Simplification and Approximation

Calculate (150)^3 = 150 × 150 × 150 = 33,75,000 = 3.375 × 10^6. Dividing by 10^5 gives 3.375 × 10^6 ÷ 10^5 = 3.375 × 10^1 = 33.75 ≈ 34. Answer B is correct.

Approximate: 16.5% of 1399.21 ≈ 16.5% of 1400 = 0.165 × 1400 = 231. 114.78% of 1211 ≈ 115% of 1210 = 1.15 × 1210 = 1391.5. Total ≈ 231 + 1391.5 = 1622.5, which rounds to 1620 (option E).

Approximate: 79.935 ≈ 80, 17.001 ≈ 17. So 80 × 17 = 1360. Then 1360 - 15.005 ≈ 1360 - 15 = 1345. The approximation 1345 is closest to option E. The actual value would be slightly less than 1345 since we rounded 79.935 up to 80.

2/5 of 95 = (2 × 95)/5 = 38. 8.95² ≈ 9² = 81 (since we're approximating). 38 + 81 = 119. The exact calculation 38 + 80.1025 = 118.1025 confirms 119 is the best approximation.

Approximating: 865 × 39 = 33,735 and 73 × 14 = 1,022. The difference is 33,735 - 1,022 = 32,713, which rounds to approximately 32,700. This matches option C when considering reasonable approximation ranges.

14.998% of 691.999 ≈ 15% of 692. 15% of 692 = 0.15 × 692 = 103.8. Rounding gives approximately 104, which is closest to 103 among the options.

Round each number to the nearest integer: 0.49 ≈ 0.5, 1.998 ≈ 2, 6.98 ≈ 7. Then multiply: 0.5 × 2 × 7 = 7. This approximation gives us the closest answer among the options. Options like 14, 28, 35 would be the result if we multiplied incorrectly, while 1 is far too small.

Perform sequential division from left to right. First: 628.905 ÷ 9.003 ≈ 69.9 (since 629 ÷ 9 ≈ 69.9). Then: 69.9 ÷ 14.01 ≈ 4.99, which rounds to approximately 5. Option A (40) would result from multiplying instead of dividing, B (50) and C (10) are incorrect calculations, and E (140) is far too large.

Approximate: (60)^2 - (9)^2 - (16)^2 = 3600 - 81 - 256 = 3263. Option A (3260) is closest. The actual with 59.99^2 - 8.9^2 - 15.9^2 is approximately 3598.8 - 79.21 - 252.81 = 3266.78, still closest to 3260.

786% of 345 equals 7.86 × 345 ≈ 2712. Subtract 784 from this result to get approximately 1928, which rounds to 1930. The word 'approximate' signals we need the closest option.

Square 65.4734 to get approximately 4287. Divide this by 6 to find the missing value, which gives approximately 714.5, rounding to 710. The word 'approximate' indicates we need the closest option.

Approximating: (36.79)^2 ≈ 37^2 = 1369 and (24.999)^2 ≈ 25^2 = 625. So 1369 - 625 = 744. Then 744 = ? - 876.95, which means ? = 744 + 877 ≈ 1621. The closest option is 1620.

Approximating: 8765 ÷ 22.5 × 20 ≈ 389.6 × 20 = 7792. The closest answer is 7790. The calculation follows order of operations: divide first, then multiply.

Following order of operations: 4992.25 ÷ 125 ≈ 39.94. Then 5866.275 + 39.94 ≈ 5906.2. The closest option is 5900. Remember to divide before adding.

Approximating: 89 × 156 ≈ 13884. Then ? = 13884 - 16 = 13868. This matches option B exactly. Round to whole numbers and subtract the constant.