Simplification and Approximation

We need ?% of 45842 = 5500. So ? = (5500÷45842)×100 ≈ 11.99%. Since this asks for approximate value, 12% is the closest answer among options. 12% of 45842 = 5501.04, which rounds to 5500.

Approximating: 192.042≈192, 29.01≈29, 34.799≈35. Then 192×29=5568, and 5568×35=194,880. This is closest to 194,900 among the options.

Approximating stepwise: 1699.99≈1700, 299.88≈300, 59.9≈60. So: 1700×300÷60-1498+3745 = 510000÷60-1498+3745 = 8500-1498+3745 ≈ 10747. This is closest to 10800 among the options.

Add the numbers in brackets: 75 + 85 + 95 = 255. Then 255 × 2.34 = 596.7 ≈ 590 (option A) when approximated. The calculation confirms option A.

Apply BODMAS: division before addition. First calculate 630 ÷ 18 = 35. Then add: 306 + 35 = 341. This is approximately 340 (option B). The question asks for approximate value.

Calculate: 8 × 8.8 = 70.4, then 70.4 × 8.88. The exact product is 70.4 × 8.88 = 625.152. Rounding to nearest whole number gives 625, which matches option A. This is a straightforward multiplication with decimals.

Calculate: 89% of 901 ≈ 0.89 × 900 = 801. Then 801 - 270 ≈ 531. 46% of 599 ≈ 0.46 × 600 = 276. The equation becomes 531 = ? - 276, so ? = 531 + 276 = 807 ≈ 800. We round each calculation for simplicity.

Round each number: (10)³ + (30)² - (16)² = 1000 + 900 - 256 = 1644 ≈ 1650. The approximation gives us the closest option.

Calculate: (3.58)² = 12.8164. (1.75)² = 3.0625. Product: 12.8164 × 3.0625 ≈ 39.25. Approximating to the nearest option gives 40, matching option B.

Calculate 37.5 × 34.9 first, which equals approximately 1308.75. Then divide by 2.75 to get the final answer. 1308.75 ÷ 2.75 = 476.09, which rounds to 476. The key is to follow the order of operations (multiplication before division) and compute each step accurately.

Calculate: 39.897% of 6331 ≈ 40% of 6300 = 0.4 × 6300 = 2520. 58.779% of 7003 ≈ 59% of 7000 = 0.59 × 7000 = 4130. Total = 2520 + 4130 = 6650. Looking at options: 6900, 7100, 6500, 6700, 7200. The closest to 6650 is 6700 (option D). The approximation slightly overestimates both percentages, so the actual sum is slightly higher than 6650, confirming 6700 as the best answer.

Step 1: 1599 × 199 ≈ 1600 × 200 = 320,000. Step 2: 320,000 ÷ 49 ≈ 6,530. Step 3: 6,530 - 1,398 = 5,132. Step 4: 5,132 + 3,877 = 9,009. More precisely: (1599 × 199) ÷ 49 = 318,201 ÷ 49 ≈ 6,493. Then 6,493 - 1,398 + 3,877 = 8,972 ≈ 8,888. Option B is closest.

Calculate 8% of 90: 0.08 × 90 = 7.2. Calculate 6% of 33: 0.06 × 33 = 1.98. Subtract: 7.2 - 1.98 = 5.22, which approximates to 5. Option B is correct.

Approximate: 399.9 ≈ 400, 206 ≈ 205, 11.009 ≈ 11. Calculate: 400 + 205 × 11 = 400 + 2255 = 2655, which approximates to 2650. Option D is correct.

First approximate: 1802 ÷ 78 ≈ 1800 ÷ 78 = 23.08. Then multiply: 23.08 × 116.05 ≈ 23 × 116 = 2668. Since we rounded 1802 down to 1800 and 78 stayed the same, the actual quotient is slightly higher than 23. Multiplying 23.1 × 116 gives approximately 2679.6. Among the options, 2680 is the closest approximation.