1. What Are Equal Ratios?

Equal ratios (or equivalent ratios) are ratios that express the same relationship between numbers. They are created by multiplying or dividing both terms of the original ratio by the same non-zero number.

2. How the Calculator Works

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: Multiplying both terms of the ratio by the same number preserves the proportional relationship while scaling the quantities.

3. Importance of Equal Ratios

Details: Equal ratios are fundamental in mathematics, especially in proportion problems, scaling recipes, map reading, 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 shows 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 both terms by a number).

Q2: How are equivalent ratios different from equal fractions?
A: While the concept is similar, ratios compare quantities while fractions represent parts of a whole. Ratios don't need to have the same denominator to be equivalent.

Q3: Can ratios have more than two terms?
A: Yes, the same principle applies to ratios with three or more terms - multiply each term by the same scaling factor.

Q4: What's the purpose of simplifying ratios?
A: Simplified ratios are easier to understand and compare, showing the relationship in its most basic form.

Q5: Are 1:2 and 3:6 equivalent ratios?
A: Yes, because 3:6 can be simplified to 1:2 by dividing both terms by 3.