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Use ratio tables

A ratio table organizes pairs of related quantities and shows equivalent ratios generated by multiplying or dividing both quantities by the same positive factor. It supports finding missing values, comparing ratios, and recognizing that additive changes do not generally preserve a ratio; at this level, the focus is on whole-number and familiar fractional scale factors in proportional situations, not generalized algebraic functions or complex rates.

Detailed Explanation: Use ratio tables

A ratio table keeps two related quantities in matching columns. To make an equivalent ratio, multiply or divide both quantities by the same positive factor.

Example: A drink recipe uses 22 cups of water for every 33 cups of juice. How much water is needed for 1212 cups of juice?

Set up the table:

Cups of juice331212
Cups of water22?
  1. Find how the juice amount changes:
3×4=123 \times 4 = 12

So, the juice amount is multiplied by 44.

  1. Multiply the water amount by the same factor:
2×4=82 \times 4 = 8
  1. Fill in the missing value:
Cups of juice331212
Cups of water2288

So, 1212 cups of juice need 88 cups of water.

Remember: Equivalent ratios come from multiplying or dividing both quantities by the same number. Simply adding the same amount to both numbers does not usually make an equivalent ratio.

Learn by doing: Use ratio tables

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    Ratios - Equivalent, Shrinking Recipes with Non-Integer Multiples - Whole Numbers

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