Question 1

Approximation and quick calculation: Evaluate (421 × 0.9) + (130 × 101) + 10000 and select the closest option.

Accepted Answer

Introduction / Context: This blends a small decimal scaling with an easy product and a large constant. Compute each piece separately, then sum. Option spacing (thousands) allows a quick precise pick without heavy computation. Given Data / Assumptions: 421 * 0.9 130 * 101 + 10000 Concept / Approach: Use 0.9 = 1 − 0.1 to scale down 421 quickly, multiply 130*101 using 130*(100+1), then add 10000. This keeps the arithmetic mental and exact to the unit place if desired. Step-by-Step Solution: 421 * 0.9 = 421 − 42.1 = 378.9 130 * 101 = 13000 + 130 = 13130 Sum = 378.9 + 13130 + 10000 = 23508.9 Closest option: 23500 Verification / Alternative check: Rounding 378.9 to 379 gives 23509; still nearest to 23500 compared to 24500 or 33500. Why Other Options Are Wrong: 33500 and 24500 deviate by thousands; 225000 is two orders of magnitude too large. Common Pitfalls: Multiplying 130*101 as 130*100 only and forgetting the additional 130; or treating 0.9 as 1.0 inadvertently, adding an extra ~42 to the sum. Final Answer: 23500

Question 2

Approximation and quick calculation: Evaluate 30.9 × 3000 − 10.1 × 1100 + 8298 − 4302 and choose the closest option.

Accepted Answer

Introduction / Context: The expression combines two scaled products and a net constant adjustment. Compute each product exactly, apply the subtraction, add the constants, and pick the nearest large-rounded option. Given Data / Assumptions: 30.9 * 3000 10.1 * 1100 + 8298 − 4302 Concept / Approach: Perform the clean multiples first, then the smaller net constant. Because options are in 5000 increments, exact arithmetic directly identifies the closest value. Step-by-Step Solution: 30.9 * 3000 = 92700 10.1 * 1100 = 11110 Difference so far = 92700 − 11110 = 81590 8298 − 4302 = 3996 Total = 81590 + 3996 = 85586 Closest option: 85000 Verification / Alternative check: Rounding constants slightly (e.g., 3996 ≈ 4000) gives 81590 + 4000 = 85590, still closest to 85000 versus 90000. Why Other Options Are Wrong: 80000 is 5586 low; 90000 is 4414 high; 105000 is far off. Common Pitfalls: Dropping a zero when multiplying by 3000 or 1100, which changes the result by orders of magnitude. Final Answer: 85000

Question 3

Approximation and quick calculation: Solve 56.001 × ? − 1000.999 = 231. Find the closest integer value of ?.

Accepted Answer

Introduction / Context: A single linear equation in one variable with coefficients near integers is ideal for quick isolation of the unknown. Since the options are integers, compute the value and select the nearest integer if needed. Given Data / Assumptions: 56.001 * ? − 1000.999 = 231 Find integer ? closest to the true value. Concept / Approach: Rearrange to ? = (231 + 1000.999) / 56.001. Note that the numerator is about 1231.999 and the denominator about 56, indicating a value near 22. Step-by-Step Solution: 231 + 1000.999 = 1231.999 ? ≈ 1231.999 / 56.001 ≈ 22.0 Nearest integer option: 22 Verification / Alternative check: Back-substitute 22: 56.001*22 − 1000.999 ≈ 1232.022 − 1000.999 ≈ 231.023, essentially exact within rounding, confirming the choice. Why Other Options Are Wrong: 45, 37, 16 produce results far from 231 when back-substituted due to the large multiplier 56.001. Common Pitfalls: Using 56 instead of 56.001 is fine here; but do not forget to add 1000.999 to 231 before dividing, or you will subtract incorrectly. Final Answer: 22

Question 4

Approximation and quick calculation: Evaluate 1010 ÷ 36 + (187 × 20.05) and select the closest option.

