Ratio Scaling Calculator: Enlarge or Shrink Proportions

What is Ratio Scaling?

Ratio scaling is a mathematical process that allows you to enlarge or shrink a ratio while maintaining its proportional relationship. This technique is useful in various fields, including mathematics, engineering, and design, where you need to adjust sizes or quantities while preserving their relative proportions.

How to Calculate Ratio Scaling

To calculate ratio scaling:

• Start with an original ratio A:B
• Decide whether to enlarge or shrink the ratio
• Choose a scaling factor
• Multiply both terms of the ratio by the scaling factor
• Simplify the new ratio if possible

Formula

The general formula for ratio scaling is:

\[ (A:B) \times S = (A \times S : B \times S) \]

Where:

• A:B is the original ratio
• S is the scaling factor
• S > 1 for enlarging, 0 < S < 1 for shrinking

Calculation Steps

1. Identify the original ratio A:B
2. Determine the scaling factor S
3. Multiply A by S to get the new first term
4. Multiply B by S to get the new second term
5. Write the new ratio (A × S) : (B × S)
6. Simplify the new ratio if possible

Example

Let's scale the ratio 3:4 by a factor of 2 (enlarging)

1. Original ratio: 3:4
2. Scaling factor: 2
3. New first term: 3 × 2 = 6
4. New second term: 4 × 2 = 8
5. New ratio: 6:8
6. Simplified: 3:4 (the proportion remains the same)

Visual representation of scaling 3:4 to 6:8