1. What is an Equivalent Ratio?

Equivalent ratios are ratios that express the same relationship between numbers. 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 by dividing both terms by their greatest common divisor (GCD).

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in mathematics, especially in proportion problems, scaling recipes, resizing images, and solving many real-world problems involving proportional relationships.

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 a fraction?
A: Yes, the scaling factor can be any non-zero number, including fractions and decimals.

Q2: What's the difference between equivalent ratios and equal ratios?
A: They are essentially the same concept - ratios that express the same proportional relationship.

Q3: How do you know if two ratios are equivalent?
A: Two ratios a:b and c:d are equivalent if a × d = b × c (cross-multiplication test).

Q4: Can equivalent ratios have different units?
A: No, equivalent ratios must compare quantities with the same units, though the actual quantities can be different.

Q5: Why simplify equivalent ratios?
A: Simplified ratios are easier to understand and compare, showing the most reduced form of the proportional relationship.