Presentation on theme: "Section 7.3 Multiplication in Different Bases"— Presentation transcript:
1Section 7.3 Multiplication in Different Bases Chapter 7Section 7.3Multiplication in Different Bases
2Multiplying Numbers in Different Bases Multiplying numbers in different bases requires the need to have learned both the basic addition and the basic multiplication facts in another base. The table below give the basic addition facts for base four.The reasoning for how we have gotten some of the entries is shown below.24 24 = 4 (base 10) = 10424 34 = 6 (base 10) = 12434 34 = 9 (base 10) = 21404142434104124214234 314341 32041 20210430 31200430 202033413224 341243 212043 20210043 300300043 1000112324The examples to the right show how to use the standard partial products algorithm in different bases. The first shows how to multiply 234 314. The second shows how to multiply 34.
3One shift in place value. 256 34632612062306100061422645 = 206 = 3 remainder 2No shift in place value.42 = 86 = 1 remainder 2One shift in place value.35 = 156 = 2 remainder 3One shift in place value.32 = 66 = 1 remainder 0Two shifts in place value.Add up all the numbersA second way to do this is to convert to base 10, do the multiplication like you ordinarily do the convert back to base 6.256346Convert Back3746 = 62 remainder 2626 = 10 remainder 2106 = 1 remainder 416 = 0 remainder 1The answer is: 14226(Like above)51 = 526 = 1241 = 436 = 181722Do the base 10 multiplication with these numbers.17 22 = 374
4The Lattice MethodAnother method for multiplying numbers which provides more structure for how you multiply is called the lattice method of multiplication. It uses a diagonally represented table and fills in the entries with the basic multiplication facts.For Example: to do the problem 317 46 = 145821. Fill in the corresponding squares with the basic multiplication facts putting the tens digit above the diagonal.2. Add down each diagonal starting at the bottom right carrying into the next diagonal.3174611121248144862582145823. The final answer you get by taking the digits going down the left side and along the bottom.
5Multiplication of Numbers in Other Bases Using the Lattice Method The lattice method for multiplication can be used to organize how numbers are multiplied. It relies on using the basic multiplication facts. Below to the right we show how to do the base four multiplication problem 3124 I have given the base 4 basic multiplication facts below to the right.04142434104124214312111112222111321312332263411The lattice to the right demonstrates how to do the base 7 multiplication problem 267 347.2164313131313137