This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. Tank starts -1.8 decimal deficit, add 3 1/2 mixed=3.5 to -1.8+3.5=1.7, leak -0.6=1.7-0.6=1.1, drain 1/4 of 1.1=0.275, 1.1-0.275=0.825 L. Interprets negative as below full, adds/subtracts, multiplies fraction last. Correct multi-step tracks amount, converting mixed to decimal. Errors: ignoring negative or draining before leak. Strategy: use decimals, step-by-step, estimate -2+3.5=1.5, -0.5=1, 1/4 drain 0.25, 1-0.25=0.75 close to 0.825, check positive reasonable after add. Common mistakes: order wrong or no estimation for negative finals.

This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. In multi-step scenarios with mixed forms, such as starting with $45 whole number, subtracting $18.50 decimal, adding $30 whole, then spending 1/4 fraction of the remainder, convert fractions to decimals for easier arithmetic, like 1/4=0.25, and apply operations sequentially while tracking values step-by-step. For this specific problem, start with $45, subtract $18.50 to get $26.50, add $30 to reach $56.50, then spend $56.50 × 0.25 = $14.125 (rounds to $14.13), and subtract to find $56.50 - $14.125 = $42.375, which rounds to $42.38. The correct approach involves proper order of operations and accurate conversions, ensuring the final amount is calculated after all steps. Common errors include incorrect operation order, like multiplying before adding the deposit, or conversion mistakes such as treating 1/4 as 0.20. Strategy: read carefully to list steps, convert to decimals for consistency, execute step-by-step with running totals, estimate like 45-19+30=56, 56/4=14 spent, 56-14=42 close to $42.38, and verify reasonableness with net spending and deposit. Avoid mistakes like skipping estimation or arithmetic errors in subtraction.

This problem tests solving multi-step problems with rational numbers (whole, fraction, decimal, positive, negative), converting between forms strategically, and checking reasonableness. Multi-step with mixed forms: combine different formats (-12 whole negative, +7.5 decimal, -9/4 fraction= -2.25), apply sequentially (add 7.5, subtract 2.25). For this specific problem: -12 + 7.5 = -4.5, -4.5 - 2.25 = -6.75 m. The correct approach involves converting fraction to decimal and handling negative positions properly. Common errors include sign error (-12 +7.5 as -19.5), conversion wrong (9/4 as 2.5), or unreasonable result (positive when diving deeper). Strategy: (1) read carefully identifying all values and operations (list steps needed), (2) convert to consistent form if easier (all decimals), (3) execute step-by-step (track running total, don't skip), (4) estimate alongside (-12+8=-4, -4-2=-6 close to -6.75✓), (5) verify reasonable (ends below sea level—logical for diver), (6) check units (meters stay meters). Common mistakes: skipping estimation (missing unreasonable answers), form conversion errors, negative operations (rise is add, drop is subtract).

This problem tests solving multi-step problems with rational numbers (whole, fraction, decimal, positive, negative), converting between forms strategically, and checking reasonableness. Multi-step with mixed forms: all whole numbers here (450, -275 descend, +180 climb), apply operations sequentially (subtract 275, add 180). For this specific problem: 450 - 275 = 175, 175 + 180 = 355 m. The correct approach involves treating descent as subtraction and climb as addition in sequence. Common errors include sign error (adding descent as positive), or unreasonable result (negative elevation when starting high). Strategy: (1) read carefully identifying all values and operations (list steps needed), (2) convert to consistent form if easier (wholes here), (3) execute step-by-step (track running total, don't skip), (4) estimate alongside (450-300=150, +200=350 close to 355✓), (5) verify reasonable (ends positive above sea level—logical), (6) check units (meters stay meters). Common mistakes: skipping estimation (missing unreasonable answers), negative operations (descent is subtract), operation order wrong.

This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. For recipe scaling with 2/3 cup per batch, multiply by 1.5 (decimal or 3/2 fraction) to get (2/3) × (3/2) = 1 cup, then subtract spilled 0.25 cup to leave 0.75 cup. This involves multiplication first for batches, then subtraction, using fraction-decimal conversions. Correct steps ensure exact preparation for 1.5 batches before spilling. Common errors: wrong multiplication like 2/3 + 1.5, or subtracting before scaling. Strategy: convert to decimals or fractions, multiply then subtract, estimate 2/3≈0.67 ×1.5≈1, 1-0.25=0.75 exact, check reasonableness for partial batch remainder. Avoid order mistakes or not verifying with estimation.

