/(21) = (189+1)/(21) = (190)/(21). Let's re-read the question carefully. "What fraction of meat did they buy altogether?" The calculation 9(27)/(28) is correct. Given the constraint to select an option, and the fact that 9(27)/(28) is very close to 10, let's consider the options that are close to 10. 10(21)/(22) is approximately 10.95. 10(1)/(21) is approximately 10.04. 9(27)/(28) ≈ 9.964. 10(1)/(21) is the closest option to 9(27)/(28) if we round 9(27)/(28) up to 10 and then consider fractions. This is a problematic question due to the options. I will state the correct calculation and then choose the closest option, noting the discrepancy. The sum is 9(27)/(28). This is not directly available in the options. However, if we consider the options, 10(1)/(21) is approximately 10.047, and 9(27)/(28) is approximately 9.964. These are quite close. It's possible there was a rounding or simplification error in the question's options. Given the options, and the fact that 9(27)/(28) is very close to 10, option C (10(1)/(21)) is the closest value among the options that are greater than 9. Let's assume there was a slight error in the question or options and choose the closest one. The difference between 10(1)/(21) and 9(27)/(28) is 10(1)/(21) - 9(27)/(28) = (211)/(21) - (279)/(28) = (211 × 4 - 279 × 3)/(84) = (844 - 837)/(84) = (7)/(84) = (1)/(12). The difference between 9(27)/(28) and $9121