{
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  "body": "\n## Statement\n\nFor all natural numbers $a$, $b$ and $c$, $a \\cdot (b + c) = a \\cdot b + a \\cdot c$.\nHere $+$ is the [[addition|0W5DSDFQ4G]] and $\\cdot$ is the [[multiplication|0JRC32D6K2]] of natural numbers.\n\n## Remarks\n\nThis is the left distributive law. With commutativity of multiplication, it gives the right law $(b + c) \\cdot a = b \\cdot a + c \\cdot a$.\nThe proof from the recursive definitions uses [[induction|0ASJVEFA9J]] on $c$.\nThe same law holds in the integers, the rationals, the reals and the complex numbers.\n\n## Explanations\n\n### L1 human\n\nTo multiply a number by a sum, you can multiply it by each part and then add.\nFor example, $3 \\cdot (10 + 2) = 30 + 6 = 36$, and this is how many people compute $3 \\cdot 12$.\n",
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