Simplification and Approximation

158% of 3943 ≈ 1.58 × 3943 ≈ 6230. So 6230 + ? = 8653 - 2051 = 6602. Therefore ? = 6602 - 6230 = 372 ≈ 370.

77.65 × 981.73 ≈ 76250. 8478.73 - 4241.68 = 4237.05. Therefore ? = 76250 - 4237.05 ≈ 72013. Option A (72360) is the closest approximation among the choices.

Solve left to right: 1111 ÷ 37 = 30.027... Multiply by 49: 30.027 × 49 = 1471.323. Divide by 24: 1471.323 ÷ 24 = 61.3. The closest answer is 60 (option E). Option D (65) is farther away.

Approximate: 19.99% of 5001 ≈ 20% of 5000 = 1000. 50.41% of 2498 ≈ 50% of 2500 = 1250. Then 1000 - 1250 = -250. Among the options, -245 is closest to this approximation. Option B is correct as the best approximate answer.

Calculate 30.5% of 3050 = 0.305 × 3050 = 930.25. Then divide by 0.1: 930.25 ÷ 0.1 = 9302.5. The approximate value closest to 9302.5 is 9300 (option C). Dividing by 0.1 is equivalent to multiplying by 10, which is the key operation here.

First calculate 39.8% of 500 ≈ 40% of 500 = 200. Let x be the unknown percentage. Then 200 + (x/100) × 450 = 430. So (x/100) × 450 = 230, which means x = (230 × 100)/450 = 51.11...%. The approximate value is 50% (option B). This is a percentage calculation problem requiring algebraic setup.

Calculate (9.115)² ≈ 83.1. Then 83.1 + 80.951 ≈ 164.05. The right side is 131.001 + 10.995 ≈ 142. So we have 164.05 - ? = 142, which means ? = 164.05 - 142 = 22.05. Approximating gives ? ≈ 20 (option A). This is a simplification problem involving squares and basic arithmetic.

Simplify: 42.07 × 7.998 ≈ 42 × 8 = 336. Since 20² = 400, we have (?)² = 400 - 336 = 64. Taking the square root gives ? = 8. Option E is correct.

Calculate using approximations: 820.15 + 2379.85 ≈ 3200 (exact). 140.01 × 4.99 ≈ 140 × 5 = 700. Total ≈ 3200 + 700 = 3900. The question asks for approximate value, so rounding the multiplication gives the answer quickly.

Approximate: 469.991 ≈ 470 and 32.435 ≈ 32.4, so 470 × 32.4 ≈ 15,228. Adding 269 gives ~15,497, which rounds to 15,514. The other options represent common approximation mistakes (e.g., using 32 instead of 32.4, or off-by-one rounding).

Approximate: 44% ≈ 44%, 550 ≈ 550, 25% ≈ 25%, 131 ≈ 130. Calculate: 44% of 550 = 0.44 × 550 = 242, and 25% of 130 = 0.25 × 130 = 32.5. Then 242 + 32.5 = 274.5 ≈ 275. This makes option D correct.

Round 4018.19 ≈ 4000 and 3.87 ≈ 4. Then: 4000 ÷ 4 = 1000. Now: 1000 - 741 = 259. Among options, 300 is closest (approximately 259 is closer to 300 than to 270). The question asks for approximate value, and 300 is the best choice among given options.

30% of 695 = 10% of x. This means 0.30 × 695 = 0.10 × x, or 3 × 695 = x. Using approximation: 3 × 700 = 2100. The exact calculation: 3 × 695 = 2085, which is closest to 2100 among the options.

Round the numbers: 1548.45 ≈ 1550 and 15.058 ≈ 15. First, 3065 ÷ 15 = 204.33 ≈ 204. Then, 1548.45 + 204.33 ≈ 1752.78 ≈ 1750. The closest option is 1750.

Approximating: (41)²+(8)²-(22)²=1681+64-484=1261≈1250. Option E (1250) is the closest approximation. Other options are too far from 1261.