1. What is an Equivalent Ratio?

An equivalent ratio is a ratio that expresses the same relationship between quantities as another ratio, but with different numbers. Equivalent ratios 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 ratio formula:

Where:

• \( a \) — First term of the original ratio
• \( b \) — Second term of the original ratio
• \( k \) — Multiplier (non-zero constant)

Explanation: The calculator multiplies both terms of the original ratio by the same factor to produce an equivalent ratio.

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in mathematics, particularly in proportional reasoning, scaling recipes, mixing solutions, and comparing quantities in various fields like chemistry, cooking, and engineering.

4. Using the Calculator

Tips: Enter the original ratio terms (a and b) and the multiplier (k). All values must be positive numbers. The calculator will show the equivalent ratio.

5. Frequently Asked Questions (FAQ)

Q1: Can the multiplier be less than 1?
A: Yes, the multiplier can be any positive number, including fractions less than 1, which would result in a simplified ratio.

Q2: How is this different from simplifying a ratio?
A: Simplifying uses division to find an equivalent ratio with the smallest whole numbers, while this calculator uses multiplication to find any equivalent ratio.

Q3: Can I use decimal numbers?
A: Yes, the calculator accepts decimal numbers for all inputs.

Q4: What if I get very large numbers in the result?
A: You can simplify the result by dividing both terms by their greatest common divisor (GCD).

Q5: Are equivalent ratios the same as equal fractions?
A: Yes, the concept is similar - equivalent ratios correspond to equal fractions when written in fraction form.