2.5 mi → m（1 mi = 1609.344 m） 单步约去 mi，结果 4023.36 m；学生答案 4023.36 判定正确。<style>
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<div class="da-wrap">
<div class="da-hero ok">
<div class="da-hero-main">4023.36 <span style="font-size:16px;font-weight:700">m</span></div>
<div class="da-hero-lbl">Units cancel to target</div>
<div class="da-hero-sub">2.5 mi → target m</div>
</div>
<div class="da-card">
<div class="da-card-title">Factor-label chain</div>
<div class="da-track da-mono"><span class="da-mono" style="font-weight:800">2.5 mi</span> × (1609.344 m / 1 mi)</div>
<div class="da-muted" style="margin-top:8px">Goal: cancel every unit except <strong>m</strong>.</div>
</div>
<div class="da-card">
<div class="da-card-title">Step-by-step cancellation</div>
<div class="da-step">
<div class="da-step-h">
<span class="da-step-n">Step 1</span>
<span class="da-pill da-pill-ok">cancels</span>
</div>
<div class="da-mono">factor written: 1 mi = 1609.344 m</div>
<div class="da-mono">applied as: × (1609.344 m / 1 mi)</div>
<div class="da-track"><span style="font-weight:800;margin-right:6px">4023.36</span><span class="da-mono">m</span></div>
<div class="da-muted">Cancel mi in the numerator using the factor as written. · canceled unit: mi</div>
</div>
</div>
<div class="da-card">
<div class="da-card-title">Result summary</div>
<div class="da-row"><span class="da-row-l">Numeric result</span><span class="da-row-v">4023.36</span></div>
<div class="da-row"><span class="da-row-l">Remaining dimensions</span><span class="da-row-v">m</span></div>
<div class="da-row"><span class="da-row-l">Matches target</span><span class="da-row-v">yes</span></div>
<div class="da-row"><span class="da-row-l">Auto-flipped factors</span><span class="da-row-v">0</span></div>
</div>
<div class="da-card">
<div class="da-card-title">Student answer check</div>
<div class="da-row"><span class="da-row-l">Your answer</span><span class="da-row-v">4023.36</span></div>
<div class="da-row"><span class="da-row-l">Calculated</span><span class="da-row-v">4023.36 m</span></div>
<div class="da-row"><span class="da-row-l">Match</span><span class="da-row-v"><span class="da-pill da-pill-ok">Correct</span></span></div>
<div class="da-row"><span class="da-row-l">Relative error</span><span class="da-row-v">0%</span></div>
</div>
<div class="da-card">
<div class="da-card-title">Teaching feedback</div>
<ul class="da-list">
<li>Units cancel cleanly to "m".</li><li>Your numeric answer matches the calculated value (within rounding tolerance).</li>
</ul>
</div>
</div>
5 gal × (4 qt/1 gal) × (0.946353 L/1 qt) → 18.9271 L，单位逐步约去。<style>
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<div class="da-wrap">
<div class="da-hero ok">
<div class="da-hero-main">18.9271 <span style="font-size:16px;font-weight:700">L</span></div>
<div class="da-hero-lbl">Units cancel to target</div>
<div class="da-hero-sub">5 gal → target L</div>
</div>
<div class="da-card">
<div class="da-card-title">Factor-label chain</div>
<div class="da-track da-mono"><span class="da-mono" style="font-weight:800">5 gal</span> × (4 qt / 1 gal) × (0.946353 L / 1 qt)</div>
<div class="da-muted" style="margin-top:8px">Goal: cancel every unit except <strong>L</strong>.</div>
</div>
<div class="da-card">
<div class="da-card-title">Step-by-step cancellation</div>
<div class="da-step">
<div class="da-step-h">
<span class="da-step-n">Step 1</span>
<span class="da-pill da-pill-ok">cancels</span>
</div>
<div class="da-mono">factor written: 1 gal = 4 qt</div>
<div class="da-mono">applied as: × (4 qt / 1 gal)</div>
<div class="da-track"><span style="font-weight:800;margin-right:6px">20</span><span class="da-mono">qt</span></div>
<div class="da-muted">Cancel gal in the numerator using the factor as written. · canceled unit: gal</div>
