1. What Are Equivalent Ratios?

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 ratios formula:

Where:

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

Explanation: The calculator multiplies both terms of your original ratio by the scaling factor to generate an equivalent ratio.

3. Importance of Equivalent Ratios

Details: Equivalent ratios are fundamental in mathematics, especially in proportion problems, 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 scaling factor (k). All values must be positive numbers. The calculator will show both the exact equivalent ratio and its simplified form if possible.

5. Frequently Asked Questions (FAQ)

Q1: Can the scaling factor be less than 1?
A: Yes, the scaling factor can be any non-zero number, including fractions and decimals less than 1.

Q2: How do equivalent ratios relate to fractions?
A: Equivalent ratios are similar to equivalent fractions - they represent the same proportional relationship.

Q3: What's the difference between equivalent ratios and simplified ratios?
A: Equivalent ratios can be scaled up or down, while simplified ratios are reduced to their smallest whole number terms.

Q4: Can negative numbers be used in ratios?
A: While mathematically possible, negative numbers in ratios are generally avoided in practical applications.

Q5: How are equivalent ratios used in real life?
A: They're used in scaling recipes, mixing chemicals, calculating dosages, creating scale models, and many other proportional applications.