To multiply two Rational Numbers we simply multiply the numerators and denominators:

$\frac{a}{b}\times\frac{c}{d}~=~\frac{ac}{bd}$

We can think of a rational number as a stretching by the numerator, and shrinking by the denominator. We can consider the product $\frac{a}{b}\times\frac{c}{d}$ as stretching both by $a$ and $c,$ and shrinking both by $b$ and $d.$ Thus we are, in total, stretching by $ac$ and shrinking by $bd.$ Hence the result.

(none) (none) ComplexConjugate
ComplexNumber
RationalisingTheDenominator
WhatIsATopic
(none) DividingComplexNumbers

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MultiplyingRationalNumbers
Denominator
Numerator
RationalNumber
(none) (none) CauchySequence
CountableSet
Integer
IrrationalNumber
Pythagoras
RealNumber
ReducingFractionsToLowestTerms
RootTwoIsIrrational