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What happens when the digit 8 simply doesn't exist? This lesson dives into multiplication and division in number bases other than 10, showing how the familiar rules of arithmetic must be rebuilt from the ground up. Drawing from Section 4.5 of OpenStax Contemporary Mathematics, the discussion walks through how repeated addition constructs entirely new multiplication tables — and why blindly applying base-10 habits leads to errors. In this video: • Multiplication as repeated addition — and why the zero and identity properties hold in any base • Step-by-step example: computing 2 × 3 in base 6 using base 6 addition rules, arriving at 10₆ • How to build a complete base 6 multiplication table using only repeated addition • Division in other bases as the reverse of multiplication, illustrated with the 72 ÷ 9 = 8 model • Error type 1: using illegal symbols (e.g., writing 8 in a base 5 answer) • Error type 2: applying base-10 facts to other bases (e.g., assuming 6₁₇ × 9₁₇ = 54₁₇) • Base system efficiency — comparing the number of multiplication rules in base 2, base 6, base 10, and base 14 #OpenStax #ContemporaryMathematics #NumberBases #Arithmetic OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US
Answer each question based only on what was presented in the video lesson. No outside knowledge is needed — all answers can be found in the video.
Apply what you learned about arithmetic in different number bases. Show all work step by step, using repeated addition to build your answers. Problems increase in difficulty.
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