How do I multiply two base 5 numbers with out converting them?

Question

The numbers are Base 5 numbers; 324 and 143. How do I multiply them? Know of any good internet sites that explain this?

Thanks for answering! Your responses are great! Thank you for taking the time to explain what to do. You have done a great job.

Answer 1

You do it the same way as you would decimals, except when you carry numbers, it's multiples of 5 instead of multiples of 10. Multiplying any two single digit numbers will yield a one or two digit answer.

For 324 x 143, the first step 3 x 4 = 22 in base 5 (that's 2x5 + 2). So you would carry the 2, and calculate (3x2)+2 = 13 (that's 1x5 + 3). Then you carry the 1, and calculate (3x3)+1 = 20 (2x5 +0). So the first product is 324 x 3 = 2032. You then repeat this process for 324 x 40 and 324 x 100 and add up all the numbers.

Answer 2

This Site Might Help You.

RE:
How do I multiply two base 5 numbers with out converting them?
The numbers are Base 5 numbers; 324 and 143. How do I multiply them? Know of any good internet sites that explain this?

Answer 3

Base 5 Multiplication Calculator

Answer 4

You multiply them the same way you do with base 10 numbers. You just need to use a base 5 multiplication table instead of the base 10 one.

Answer 5

You need a base 5 multiplication table and addition table. With those in hand, multiply just like you would with decimal numbers:

3x4 = 22, write down 2,carry 2
3x2 = 11, + 2 carried = 13, write down 3, carry 1
3x3 = 14, + 1 carried = 20, write down 20.

so .......324
............143
.........-------
..........2032

4x4 = 31, write down 1 under the 3, carry 3
4x2 = 13, + 3 = 21, write down 1, carry 2
4x3 = 22, + 2 = 24, write down 24

............324
............143
.........-------
..........2032
........2411

and so on. actually, I'm converting to base 5 as I go.

............324
............143
.........-------
..........2032
........2411
........324
.......---------
......114042

not easy. I checked by converting the 2 originals to decimal, multiplied, and converted back. found 3 errors.

Answer 6

5^5---5^4---5³---5²---5----1
------------------3----2-----4
------------------1----4-----3
-----------2-----0-----3-----2
---2------4-----1------1
----3------2-----4

1---1-----4----0------4-----2
is the answer.

Difficult to set out:-
Headings are powers of 5
324 X143 in base 5 is calculation.
The method is to perform a multiplication such as 3 x 4 = 12 = 2 remainder 2
remainder 2 is entered and the other 2 is carried to next column which becomes 3 x 2 plus the 2 that was carried = 8 = 1 r 3 in base 5
3 is entered and 1 is carried to next column
etc
3 x 3 = 9 plus 1 that was carried = 10 = 2 r 0
etc

Answer 7

The only way I'm sure of is building a base 5 multiplication table. Otherwise you end up doing conversions on each step.

Answer 8

Do you mean the base of an exponent? Say you have a^x, and you want to convert this to a term with base b. The first step is to solve the equation: a = b^y log a = y log b y = (log a)/(log b) Now, since a = b^y: a^x = (b^y)^x = b^(xy) = b^((x log a)/(log b)) Well, there's a simple conversion formula. If that's what you were looking for, anyway.