Subject: base 5

my daughter is 9 and has been aske to solve the following in base 5


Cupld you please explain the formula for working in base 5 many thanks lesley emerson

Hi Lesley,

The key to understanding arithmetic in a base other than 10 is to understand the notation we use in base ten. For example in base ten we write the number twenty-three as 23, meaning 2 tens and 3 ones. It may help your daughter to think about some objects, like sticks. The idea is to take the twenty-three sticks and arrange them in groups of ten. You get 2 groups of ten and three extra. If you then add 23 and 59 you put together the 3 ones with the 9 ones giving twelve ones, which is 1 ten and 2 extra. That is you get one more group of ten sticks. That is the "carry". So altogether you have 5 + 2 + 1 tens and 2 ones, for a sum of 82.

In base five you want to collect the objects in groups of fives rather than tens. So if you have nine objects you can arrange them into one group of five and 4 ones. Thus nine, written in base 5 is 14 (1 five plus 4 ones). Your daughter's text may say 145 where the "5" indicates that this is in base 5.

Now to add 2 and 3 using base 5 notation, 2 + 3 is five, which in base 5 is one group of five and no ones. That is 2 + 3 = 10 in base five. (You should read this as two plus three is one zero in base 5.) For the next problem, 10 in base 5 is five (one five and no ones) so 4 + 10 in base five is four plus five which is nine, and nine in base five is written 14 (1 five and 4 ones). Remember to read this as one four in base 5; it's not fourteen.

Lets do one more addition, 11 + 2 + 13. (When in doubt think about the sticks.) The sum of the units column is 1 + 2 + 3 which is six, that is 1 five and 1 one. The 1 five is a carry (group of five sticks) and the sum of the next column, called the fives column, is 1 + 1 + "the carry" which is 3. Thus 11 + 2 + 13 is 31 in base 5.

Finally I'll do one multiplication. 3 x 4 is twelve which is 2 fives and 2 ones, so 3 x 4 in base 5 is 22.

I hope this helps,
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