Simplification and Approximation

5248 ÷ 4 ÷ 7 = 5248 ÷ (4 × 7) = 5248 ÷ 28 = 187.43. Approximating: 5248 ≈ 5250, so 5250 ÷ 28 ≈ 187.5. Among options, 190 is closest.

886% of 333 ≈ 8.86 × 333 ≈ 2950. Adding 1230 gives approximately 4180. This matches option E.

Left side: 1111 × 111 × 11 - 221000 = 1234321 - 221000 = 1013321. Right side: ? - 478000. So ? = 1013321 + 478000 = 1491321, closest to 1478000. The question asks for approximate value.

Approximate: 59.99% ≈ 60%, 22.98% ≈ 23%. Calculate 60% of 155 = 0.60 × 155 = 93, and 23% of 72 ≈ 0.23 × 72 = 16.56. Adding: 93 + 16.56 ≈ 109.56, which rounds to 110. The approximation method saves time on complex calculations.

Calculate stepwise: 35² = 1225. Then 1225 ÷ 274 ≈ 4.47. Then 4.47 × 5.5 ≈ 24.6. Approximating to nearest option gives 25. Option B is correct for approximate value.

This approximation problem asks for (4.0123)³ + (29.997)². Round to: 4³ + 30² = 64 + 900 = 964. The actual values are very close: 4.0123³ ≈ 64.6 and 29.997² ≈ 899.8, sum ≈ 964.4. Option A (1025) is too high. Options C, D, and E are too low or don't match the calculation.

Using exponent rule: 8^1.38 × 8^1.62 = 8^(1.38+1.62) = 8^3 = 512. When multiplying powers with the same base, add the exponents. 8³ = 512.

First calculate 88.25% of 450: 88.25/100 × 450 = 0.8825 × 450 ≈ 0.88 × 450 = 396. Now find what percent 396 is of 530: 396/530 × 100 ≈ 396/5.3 ≈ 74.7%. Approximating: 0.88 × 450 = 396, then 396/530 × 100 = 39600/530 ≈ 75%. Option C is 75%, which is the closest approximation. The calculation shows 75% of 530 = 397.5, very close to 396.

Calculate: 79.7 + 89.6 + 99.5 = 268.8. Approximating to nearest ten: 270. Option C is correct. This is straightforward addition with approximation.

Calculate: 39.4 - 49.7 = -10.3. Then 77 × 99 = 7623. Add: 7623 - 10.3 = 7612.7 ≈ 7600. Option A is correct. The multiplication dominates, so the answer is close to 7600.

Round 459.88 ≈ 460 and 143.02 ≈ 143. Calculate 117% of 460 = 1.17 × 460 = 538.2. Calculate 162% of 143 = 1.62 × 143 = 231.66. Subtract: 538.2 - 231.66 = 306.54 ≈ 306. Option D matches.

Calculate each term approximately: 349% of 609 ≈ 3.5 × 609 ≈ 2131.5, and 67.8% of 1007 ≈ 0.68 × 1007 ≈ 684.76. Adding: 2131.5 + 684.76 ≈ 2816.26. The closest option is 2800. Note that 349% ≈ 3.5 (not 3.49) and 67.8% ≈ 0.68 for quick approximation.

Calculate each part: 16.78% of 1667 ≈ 0.1678 × 1667 ≈ 279.7 (approximately 280). For the division: 31.013 ÷ 9.97 ≈ 31 ÷ 10 ≈ 3.1. So the expression becomes 280 - 3.1 ≈ 276.9. The closest option is 275. The approximation slightly overestimates the first term, making 275 the better choice than 280.

7.34% of 883 ≈ 7% of 883 = 61.81 (or 7.34 × 8.83 ≈ 64.8). 12.51% of 186 ≈ 12.5% of 186 = 23.25 (or 12.5 × 1.86 = 23.25). Difference = 64.8 - 23.25 ≈ 41.55, closest to 40 (option D). The question asks for approximate value, so rounding is expected.

928 ÷ 32 ≈ 928 ÷ 32 = 29 exactly. Options A-D are far off (21, 16, 38, 35). This is straightforward division.