</div><div class="da-step">
<div class="da-step-h">
<span class="da-step-n">Step 2</span>
<span class="da-pill da-pill-ok">cancels</span>
</div>
<div class="da-mono">factor written: 1 qt = 0.946353 L</div>
<div class="da-mono">applied as: × (0.946353 L / 1 qt)</div>
<div class="da-track"><span style="font-weight:800;margin-right:6px">18.9271</span><span class="da-mono">L</span></div>
<div class="da-muted">Cancel qt in the numerator using the factor as written. · canceled unit: qt</div>
</div>
</div>
<div class="da-card">
<div class="da-card-title">Result summary</div>
<div class="da-row"><span class="da-row-l">Numeric result</span><span class="da-row-v">18.9271</span></div>
<div class="da-row"><span class="da-row-l">Remaining dimensions</span><span class="da-row-v">L</span></div>
<div class="da-row"><span class="da-row-l">Matches target</span><span class="da-row-v">yes</span></div>
<div class="da-row"><span class="da-row-l">Auto-flipped factors</span><span class="da-row-v">0</span></div>
</div>
<div class="da-card">
<div class="da-card-title">Teaching feedback</div>
<ul class="da-list">
<li>Units cancel cleanly to "L".</li>
</ul>
</div>
</div>
3 km 配上颠倒因子得到 0.003 m（单位仍可约去），学生答案 3000 被标为数值不匹配——典型倒置因子错误。<style>
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.da-row-l{color:#475569}
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<div class="da-wrap">
<div class="da-hero ok">
<div class="da-hero-main">0.003 <span style="font-size:16px;font-weight:700">m</span></div>
<div class="da-hero-lbl">Units cancel to target</div>
<div class="da-hero-sub">3 km → target m</div>
</div>
<div class="da-card">
<div class="da-card-title">Factor-label chain</div>
<div class="da-track da-mono"><span class="da-mono" style="font-weight:800">3 km</span> × (1 m / 1000 km)</div>
<div class="da-muted" style="margin-top:8px">Goal: cancel every unit except <strong>m</strong>.</div>
</div>
<div class="da-card">
<div class="da-card-title">Step-by-step cancellation</div>
<div class="da-step">
<div class="da-step-h">
<span class="da-step-n">Step 1</span>
<span class="da-pill da-pill-ok">cancels</span>
</div>
<div class="da-mono">factor written: 1000 km = 1 m</div>
<div class="da-mono">applied as: × (1 m / 1000 km)</div>
<div class="da-track"><span style="font-weight:800;margin-right:6px">0.003</span><span class="da-mono">m</span></div>
<div class="da-muted">Cancel km in the numerator using the factor as written. · canceled unit: km</div>
</div>
</div>
<div class="da-card">
<div class="da-card-title">Result summary</div>
<div class="da-row"><span class="da-row-l">Numeric result</span><span class="da-row-v">0.003</span></div>
<div class="da-row"><span class="da-row-l">Remaining dimensions</span><span class="da-row-v">m</span></div>
<div class="da-row"><span class="da-row-l">Matches target</span><span class="da-row-v">yes</span></div>
<div class="da-row"><span class="da-row-l">Auto-flipped factors</span><span class="da-row-v">0</span></div>
</div>
<div class="da-card">
<div class="da-card-title">Student answer check</div>
<div class="da-row"><span class="da-row-l">Your answer</span><span class="da-row-v">3000</span></div>
<div class="da-row"><span class="da-row-l">Calculated</span><span class="da-row-v">0.003 m</span></div>
<div class="da-row"><span class="da-row-l">Match</span><span class="da-row-v"><span class="da-pill da-pill-warn">Mismatch</span></span></div>
<div class="da-row"><span class="da-row-l">Relative error</span><span class="da-row-v">99999900%</span></div>
</div>
<div class="da-card">
<div class="da-card-title">Teaching feedback</div>
<ul class="da-list">
<li>Units cancel cleanly to "m".</li><li>Your answer 3000 differs from the calculated 0.003 (~99999900% error). Recheck arithmetic and whether a factor was flipped twice.</li>
</ul>
</div>
</div>