1. What is an Equivalent Ratios Calculator?

Definition: This calculator finds equivalent ratios by dividing both terms of a ratio by the same factor (k).

Purpose: It helps simplify ratios or find equivalent ratios for proportional relationships in mathematics, chemistry, and everyday calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — First term of the original ratio
• \( b \) — Second term of the original ratio
• \( k \) — Factor to divide both terms by (must be > 0)

Explanation: Dividing both terms of a ratio by the same number produces an equivalent ratio.

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in proportion problems, scaling recipes, mixing solutions, and comparing quantities in similar proportions.

4. Using the Calculator

Tips: Enter the original ratio terms (a and b) and the factor (k) to divide by. For simplification, use the greatest common divisor as k.

5. Frequently Asked Questions (FAQ)

Q1: What makes two ratios equivalent?
A: Two ratios are equivalent when they represent the same proportion, meaning a/b = (a/k)/(b/k) for any positive k.

Q2: How is this different from solving proportions?
A: Equivalent ratios maintain the same proportion within one ratio, while proportions compare two ratios for equality.

Q3: Can k be a decimal or fraction?
A: Yes, k can be any positive number, including fractions and decimals.

Q4: What if I want to multiply instead of divide?
A: Simply use 1/k as your factor to effectively multiply both terms by k.

Q5: How do I simplify a ratio to lowest terms?
A: Find the GCD of a and b, then use that as k to create the simplest form.