Base 5 fill in the blank

[rchristian]

I need to fill in the blanks using base 5.

204_ ₅
_4 _{5
_______________}
_ _ 332
_ 141



I don't understand where to even start, please help.

 

[soroban]

Hello, rchristian!

I need to fill in the blanks using base 5.
I assume this is a multiplication problem.

. . \(\displaystyle \begin{array}{ccccccc} && 2 & 0 & 4 & p \\ & \times &&& q & 4 \\ \hline & r & s & 3 & 3 & 2 \\ & t & 1 & 4 & 1 \\ \hline u & v & w & x & y & z \end{array} \)

In the first multiplication, \(\displaystyle 4 \times p\) ends in 2.
. . Hence: .\(\displaystyle p = 3.\)

Multiplying \(\displaystyle 4 \times 2043\), we have the first partial product: .\(\displaystyle 13332\)

. . \(\displaystyle \begin{array}{ccccccc} && 2 & 0 & 4 & {\bf3} \\ & \times &&& q & 4 \\ \hline & {\bf1} & {\bf3} & 3 & 3 & 2 \\ & t & 1 & 4 & 1 \\ \hline u & v & w & x & y & z \end{array} \)


In the second multiplication, \(\displaystyle q \times 3\) ends in 1.
. . Hence, \(\displaystyle q = 2.\)

. . \(\displaystyle \begin{array}{ccccccc} && 2 & 0 & 4 & 3 \\ & \times &&& {\bf2} & 4 \\ \hline & 1 & 3 & 3 & 3 & 2 \\ & {\bf4} & 1 & 4 & 1 \\ \hline u & v & w & x & y & z \end{array} \)


Finally, perform the addtion.

. . \(\displaystyle \begin{array}{ccccccc} && 2 & 0 & 4 & 3 \\ & \times &&& 2 & 4 \\ \hline & 1 & 3 & 3 & 3 & 2 \\ & 4 & 1 & 4 & 1 \\ \hline {\bf1} & {\bf1} & {\bf0} & {\bf2} & {\bf4} & {\bf2} \end{array} \)