# Multiplication by 2

Multiplication by 2 is the simplest of the arithmetic tasks. Yet, it could be carried out in a number of ways. If you multiply by 2 in your head then it is often more convenient to multiply left-to-right and not right-to-left as we are all conditioned to do by the long multiplication algorithm. For example

1375×2 | = (1000 + 300 + 70 + 5)×2 | |

= 2000 + 600 + 140 + 10 | ||

= 2750. |

and also

7205×2 | = (7000 + 200 + 5)×2 | |

= 14000 + 400 + 10 | ||

= 14410. |

Note how useful here was the distributive law.

In the two examples above, we split a 4-digit number into four (decimal) pieces. There was no obligation to do so. For example, 1684×2 may be computed as

1684×2 | = (1000 + 600 + 80 + 4)×2 | |

= 2000 + 1200 + 160 + 8 | ||

= 3368. |

But here is another valid way:

1684×2 | = (1500 + 100 + 50 + 34)×2 | |

= 3000 + 200 + 100 + 68 | ||

= 3368. |

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