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Equivalent Ratio Formula:
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Equivalent ratios are ratios that express the same relationship between quantities. They are calculated by multiplying or dividing both terms of the ratio by the same non-zero number.
The calculator uses the equivalent ratio formula:
Where:
Explanation: The calculator multiplies both terms of the original ratio by the scaling factor to generate an equivalent ratio, then simplifies it by dividing both terms by their greatest common divisor (GCD).
Details: Equivalent ratios are fundamental in mathematics, especially in proportion problems, scaling recipes, map reading, and solving many real-world problems involving proportional relationships.
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.
Q1: Can the scaling factor be less than 1?
A: Yes, the scaling factor can be any positive number. Values less than 1 will reduce the ratio terms proportionally.
Q2: What's the difference between equivalent and simplified ratios?
A: Equivalent ratios have the same proportional relationship, while simplified ratios are equivalent ratios reduced to their smallest whole number terms.
Q3: Can I use fractions or decimals in the ratio?
A: Yes, the calculator accepts decimal inputs, but the simplified form will show whole numbers when possible.
Q4: How are equivalent ratios used in real life?
A: They're used in cooking (scaling recipes), construction (blueprint scaling), finance (currency conversion), and many other proportional applications.
Q5: What if I get a ratio with very large numbers?
A: The simplified form will show the ratio in its most reduced terms, making it easier to understand and work with.