1. What Are Equivalent Ratios?

Equivalent ratios are ratios that express the same relationship between numbers. They are obtained by multiplying or dividing both terms of a ratio by the same non-zero number.

2. How Does the Calculator Work?

The calculator uses the equivalent ratios formula:

Where:

• \( \text{Ratio} \) — Original ratio (unitless)
• \( \text{Factor} \) — Multiplication factor (unitless)

Explanation: The calculator multiplies the original ratio by the factor to produce an equivalent ratio that maintains the same proportional relationship.

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in mathematics, especially in proportions, scaling recipes, mixing solutions, and comparing quantities in various fields like chemistry, cooking, and engineering.

4. Using the Calculator

Tips: Enter the original ratio and the multiplication factor. Both values must be non-negative numbers. The calculator will show the equivalent ratio.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between ratio and equivalent ratio?
A: A ratio compares two quantities, while equivalent ratios are different expressions of the same comparison.

Q2: Can equivalent ratios be simplified?
A: Yes, equivalent ratios can often be simplified to their lowest terms by dividing both numbers by their greatest common divisor.

Q3: How are equivalent ratios used in real life?
A: They're used in scaling recipes, mixing paints or chemicals, calculating dosages, and creating scale models.

Q4: Can the factor be less than 1?
A: Yes, factors less than 1 will produce equivalent ratios that are scaled down versions of the original.

Q5: Are 1:2 and 2:4 equivalent ratios?
A: Yes, they represent the same proportional relationship (2:4 simplifies to 1:2).