Accepted Answer

Introduction / Context: Blend a small division with a product near a clean multiple. The product dominates the sum, so compute it accurately and add the modest quotient to pick the nearest option among values in the 3700–3800s. Given Data / Assumptions: 1010 / 36 is roughly 28.06 187 * 20.05 ≈ 187*(20 + 0.05) Concept / Approach: Compute 187*20 quickly and add 187*0.05, then add the division result. Because options differ by tens, accuracy to within a few units is enough. Step-by-Step Solution: 187 * 20 = 3740 187 * 0.05 = 9.35 Product total = 3749.35 1010 / 36 ≈ 28.06 Sum ≈ 3749.35 + 28.06 ≈ 3777.41 Closest listed option: 3770 Verification / Alternative check: Exact computation yields about 3777.41; among 3650, 3770, 3825, 3800, the nearest is 3770 (distance ~7.4). Why Other Options Are Wrong: 3650 is too low; 3825 and 3800 are higher by 47–23 respectively; 3770 is closest. Common Pitfalls: Missing the 0.05 component (9.35), which would understate the sum and skew the choice downward. Final Answer: 3770

Question 5

Approximation and quick calculation: Evaluate (724 ÷ 25) × 31.05 + 101 and choose the closest option.

Accepted Answer

Introduction / Context: Convert the division by 25 to a multiplication by 4/100 for quicker mental math: dividing by 25 equals multiplying by 0.04. Then scale by 31.05 and add 101. Options are in the hundreds, so a tight estimate suffices. Given Data / Assumptions: (724 / 25) * 31.05 + 101 Concept / Approach: First compute 724/25 exactly as 28.96. Multiply by 31.05, then add 101 and pick the nearest hundred-level option. Step-by-Step Solution: 724 / 25 = 28.96 28.96 * 31.05 ≈ 899.208 Add 101 ⇒ total ≈ 1000.208 Nearest option: 1000 Verification / Alternative check: Even if 31.05 were rounded to 31, product 28.96*31 = 897.76; add 101 = 998.76 still closest to 1000. Why Other Options Are Wrong: 900 and 950 are too low; 1050 is too high. 1000 is closest to ~1000.21. Common Pitfalls: Approximating 724/25 as 29 without adjusting can push the result slightly higher, but the nearest option remains 1000. Final Answer: 1000

Question 6

Approximation and quick calculation: Evaluate 6.39 × 128.948 + (5.215 ÷ 12.189) + 25.056 and select the closest option.

Accepted Answer

Introduction / Context: The expression is dominated by the product 6.39*128.948. The division term is small (≈0.43), and the constant is modest. A careful product estimate plus the small add-ons will point clearly to the nearest option. Given Data / Assumptions: Main term: 6.39 * 128.948 Small term: 5.215 / 12.189 Constant: 25.056 Concept / Approach: Approximate 128.948 ≈ 129; 6.39*129 = 6.39*(130 − 1) = 830.7 − 6.39 = 824.31. Add the small division (~0.43) and the constant 25.056 to reach the final estimate near 850. Step-by-Step Solution: 6.39 * 128.948 ≈ 824.0–824.3 (tight range) 5.215 / 12.189 ≈ 0.43 Add constant 25.056 Total ≈ 824.2 + 0.43 + 25.056 ≈ 849.69 Nearest option: 850 Verification / Alternative check: Exact computation gives about 849.46, still nearest to 850 compared with 800, 900, or 950. Why Other Options Are Wrong: 800 is too low by ~49; 900 and 950 are too high. 850 is closest. Common Pitfalls: Ignoring the constant 25.056 or over-rounding 128.948 to 130 without subtracting the 6.39 correction. Final Answer: 850

Question 7

Approximation and quick calculation: Evaluate 1559.999 ÷ 24.001 + (11.005 × 6.999) and choose the closest option.

Accepted Answer

Introduction / Context: The sum combines a division near 65 with a product a little over 77. Keeping each term accurate to 0.5 is enough to choose among the options in the 130–150 range confidently. Given Data / Assumptions: Term1 ≈ 1559.999 / 24.001 Term2 ≈ 11.005 * 6.999 Concept / Approach: Approximate Term1 with 1560/24 = 65. Term2 is close to 11*7 = 77; small adjustments push it near 77.03. Sum around 142 confirms the nearest option. Step-by-Step Solution: Term1 ≈ 65.00 (very close) Term2 ≈ 11.005 * 6.999 ≈ 77.02 Sum ≈ 65.00 + 77.02 ≈ 142.02 Nearest option: 142 Verification / Alternative check: Exact calculation yields about 142.02, confirming 142 is the best choice relative to the other options. Why Other Options Are Wrong: 137 and 132 are too low; 152 is too high versus the tight sum around 142. Common Pitfalls: Over-rounding 1559.999/24.001 to 65 and then subtracting a large correction; the correction is tiny and does not change the nearest option. Final Answer: 142

Question 8

Approximation and quick calculation: Evaluate 3.2 × 8.1 + (3185 ÷ 4.95) and select the closest option.

