1. What Are Equivalent Ratios?

Equivalent ratios are ratios that express the same relationship between quantities. 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 ratio formula:

Where:

• \( a \) — First term of the original ratio
• \( b \) — Second term of the original ratio
• \( k \) — Scaling factor (non-zero number)

Explanation: The calculator multiplies both terms of the original ratio by the scaling factor to generate an equivalent ratio, then simplifies it by dividing both terms by their greatest common divisor (GCD).

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in mathematics for comparing quantities proportionally. They're used in scaling recipes, creating scale models, mixing chemicals, and solving proportion problems.

4. Using the Calculator

Tips: Enter the original ratio terms (a and b) and the scaling factor (k). All values must be positive numbers. The calculator will show both the exact equivalent ratio and its simplified form.

5. Frequently Asked Questions (FAQ)

Q1: Can the scaling factor be less than 1?
A: Yes, using a scaling factor between 0 and 1 will reduce the ratio (equivalent to dividing by a number greater than 1).

Q2: What if I get decimal numbers in the result?
A: Decimal numbers are valid in ratios. For whole numbers, choose a scaling factor that eliminates denominators.

Q3: How is the simplified form calculated?
A: The simplified form divides both terms by their greatest common divisor (GCD) to show the ratio in its simplest terms.

Q4: Can I use negative numbers?
A: While mathematically possible, negative numbers in ratios are generally avoided as they don't make practical sense in most contexts.

Q5: What's the difference between equivalent ratios and equal ratios?
A: They're essentially the same concept - two ratios that represent the same proportional relationship.