Formula
\frac{a}{b} = \frac{c}{d}Used to calculate: Whether two ratios are equal and to find an unknown value when three terms of a proportion are known.
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What Is the Proportion Formula?
The proportion formula states that two ratios are equal. It represents a relationship in which the quantities in one ratio have the same relative relationship as the quantities in another ratio. Proportions are commonly used to find an unknown quantity from equivalent ratios.
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Formula and Variables
\frac{a}{b} = \frac{c}{d}| Symbol | Meaning | Unit |
| a | First term of the first ratio | Depends on the problem |
| b | Second term of the first ratio | Depends on the problem |
| c | First term of the second ratio | Depends on the problem |
| d | Second term of the second ratio | Depends on the problem |
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How to Use the Formula
Arrange the quantities so that corresponding values occupy the same positions in each ratio. Substitute the known values into the proportion and solve for the unknown value. Cross multiplication can be used to rewrite the proportion as ad = bc, which is often convenient when solving for an unknown term.
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When Is This Formula Used?
The proportion formula is used when two ratios represent the same relative relationship and an unknown quantity needs to be determined or the equality of two ratios needs to be tested.
Common uses:
– Scaling measurements or quantities
– Converting between proportional quantities
– Solving problems involving similar figures, rates, recipes, and maps
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Important Notes
– A valid proportion represents two equivalent ratios.
– The denominators b and d cannot equal zero because division by zero is undefined.
– Corresponding quantities should use compatible units, with any necessary unit conversions performed before comparing the ratios.
– A common point of confusion is matching quantities in the wrong order. Corresponding quantities must occupy equivalent positions in both ratios.
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Alternate Forms
Alternate form:
ad = bc
Alternate form:
a = \frac{bc}{d}Alternate form:
b = \frac{ad}{c}Alternate form:
c = \frac{ad}{b}Alternate form:
d = \frac{bc}{a}—
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