Accepted Answer

Introduction / Context: The division term dominates. Approximating 4.95 as 5 gives a baseline, and a small upward correction (because the actual divisor is slightly less than 5) refines it enough to select the nearest ten-level option. Given Data / Assumptions: Main term: 3185 / 4.95 Small term: 3.2 * 8.1 Concept / Approach: First compute 3185/5 = 637. Then adjust upward because dividing by 4.95 (smaller divisor) yields a slightly larger quotient. Add the small product 3.2*8.1 ≈ 25.92 to reach the final estimate near 670. Step-by-Step Solution: 3.2 * 8.1 ≈ 25.92 3185 / 4.95 ≈ 643.43 (exactly is about 643.43) Total ≈ 643.43 + 25.92 ≈ 669.35 Nearest option: 670 Verification / Alternative check: Exact computation gives about 669.35; among the choices 660, 645, 690, the closest is 670 by less than 1. Why Other Options Are Wrong: 660 and 645 are too low; 690 is too high. 670 is nearly exact. Common Pitfalls: Forgetting to add the product term or using 3185/5 without the correction for the slightly smaller divisor 4.95. Final Answer: 670

Question 9

Approximation and quick calculation: Evaluate 1205 ÷ 2.5 and select the closest option.

Accepted Answer

Introduction / Context: Dividing by 2.5 is the same as multiplying by 10/25 = 2/5 and then by a factor of 2: a quick trick is to double the numerator and divide by 5. This keeps the arithmetic exact and mental-friendly. Given Data / Assumptions: Compute 1205 / 2.5 and choose the closest option. Concept / Approach: 2.5 = 5/2. So 1205 / 2.5 = 1205 / (5/2) = 1205 * (2/5) = (2410) / 5. This eliminates decimals and gives an exact integer result when divisible by 5. Step-by-Step Solution: Compute 1205 * 2 = 2410 2410 / 5 = 482 Exact value = 482; nearest provided choice = 480 Verification / Alternative check: Direct long division: 2.5 * 480 = 1200; remainder 5; 2.5 * 2 = 5; hence exact is 482. Since 482 is not listed, choose the nearest, 480. Why Other Options Are Wrong: 300 and 3000/4800 are far from the exact 482; 480 is the only close option. Common Pitfalls: Dividing by 25 or 2 instead of 2.5 or forgetting the multiply-by-2 step before dividing by 5. Final Answer: 480

Question 10

Approximation and quick calculation: Evaluate 22020 ÷ 0.011 and choose the closest option.

Accepted Answer

Introduction / Context: Dividing by a small decimal increases the value substantially. Recognize that 0.011 equals 11/1000; thus, the division turns into multiplication by 1000/11, producing a number near two million. Given Data / Assumptions: Compute 22020 / 0.011 and select the nearest option. Concept / Approach: 0.011 = 11/1000. So 22020 / 0.011 = 22020 * (1000/11) = (22020/11) * 1000. Now compute 22020 / 11 exactly, then scale by 1000. Step-by-Step Solution: 22020 / 11 = 2001 remainder 9 (i.e., 2001.818…) Value ≈ 2001.818… * 1000 ≈ 2,001,818.18 Nearest listed option: 2,000,000 Verification / Alternative check: Check scales: Dividing by 0.01 would give 2,202,000; since 0.011 is slightly larger, the result should be slightly less than 2.202 million. 2.002 million is consistent with that expectation, and the closest option is 2,000,000. Why Other Options Are Wrong: 20020 and 200002 are far too small; 200200 is still ~10 times smaller than the true magnitude. Common Pitfalls: Treating 0.011 as 0.11 or 0.001, which would shift the result by factors of 10 or 1000 and completely change the magnitude. Final Answer: 2000000

Question 11

Approximation with near-integers: Evaluate 4182.395 ÷ 20.886 and choose the closest value among the options (use sensible rounding/estimation where helpful).

