Lazy Liz divide and conquer

Algebra Level 4

Division of fractions can sometimes be tricky. Lazy Liz thinks that

\[ \frac{ a } { b} \div \frac{c}{d} = \frac { a \div c } { b \div d }, \]

because "you should just divide the numerator and the denominator". Can you tell her, how many ordered quadruples of integers \((a,b,c,d) \) are there, such that each term is between 1 and 5 (inclusive), and

\[ \frac{ a } { b} \div \frac{c}{d} = \frac { a \div c } { b \div d }? \]

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