Simplification and Approximation

2371 ÷ 6 ≈ 395. 43 × 4.35 ≈ 43 × 4.35 = 187.05. Sum = 395 + 187 = 582. Closest approximation is 580. Using 4 1/3 instead of 4.35: 43 × 13/3 = 559/3 ≈ 186, 395 + 186 = 581.

240% of 5.6 = 2.4 × 5.6 = 13.44. 0.3% of 480 = 0.003 × 480 = 1.44. So 13.44 ÷ 1.44 ≈ 9.33. Approximating: 2.4 × 5.6 ≈ 13.4 and 0.003 × 480 = 1.44, giving 13.4 ÷ 1.44 ≈ 9.3. Option E (9) is closest.

Approximate: 8725 × 4 = 34,900. Then 34,900 ÷ 16 = 2,181.25. So 2,181.25 = ? + 821.44. Therefore ? = 2,181.25 - 821.44 ≈ 1,359.81 ≈ 1,360. The key is using approximations (8725 instead of 8724.997, 4 instead of 3.987, 16 instead of 16.009) to simplify mental calculation.

Convert all to base 5: 5^(3×2.21)×5^3.2×5^(2×3.11)=5^(6.63+3.2+6.22)=5^16.05. RHS: 125^13.02÷125^x=5^(3×13.92)÷5^(3x)=5^(41.76-3x). Equating: 16.05=41.76-3x, so 3x=25.71, x=8.57≈8.

Approximate: 18001 ÷ 91 ≈ 200. Then 200 × 29 = 5800. If ? × 19 = 5800, then ? = 5800 ÷ 19 ≈ 305, closest to 300. Option C is correct.

Approximating: 192 × 29 × 35 = 192 × 1015 ≈ 194,880. This is closest to 194,900. The approximation works because rounding 29.01 to 29 and 34.799 to 35 nearly balances out.

First compute 54435 ÷ 45 ≈ 1210 (since 45 × 1200 = 54000). Then 1210 × 7 = 8470. Finally, 8470 - 4065 = 4405. This is closest to 4400.

First calculate the multiplication: 164 × 27 = 4428. Then add to 3739: 3739 + 4428 = 8167. This rounds to approximately 8200, which matches option C.

Sum the numerator: 9321 + 5406 + 1001 = 15728. Sum the denominator: 498 + 929 + 660 = 2087. Divide: 15728 ÷ 2087 ≈ 7.54, which rounds to 7.5.

Calculate (0.01 × 0.1 × 0.001) + (0.2 × 0.001 × 0.2). First term: 0.01 × 0.1 = 0.001, then 0.001 × 0.001 = 0.000001. Second term: 0.2 × 0.001 = 0.0002, then 0.0002 × 0.2 = 0.00004. Adding: 0.000001 + 0.00004 = 0.000041, which rounds to 0.00004. Option E is correct.

First solve the numerator: 638 + 9709 = 10347, then 10347 - 216 = 10131. Now divide by 26: 10131 ÷ 26 = 389.65... which rounds to 390. Option E is correct. Options A (275), B (365), C (420), and D (300) are miscalculations - likely from errors in the addition/subtraction steps or incorrect division.

Approximate: 30% of 4530 ≈ 1359, 22% of 4600 ≈ 1012. So 1359 - 1012 = 347. Then 347 = ? + 126, so ? = 347 - 126 = 221. More precisely: 30% of 4530 = 0.3×4530 = 1359. 22% of 4600 = 0.22×4600 = 1012. 1359 - 1012 = 347. 347 - 126 = 221. The answer matches option B (221). The approximate values work because the original percentages (29.989% and 22.04%) are very close to 30% and 22% respectively.

Calculate: 67% of 801 ≈ 537, so 537 - 231 = 306. On the right side: ? - 23% of 789, where 23% of 789 ≈ 181. Setting up: 306 = ? - 181, giving ? = 487. The closest answer is 500 (option D), suggesting the approximation should yield ? ≈ 500.

Using approximations: 85% of 225 = 0.85 × 225 = 191.25 ≈ 191. 43.013 × 42.918 ≈ 43 × 43 = 1849. 40% of 149.965 = 0.4 × 149.965 ≈ 60. So: 191 + 1849 - 60 = 1980. This matches option B.

Calculate 9% of 486 = 0.09 x 486 = 43.74. Then calculate 5.5% of 124 = 0.055 x 124 = 6.82. Multiply these results: 43.74 x 6.82 = 298.3, which rounds to approximately 300. The answer A (300) is correct as it asks for the approximate value. The calculation tests your ability to compute percentages and multiply decimal numbers.