Next, note that \(400 = 4 \cdot 100\text{,}\) and \(100 \equiv 1 \pmod 9\) (since \(9 \mid 99\)). So we can in fact replace the 400 with simply a 4. Again, we are appealing to our claim that we can replace congruent elements, but we are really appealing to property 3 about the arithmetic of congruence: we know \(100 \equiv 1 \pmod{9}\text{,}\) so if we multiply both sides by \(4\text{,}\) we get \(400 \equiv 4 \pmod 9\text{.}\)
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