CHAPTER ONE.pdf

1.0 Addition of bases 1.1 Subtraction of bases (a) 4531six+523six Guide: 2-3 is not possible, so we “borrow” 1 from 7, and this is added to 2 as eight (because of the base). So we have 8+2=10. Therefore, now 10-3=7. So we write 7. And the process continues to the left. 2102three (d) 1001two+111two Guide: - 43eight Workout the following numbers. (f) 965ten+354ten (g) 223eight+254eight (a) 2131four-1213four (d) 242five-43five (b) 4125six-512six + 1211three (c) 1235ten-732ten 11020three Example: Subtract 43eight from 72eight. Into A Maths Genius Exercise: From the right, 2 + 1 = 3. But 3 in base three is 10, i.e. 3 ÷ 3 = 1 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟 0. So, we write 0 (the rem), and carry 1. On the left of 2, it’s no longer now 7, because of the 1 we removed. Its now 6. So 6-4=2.so we write 2. Therefore the answer is 27eight (b) 1890ten+4592ten (c) 6137eight+702eight 72eight Exercise: Solution. (e) 2031four+330four (h) 1134nine+2476nine CHAPTER 1: NUMBER BASES Example: Work out 2102three+1211three. Workout the following numbers. 27eight Sixes Tens 1.2 Identifying numbers of any base using the abacus Mathematics Book 1. Transform into A Maths Genius 1 | P a g e Ones Guide: Example: Represent 4508ten on the abacus. In “ones” place we draw 8 beads, in “tens” no bead, in “hundreds” we draw 5 beads and in “thousands we draw 4 beads. Exercise1: Identify the number represented on each of the abacus below and the corresponding base. (e) 203eight-46eight Hundreds Six-sixes Tens (h) 2210three-211three In t