This problem tests solving multi-step problems with rational numbers (whole, fraction, decimal, positive, negative), converting between forms strategically, and checking reasonableness. Multi-step with mixed forms: combine different formats (-2.5 decimal negative, +7 1/2 mixed, -3/4 fraction), convert for operations (7.5, 0.75 decimals), apply sequentially (add 7.5, subtract 0.75). For this specific problem: -2.5 + 7.5 = 5, 5 - 0.75 = 4.25°C. The correct approach involves converting all to decimals and handling signs properly. Common errors include conversion wrong (7 1/2 as 7.2), sign error (-2.5 +7.5 as -10), or unreasonable result (negative final when warming). Strategy: (1) read carefully identifying all values and operations (list steps needed), (2) convert to consistent form if easier (all decimals), (3) execute step-by-step (track running total, don't skip), (4) estimate alongside (-3+8=5, 5-1=4 close to 4.25✓), (5) verify reasonable (starts negative, net rise positive), (6) check units (°C throughout). Common mistakes: skipping estimation (missing unreasonable answers), form conversion errors, negative operations wrong.

This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. In elevation changes with mixed forms, like starting at 450 whole, down 275 whole, up 180 whole, down 1/2 of 60 (fraction times whole=30), handle subtractions and additions sequentially while interpreting '1/2 of 60' as multiplication before subtracting. Specifically, 450 - 275 = 175, 175 + 180 = 355, then 355 - (1/2 × 60) = 355 - 30 = 325 m. Correct execution follows order: downs and ups as add/subtract, with fraction multiplication for the last descent. Common errors: misordering by subtracting 30 before up 180, or wrong fraction like 1/2 as 0.4. Strategy: list steps, convert fractions to decimals if needed, track elevation step-by-step, estimate 450-300+200-30≈320 close to 325, verify reasonableness with net down 125 m from start. Avoid propagating arithmetic errors or skipping estimation for unreasonable elevations.

This problem tests solving multi-step problems with rational numbers (whole, fraction, decimal, positive, negative), converting between forms strategically, and checking reasonableness. Multi-step with mixed forms: combine different formats (temperature -8 whole negative, +15 whole positive, -3.5 decimal), apply operations sequentially (add 15, subtract 3.5—tracking values step-by-step). For this specific problem: start at -8°C, rise 15°C (-8+15=7), drop 3.5°C (7-3.5=3.5°C). The correct approach involves handling negative numbers properly, adding the rise and subtracting the drop in sequence. Common errors include sign errors with negatives (-8+15 mistaken as -23 by adding negatively), or unreasonable result not questioned (ending negative in a warming scenario might be wrong). Strategy: (1) read carefully identifying all values and operations (list steps needed), (2) convert to consistent form if easier (all decimals here), (3) execute step-by-step (track running total, don't skip), (4) estimate alongside (round: -8+15=7, 7-4=3 close to 3.5✓), (5) verify reasonable (starting negative, net rise positive, ends positive—logical), (6) check units (°C throughout). Common mistakes: skipping estimation (missing unreasonable answers), negative number operations (forgetting rules: adding positive increases), operation order wrong.

This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. For centering with mixed numbers like door 27 1/2 (fraction) and bar 9 3/4 (fraction), convert to improper fractions or decimals, subtract lengths, then divide by 2 for each side. Here, 27.5 - 9.75 = 17.75, then 17.75 / 2 = 8.875 inches, or in fractions 55/2 - 39/4 = (110/4 - 39/4) = 71/4, then (71/4)/2 = 71/8 = 8 7/8. Correct steps ensure subtraction first, then equal division, converting back to mixed numbers. Errors include dividing before subtracting or conversion slips like 1/2 as 0.6. Strategy: convert to decimals for ease, subtract, divide, estimate 28-10=18, 18/2=9 close to 8.875, check reasonableness for balanced spacing. Common mistakes: operation order wrong or not estimating to spot tiny spacings.

This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. Diver position -6 1/2 mixed negative, +4.75 decimal, -3/4 fraction, +2 1/4 mixed: convert to decimals -6.5 + 4.75 = -1.75, -1.75 - 0.75 = -2.5, -2.5 + 2.25 = -0.25 m. Sequential add/subtract with signs for rises and descents. Correct multi-step maintains negative for below surface, converting fractions accurately. Errors: sign flips like adding descent, or wrong conversions. Strategy: use decimals, track position, estimate -6.5+5-1+2≈-0.5 close to -0.25, check reasonableness still below surface. Avoid negative rule mistakes or not estimating for impossible positives.