Accepted Answer

Introduction / Context: This is a division-based approximation problem. The decimal numbers 4182.395 and 20.886 are close to round figures, so we can estimate quickly without a calculator. The goal is to convert to a simple mental-math division while keeping the ratio nearly the same. Given Data / Assumptions: Numerator = 4182.395 (close to 4182 or 4200) Denominator = 20.886 (close to 21) We must select the closest option to the exact quotient. Concept / Approach: When both numbers are near convenient round numbers, approximate each minimally so the ratio stays stable. Use 4182/20.9 or 4182/21 as quick proxies. Always sanity-check by multiplying a candidate answer by the divisor to see if we return near the dividend. Step-by-Step Solution: Use a tight rounding: 4182.395 ≈ 4182; 20.886 ≈ 20.9Compute 4182 ÷ 20.9 ≈ 200.1 (since 20.9 * 200 = 4180)Using the exact values gives about 200.25, still ≈ 200 Verification / Alternative check: Multiply 200 * 20.886 = 4177.2 (slightly low). Adding one more unit (201) gives ≈ 4198.9 (slightly high). The true answer lies near 200.2, so 200 is the closest choice. Why Other Options Are Wrong: 250: 250 * 20.886 ≈ 5221, far too large. 300: 300 * 20.886 ≈ 6266, much too large. 150: 150 * 20.886 ≈ 3133, too small. 180: 180 * 20.886 ≈ 3759, still low. Common Pitfalls: Over-rounding both numbers in the same direction can distort the ratio. Keep the rounding tight and check by back-multiplying the candidate answer. Final Answer: 200

Question 12

Approximation using complements: Compute 98743 ÷ 198 and express it as 800 − ?, then determine the missing value (closest option).

Accepted Answer

Introduction / Context: This problem reframes a division as a complement-to-800 calculation. By first approximating or computing 98743 ÷ 198, we can subtract the quotient from 800 to obtain the required missing amount. This is a common trick to make mental computation easier when the target figure is a round number like 800. Given Data / Assumptions: N = 98743 D = 198 We want 800 − (N ÷ D) Concept / Approach: Compute or estimate the quotient Q = N / D. Then the answer is 800 − Q. Because 198 is very close to 200, we can use 98743/200 as a quick ballpark and refine slightly since dividing by 198 gives a slightly larger quotient than dividing by 200. Step-by-Step Solution: Rough: 98743 ÷ 200 ≈ 493.7Since the real divisor (198) is smaller, the real quotient is slightly bigger, ≈ 499Exact computation gives about 498.70Therefore 800 − 498.70 ≈ 301.3 Verification / Alternative check: Use back-multiplication: if the answer were exactly 300, then the quotient would be 800 − 300 = 500. That is very close to 498.7, and 300 is the nearest given option to 301.3. Why Other Options Are Wrong: 200: Implies quotient 600, too high. 250: Implies quotient 550, too high. 350: Implies quotient 450, too low. 275: Implies quotient 525, still too high. Common Pitfalls: Forgetting that a smaller divisor (198 vs. 200) increases the quotient; also, rounding too coarsely can push the complement far away from the true value. Final Answer: 300

Question 13

Operate with very small decimals: Evaluate 0.0004 ÷ 0.0001 × 36.000009 and select the closest option.

Accepted Answer

Introduction / Context: When dividing tiny decimals, it often helps to scale both numbers by the same power of 10 to remove leading zeros. Here, 0.0004 ÷ 0.0001 is a clean ratio that dramatically simplifies the expression before multiplying by a number very close to 36. Given Data / Assumptions: a = 0.0004 b = 0.0001 c = 36.000009 (very close to 36) Concept / Approach: Compute the division first to reduce the expression. Since 0.0004 / 0.0001 = 4, the original expression becomes 4 × 36.000009. Multiplying by 4 is straightforward and keeps small rounding error contained. Step-by-Step Solution: 0.0004 ÷ 0.0001 = 44 × 36.000009 = 144.000036 Verification / Alternative check: Because 36.000009 is only 0.000009 more than 36, the product is only 0.000036 above 144. The nearest listed option to 144.000036 is 145 (the other choices differ by an order of magnitude or more). Why Other Options Are Wrong: 14.5, 1.45, 0.10: off by factors of 10 to 1000; they ignore the 4× scaling. 150: slightly larger than 144 by 6, not a close approximation here. Common Pitfalls: Misplacing decimal points when dividing small numbers; forgetting that 0.0004 is 4× 0.0001, not 40× or 0.4×. Final Answer: 145

Question 14

Solve for the unknown factor: 425 ÷ 16.95 × ? = 225. Find the value of ? (choose the closest integer from the list).

