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Great question! :)

The numerator and denominator are relatively prime.

If you factor the numerator into the product of its primes, and factor the denominator into its product of primes, there are no primes to cancel:

4 / 5 = 2 * 2 / 5

since the only primes in the numerator are 2, and the only ones in the denominator are 5, they cannot divide into each other for further simplication.

For a contrast, consider 4 / 6.

Here you can rewrite 4 / 6 as (2 * 2) / (2 * 3).

In this case, a 2 in the numerator cancels with a 2 in the denominator, reducing the fraction to 2/3. One way of visualizing the cancellation is below:

(2 * 2) / (2 * 3) = 2 / 3.

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13y ago

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