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Original
2026-01-01
Modified
2026-02-28
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<p>Let’s explore the key<a>formulas</a>for ratios and proportions in detail.</p>
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<p>Let’s explore the key<a>formulas</a>for ratios and proportions in detail.</p>
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<p><strong>1. Compound Ratios</strong></p>
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<p><strong>1. Compound Ratios</strong></p>
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<p>When two ratios are multiplied, the resulting ratio is called a compound ratio. Example: If a : b and c : d are two ratios, the compound ratio is: ac : bd</p>
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<p>When two ratios are multiplied, the resulting ratio is called a compound ratio. Example: If a : b and c : d are two ratios, the compound ratio is: ac : bd</p>
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<p><strong>2. Special Ratios</strong></p>
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<p><strong>2. Special Ratios</strong></p>
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<p>Duplicate Ratio: For a : b, the duplicate ratio is a² : b²</p>
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<p>Duplicate Ratio: For a : b, the duplicate ratio is a² : b²</p>
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<p>Sub-duplicate Ratio: For a : b, the sub-duplicate ratio is √a : √b</p>
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<p>Sub-duplicate Ratio: For a : b, the sub-duplicate ratio is √a : √b</p>
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<p>Triplicate Ratio: For a : b, the triplicate ratio is a³ : b³</p>
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<p>Triplicate Ratio: For a : b, the triplicate ratio is a³ : b³</p>
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<p><strong>3. Proportion Formulas</strong></p>
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<p><strong>3. Proportion Formulas</strong></p>
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<p>If a : b = c : d, the following formulas help solve proportion problems:</p>
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<p>If a : b = c : d, the following formulas help solve proportion problems:</p>
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<p>Addendo: (a + c) : (b + d)</p>
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<p>Addendo: (a + c) : (b + d)</p>
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<p>Subtrahendo: (a - c) : (b - d)</p>
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<p>Subtrahendo: (a - c) : (b - d)</p>
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<p>Dividendo: (a - b)/b = (c - d)/d</p>
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<p>Dividendo: (a - b)/b = (c - d)/d</p>
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<p>Componendo: (a + b)/b = (c + d)/d</p>
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<p>Componendo: (a + b)/b = (c + d)/d</p>
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<p>Alternendo: a : c = b : d</p>
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<p>Alternendo: a : c = b : d</p>
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<p>Invertendo: b : a = d : c</p>
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<p>Invertendo: b : a = d : c</p>
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<p>Componendo and Dividendo: (a + b) : (a - b) = (c + d) : (c - d)</p>
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<p>Componendo and Dividendo: (a + b) : (a - b) = (c + d) : (c - d)</p>
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<p><strong>4. Proportionality</strong></p>
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<p><strong>4. Proportionality</strong></p>
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<p>Direct Proportion: If a is proportional to b, then a = k × b, where k is a<a>constant</a>.</p>
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<p>Direct Proportion: If a is proportional to b, then a = k × b, where k is a<a>constant</a>.</p>
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<p>Inverse Proportion: If a is inversely proportional to b, then a = k / b, where k is a constant.</p>
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<p>Inverse Proportion: If a is inversely proportional to b, then a = k / b, where k is a constant.</p>
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<p><strong>5. Equivalent Ratios</strong></p>
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<p><strong>5. Equivalent Ratios</strong></p>
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<p>Multiplying or dividing both terms of a ratio by the same number gives an equivalent ratio. Example: a : b = n × a : n × b or a/n : b/n</p>
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<p>Multiplying or dividing both terms of a ratio by the same number gives an equivalent ratio. Example: a : b = n × a : n × b or a/n : b/n</p>