Accepted Answer

Introduction / Context: This is a straightforward equation involving division and multiplication. We must isolate the unknown factor ? by moving known quantities to the other side. Since the numbers are not extreme, the exact computation is simple and produces a value very close to an integer. Given Data / Assumptions: 425 ÷ 16.95 × ? = 225 All values are positive real numbers. Concept / Approach: Rearrange to solve for ?: ? = 225 × 16.95 / 425. This uses the rule that if A/B × x = C, then x = C × B / A. After that, pick the closest option (the result is essentially 9). Step-by-Step Solution: ? = 225 * 16.95 / 425Compute the numerator: 225 * 16.95 = 3813.75Divide by 425: 3813.75 / 425 ≈ 8.9735Round to the nearest integer: ≈ 9 Verification / Alternative check: Plug back: 425/16.95 ≈ 25.07; 25.07 × 9 ≈ 225.6 (very close to 225). Small rounding arises from decimal truncation; 9 is the best fit among options. Why Other Options Are Wrong: 11, 19: would overshoot the product significantly. 0.8, 8: yield totals far below 225. Common Pitfalls: Inverting the 425 and 16.95 incorrectly, or rounding too early before the final division, which can distort the choice selection. Final Answer: 9

Question 15

Evaluate mixed operations carefully: Compute 26.003 − (154.001 ÷ 6.995). Choose the nearest option.

Accepted Answer

Introduction / Context: This expression mixes subtraction and division. Per operation precedence, the division must be evaluated first, then subtracted from 26.003. Because the inputs are close to convenient values, estimates align well with the nearest integer result. Given Data / Assumptions: a = 26.003 b = 154.001 c = 6.995 Expression: a − (b / c) Concept / Approach: First compute b/c. Since 154/7 ≈ 22, we expect b/c to be about 22. Then subtract from a = 26.003 to get a result near 4. Small decimals will not change the nearest-integer choice. Step-by-Step Solution: Estimate: 154.001 ÷ 6.995 ≈ 22.01Compute a − (b / c) ≈ 26.003 − 22.01 ≈ 3.99Nearest integer option is 4 Verification / Alternative check: Using tighter computation gives about 3.987, still closest to 4 among the options. The small negative correction from 22.01 to 21.99 does not change the nearest option. Why Other Options Are Wrong: 9, 10, 18: far larger than the computed difference. 6: still too large compared to the ~4 outcome. Common Pitfalls: Subtracting before dividing, or mistakenly treating the expression as (26.003 − 154.001) ÷ 6.995, which would be incorrect due to operator precedence. Final Answer: 4

Question 16

Quick division estimate near round numbers: Evaluate 750.0003 ÷ 19.999 and select the nearest option.

Accepted Answer

Introduction / Context: This division is very close to 750 ÷ 20, a classic mental-math benchmark. Small deviations (750.0003 instead of 750, and 19.999 instead of 20) create only tiny changes to the exact quotient, so the nearest choice is apparent after a quick check. Given Data / Assumptions: N ≈ 750 D ≈ 20 We need the nearest option to N/D. Concept / Approach: Compute the basic benchmark: 750 ÷ 20 = 37.5. Since the actual denominator is slightly smaller (19.999), the true quotient will be slightly larger than 37.5. Hence, the best nearby whole-number choice is 38. Step-by-Step Solution: Baseline: 750 ÷ 20 = 37.5Adjust for 19.999 (smaller than 20): quotient rises slightly above 37.5Therefore nearest integer option is 38 Verification / Alternative check: Compute more tightly: 750.0003 ÷ 19.999 ≈ 37.502, which rounds to 38. Back-multiplication: 38 * 19.999 ≈ 759.962, reasonably near 750 with rounding tolerance for a nearest-choice question. Why Other Options Are Wrong: 49, 22, 18, 35: not near the 37.5–38 reference range. Common Pitfalls: Rounding in the wrong direction (assuming a larger denominator) or forgetting that a smaller denominator increases the quotient slightly above the 37.5 baseline. Final Answer: 38

Question 17

Subtraction with near-integers: Compute 6888.009 − 487.999 − 87.989 and choose the closest value.

Accepted Answer

Introduction / Context: When subtracting several numbers close to integers, it is efficient to combine the subtrahends first, then subtract once. Tiny decimal parts usually shift the result by only a few thousandths, so the nearest ten or hundred is stable. Given Data / Assumptions: Start = 6888.009 Subtract 487.999 and 87.989 Concept / Approach: Add the numbers being subtracted: 487.999 + 87.989. Subtract that sum from 6888.009. Compare with the options and pick the closest. Step-by-Step Solution: 487.999 + 87.989 = 575.9886888.009 − 575.988 = 6312.021Nearest listed option is 6310 Verification / Alternative check: Round early to visualize: 6888 − (488 + 88) ≈ 6888 − 576 ≈ 6312. This matches our precise 6312.021 and confirms 6310 as the nearest choice. Why Other Options Are Wrong: 6430, 6390, 6570, 6000: each is farther from 6312 than 6310. Common Pitfalls: Subtracting sequentially without grouping (invites small arithmetic slips) or forgetting to carry decimal places correctly when adding 487.999 and 87.989. Final Answer: 6310

Question 18

Approximate square of a decimal: Compute (9.2)^2 to the nearest option.

