Simplification and Approximation

Approximating: 54.123% of 345.947 ≈ 54% of 346 ≈ 187, 25.451% of 758.79 ≈ 25% of 759 ≈ 190, 32% of 88.7698 ≈ 32% of 89 ≈ 28. So 187 + 190 - 28 = 349, which rounds to 350. This tests percentage calculations with decimal numbers.

First calculate 69.89% of 870 ≈ 608 (0.6989 × 870). Then 39.8% of 85.80 ≈ 34.16. The equation becomes: 608 = ? - 34.16 - 72.98. Solving: ? = 608 + 34.16 + 72.98 = 715.14 ≈ 720. Option E (720) is the correct approximation. Set up the equation with the calculated values and solve for the unknown.

Calculate 18564.5 ÷ 18 ≈ 1031.36 and 172 × 15 = 2580. Sum = 3611.36. Taking square root gives ≈ 60.09. Thus ? ≈ 60. Option C is correct. Option A (78) is too high, B (44) too low, D (56) and E (52) are close but not as accurate as 60.

Calculate each percentage: 149% of 559 ≈ 834.91, 870% of 221 = 1922.7, 89% of 720 ≈ 640.8. Sum: 834.91 + 1922.7 - 640.8 ≈ 2116.61. Approximating to nearest option: 2110. Option A (2000) is too low. Option C (2510) is too high. Option D (2400) is too high. Option E (2850) is too high.

Approximate all decimals as 2: the expression becomes 2 ÷ 2 ÷ 2 × 2 ÷ 2 ÷ 2. Working left to right: (2÷2)=1, then 1÷2=0.5, then 0.5×2=1, then 1÷2=0.5, then 0.5÷2=0.25. The key is maintaining order of operations and recognizing that consecutive divisions and multiplications cancel out strategically.

Following order of operations: 256.5 × 54 = 13851, then 13851 ÷ 81 ≈ 171, then 171 + 72 = 243, finally 243 ÷ 89.89 ≈ 2.703. The approximation to one decimal place gives 2.7. The key is working left to right with multiplication and division before addition, then approximating the final division.

Let x% be the unknown. x% of 415.8 + 39.0625 = x% of 550.2. x/100 × (550.2 - 415.8) = 39.0625. x/100 × 134.4 ≈ 39.0625. x ≈ 39.0625 × 100/134.4 ≈ 29.06. Option E (30) is closest. This makes sense as a percentage-based allocation problem.

Calculate step by step: 87 × 129 = 11223, then 11223 ÷ 15 = 748.2. 12.5% of 1378 = 172.25. So the equation becomes 748.2 = ?² + 172.25. Therefore ?² = 748.2 - 172.25 = 575.95, and ? = √575.95 ≈ 24. Answer D is correct.

Calculate 79% of 488 ≈ 386, and 129% of 248 ≈ 320. So LHS ≈ 386 - 320 = 66. The equation becomes 66 = ?² - 10.2², which means 66 = ?² - 104, so ?² = 170, and ? ≈ 13. Answer C (13) is correct.

?³ = 100008 + 3700 + 800 = 104508. The cube root of 104508 is approximately 47.2, since 47³ = 103823. Checking: 47³ = 103823, 48³ = 110592. 47 is closest. Answer C is correct.

Using approximation: 2795 ÷ 215 ≈ 13.01, then 13.01 × 31.24 ≈ 406.4, finally 406.4 + 21.543 ≈ 428. Rounding throughout: 2800 ÷ 215 ≈ 13, 13 × 31 ≈ 403, 403 + 22 ≈ 425. Option E (425) is the closest approximation.

Calculate: 145% of 1280 - 89% of 1870 = ?% of 1729. First, 145% of 1280 = 1.45 x 1280 = 1856. Then, 89% of 1870 = 0.89 x 1870 = 1664.3. Now, 1856 - 1664.3 = 191.7. So, 191.7 = ?% of 1729. Therefore, ?% = 191.7 / 1729 x 100 = 11.09%. The closest answer is 10%. The small difference is due to rounding in calculations.

Calculate each product: 192 × 73 = 14016 and 155 × 44 = 6820. Subtract: 14016 - 6820 = 7196. Since ?² = 7196, we find ? = √7196 ≈ 84.8, which rounds to approximately 85.

Using approximate values: 131.8% of 924 ≈ 132% of 924 = 1.32 × 924 ≈ 1219.68. 71.07% of 645 ≈ 71% of 645 = 0.71 × 645 ≈ 457.95. The difference is 1219.68 - 457.95 ≈ 761.73. Now find what percentage this is of 750: (761.73 / 750) × 100 ≈ 101.56%, which rounds to approximately 102%.

Calculate: 3968 ÷ 6985 × 100 = 56.79%, which rounds to approximately 57%. Among the options, 55% is the closest to 57%. The question asks for the approximate value, so 55% is the correct choice. Option A (55%) is approximately correct while option B (60%) is farther from the actual value.