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Rule

Cross Products Property

In a proportion, the product of the extremes is equal to the product of the means.

\frac{a}{b} = \frac{c}{d} \Rightarrow a d = b c

This property is also known as cross-multiplication or Means-Extremes Property of Proportion.

Proof

Cross Products Property

The Cross Products Property can be proven by using the Properties of Equality.

\frac{a}{b} = \frac{c}{d}

$LHS \cdot b = RHS \cdot b$

a = \frac{c}{d} \cdot b

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

a = \frac{c b}{d}

$LHS \cdot d = RHS \cdot d$

a d = c b

CommutativePropMult

Commutative Property of Multiplication

a d = b c

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