1. What is an Equivalent Ratio Calculator?

Definition: This calculator determines equivalent ratios by multiplying both terms of the original ratio by the same scaling factor.

Purpose: It helps find proportional ratios that maintain the same relationship between quantities, useful in scaling recipes, mixtures, or mathematical problems.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — First term of the ratio (dimensionless)
• \( B \) — Second term of the ratio (dimensionless)
• \( k \) — Scaling factor (dimensionless)

Explanation: Both terms of the original ratio are multiplied by the same number to create an equivalent ratio that maintains the same proportion.

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in scaling recipes, mixing chemicals, creating scale models, and solving proportion problems in mathematics.

4. Using the Calculator

Tips: Enter the original ratio terms (A and B) and the scaling factor (k). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What makes ratios equivalent?
A: Ratios are equivalent when they represent the same proportional relationship, just scaled up or down by the same factor.

Q2: Can the scaling factor be less than 1?
A: Yes, a factor between 0 and 1 will reduce the ratio (e.g., 0.5 halves both terms).

Q3: What's the simplest form of a ratio?
A: The form where terms have no common divisors (e.g., 3:2 instead of 6:4).

Q4: How is this different from percentage calculations?
A: While related, ratios compare parts to parts, while percentages compare parts to whole.

Q5: Can I use decimal numbers in ratios?
A: Yes, though it's often preferable to convert to whole numbers by multiplying by 10, 100, etc.