Accepted Answer

Introduction / Context: Squaring a decimal near 10 can be done quickly by the identity (a − b)^2 = a^2 − 2ab + b^2 with a convenient anchor, such as a = 10 and b = 0.8 for 9.2. This keeps mental arithmetic manageable and accurate to within a small margin. Given Data / Assumptions: We need (9.2)^2 Compare to options to select the closest Concept / Approach: Use 9.2 = 10 − 0.8. Then (10 − 0.8)^2 = 100 − 2*10*0.8 + 0.8^2 = 100 − 16 + 0.64 = 84.64. The nearest provided option is 90 (difference 5.36) versus 75 (difference 9.64). Step-by-Step Solution: Compute (9.2)^2 = 84.64Compare distances: |90 − 84.64| = 5.36; |75 − 84.64| = 9.64Hence 90 is the closest listed value Verification / Alternative check: Direct multiplication: 9.2 × 9.2 = 84.64 confirms the identity method. The options are coarse, so select the nearest. Why Other Options Are Wrong: 75: too low by nearly 10. 110, 125: far above the true square. 85: closer than 75, but still farther than 90 from 84.64. Common Pitfalls: Rounding 9.2 to 9 or 10 without compensating can overshoot. Using the binomial square keeps the approximation tight. Final Answer: 90

Question 19

Multiply near-round decimals and adjust: Estimate 19.003 × 22.998 − 280.010 and pick the nearest option.

Accepted Answer

Introduction / Context: Products of numbers close to integers can be computed by anchoring to the round values and applying small corrections. Here 19.003 ≈ 19 and 22.998 ≈ 23. After multiplying, subtracting 280.010 refines the estimate to the nearest listed choice. Given Data / Assumptions: x ≈ 19, y ≈ 23 Expression: x * y − 280.010 Concept / Approach: First compute the rounded product 19 × 23 = 437. Small deviations (0.003 low or high) adjust the product by only a few hundredths. Then subtract 280.010 to locate the nearest option. Step-by-Step Solution: 19.003 × 22.998 ≈ (19 × 23) plus tiny corrections ≈ 437.0 ± smallExact multiplication gives ≈ 437.031Subtract 280.010 ⇒ ≈ 157.02Nearest option is 160 Verification / Alternative check: Direct computation: 19.003 × 22.998 − 280.010 ≈ 157.02, which is closer to 160 than to 150 or 170 (not listed). Why Other Options Are Wrong: 220, 180: too large relative to the computed 157. 110, 90: too small. Common Pitfalls: Multiplying the rounded numbers and then forgetting to subtract the given 280.010, which would leave the estimate near 437 rather than around 157. Final Answer: 160

Question 20

Fraction chain simplification: Compute (3/5) of (4/7) of (7/9) of 425 using cancellation for speed.

Accepted Answer

Introduction / Context: Successive fractions can often be simplified by cancellation before multiplying. Here, the factor 7 appears in both a numerator and a denominator, making the product much simpler and enabling quick mental calculation with minimal risk of error. Given Data / Assumptions: Expression: (3/5) * (4/7) * (7/9) * 425 All numbers are exact; a neat cancellation exists. Concept / Approach: Cancel the 7 in (4/7) with the 7 in (7/9), leaving (3/5) * (4/9) * 425. Multiply constants first or simplify with 425 to avoid large intermediate numbers. Step-by-Step Solution: After canceling 7: (3/5) * (4/9) * 425Combine fractions: 12/45 = 4/15Compute 425 * (4/15) = (425/15) * 4425/15 = 28.333..., so product ≈ 113.333...Nearest integer option is 113 Verification / Alternative check: Exact fraction: 425 * 12/45 = 425 * 4/15 = 1700/15 = 340/3 ≈ 113.333..., confirming 113 as the correct nearest integer option. Why Other Options Are Wrong: 110, 118, 115, 121: all differ from 113.33; 113 is the integer part of the exact value. Common Pitfalls: Multiplying all numerators first and all denominators next without simplifying can lead to bulky numbers and errors. Cancel early to stay accurate. Final Answer: 113

Approximation Questions