1. What is an Equivalent Ratio?

Equivalent ratios are ratios that express the same relationship between quantities. They are calculated by multiplying or dividing both terms of the 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 original ratio
• \( b \) — Second term of 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 to its lowest terms.

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 scaled 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).

Q2: What if I get decimal numbers in the simplified ratio?
A: The simplified form should be in whole numbers. If you get decimals, your original ratio might not be in whole numbers.

Q3: Can I use negative numbers?
A: No, all values must be positive numbers as ratios compare magnitudes.

Q4: How is the simplified form calculated?
A: The calculator divides both terms by their greatest common divisor (GCD).

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