Formula
R = \frac{a}{b}Used to calculate: The relative size of one quantity compared with another quantity.
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What Is the Ratio Formula?
The ratio formula compares two quantities by dividing one quantity by another. A ratio describes how much of one quantity there is relative to another and can be written as a fraction, with a colon, or in words.
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Formula and Variables
R = \frac{a}{b}| Symbol | Meaning | Unit |
| R | Ratio of the first quantity to the second quantity | None when comparing like units; may have units for unlike quantities |
| a | First quantity, or antecedent | Depends on the quantities |
| b | Second quantity, or consequent | Depends on the quantities |
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How to Use the Formula
Identify the two quantities being compared and place the first quantity in the numerator and the second quantity in the denominator. Divide the first quantity by the second to determine their ratio. When comparing quantities of the same type, convert them to the same units before calculating the ratio.
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When Is This Formula Used?
The ratio formula is used whenever two quantities need to be compared relative to one another.
Common uses:
– Comparing quantities or measurements
– Describing proportions and rates
– Comparing quantities in mathematics, science, finance, and everyday situations
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Important Notes
– Multiplying or dividing both terms of a ratio by the same nonzero number produces an equivalent ratio.
– The second quantity, b, cannot equal zero because division by zero is undefined.
– When comparing quantities of the same type, they should be expressed in the same units; the resulting ratio is dimensionless. Ratios of unlike quantities may retain compound units and are often called rates.
– A common point of confusion is reversing the order of the quantities. The ratio of a to b is a/b, not b/a.
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Alternate Forms
Alternate form:
a:b
Alternate form:
\frac{a}{b} = \frac{ka}{kb}, \quad k \ne 0—
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