Use ratio tables and double number lines to solve missing-value and scaling problems.
Find a missing value on a double number line
Problem
A double number line shows cups of juice on the top line and servings on the bottom line. The aligned labels include \(2~\text{cups}\) with \(6~\text{servings}\) and \(4~\text{cups}\) with \(12~\text{servings}\). What number of servings should be at the tick aligned with \(5~\text{cups}\)?
Values at the same vertical tick form a proportional cups-and-servings pair. We’ll use a labeled pair to divide servings by cups, giving the number of servings for one cup, and then scale that rate to the five-cup tick. The four-cup and twelve-serving pair provides an independent check on the constant relationship.
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