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            "principle": "To solve problems involving a total quantity and sequential consumption or addition, first calculate the cumulative change by summing individual steps, then subtract this cumulative total from the initial quantity to determine the remaining amount, and finally apply any subsequent proportional operations to that remaining value."
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            "principle": "Decompose a multi-step rate problem by first calculating the output per single time unit (e.g., per session or per event), then scaling that unit rate by the frequency of occurrence within a larger interval (e.g., weeks to year) to determine the total aggregate."
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            "principle": "When a total value is composed of several distinct components and one component's quantity is unknown, first calculate the total value from known inputs (e.g., final amount + remaining change). Next, subtract the values of all known components (e.g., fixed income, known work units) from the total to isolate the monetary value of the unknown component. Finally, divide this isolated value by the unit rate of the unknown component to determine its quantity."
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            "principle": "When item costs are defined relative to a known base price (e.g., 'half the price' or 'twice the price'), first calculate the absolute value of each dependent item by applying the specified multiplier or divisor to the base value, then sum all individual costs to determine the total expenditure."
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            "principle": "To solve rate problems involving time, first normalize the given rate to a standard time unit (e.g., per hour) by determining how many of the original time intervals fit into that standard unit, then multiply the base quantity by this factor to find the standard rate, and finally divide the total target quantity by this new standard rate to find the required time."
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            "principle": "To solve problems involving shared quantities based on a ratio, first identify the total value associated with a specific number of parts from the given data. Divide this total value by the number of parts it represents to determine the monetary (or unit) value of a single part. Once the unit value is established, multiply it by the number of parts corresponding to the target entity to find their total share."
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