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 the original ratio by the same non-zero number.

2. How Does the Calculator Work?

The calculator uses the equivalent ratios formula:

Where:

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

Explanation: Multiplying both terms of the ratio by the same number preserves the proportional relationship while changing the absolute values.

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in scaling recipes, creating scale models, mixing solutions, and solving proportion problems in mathematics and real-world applications.

4. Using the Calculator

Tips: Enter the original ratio terms (a and b) and the scaling factor (k). All values must be valid (a and b > 0, k ≠ 0). The calculator shows both the exact equivalent ratio and its simplified form.

5. Frequently Asked Questions (FAQ)

Q1: Can the scaling factor be negative?
A: Yes, but negative ratios are less common. A negative scaling factor inverts the ratio's direction (e.g., 2:3 becomes -2:-3, which is equivalent to 2:3).

Q2: How is the simplified form calculated?
A: The simplified form divides both terms by their greatest common divisor (GCD) to express the ratio in its simplest terms.

Q3: What's the difference between equivalent ratios and equal ratios?
A: They are essentially the same concept - ratios that represent the same proportional relationship.

Q4: Can I use fractions or decimals in the ratio?
A: Yes, the calculator accepts decimal inputs and will calculate the equivalent ratio accordingly.

Q5: How are equivalent ratios used in real life?
A: They're used in cooking (scaling recipes), construction (blueprint scaling), chemistry (solution mixing), and many other fields requiring proportional relationships.