Scaling in Both Directions Using Ratio Tables

To find a missing value in a ratio table, you can scale in both directions. First, scale backward by dividing both terms by a common factor to find a simpler equivalent ratio.

Example: Example 1: A recipe uses 8 cups of flour for every 12 tablespoons of honey. How much honey is needed for 10 cups of flour? First, scale backward by dividing by 4. Then, scale forward by multiplying by 5. | Flour (cups) | Honey (tbsp) | | :--- | :--- | | 8 | 12

Example 2: A school has a ratio of 15 students for every 20 chairs. How many chairs are needed for 9 students? First, scale backward by dividing by 5. Then, scale forward by multiplying by 3. | Students | Chairs | | :--- | :--- | | 15 | 20 | | 3 | 4 | | 9 | 12

Sometimes, you cannot easily multiply by a whole number to jump directly from one value in a ratio table to another. When this happens, you can scale in both directions to find the missing value.

Scaling in Both Directions Using Ratio Tables is a Grade 6 math topic covered in Reveal Math, Course 1 in Module 1: Ratios and Rates. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.

First, scale backward by dividing both terms by a common factor to find a simpler equivalent ratio. Then, scale forward by multiplying both terms by a new factor to reach the target value. \text{Original Ratio} \xrightarrow{\div c} \text{Simpler Ratio} \xrightarrow{\times d} \text{Target Ratio}.

When this happens, you can scale in both directions to find the missing value. First, scale backward (divide) to find a simpler equivalent ratio, and then use that simpler ratio to scale forward (multiply) to your target number..