# Thread: help with opererations and bases

1. ## help with opererations and bases

i am really confused about how to do these problems. i look at the examples but am still confused. any help would be graetly appreciated

1) AFCE base 16

3) 4341 base 5
x 3412 base 5

4) 1101 1001 0100
- 1010 1011 1010

2. Hello, dblbac!

Who assigned these problems? . . . They're awful!

And what methods are you allowed to use?

I'll explain the first one . . .

$\displaystyle 1)\quad\begin{array}{cc}& AFCE \\ - & FAD\,2 \\ \hline \end{array}\;\;\text{(base 16)}$ . . . . a dirty trick!
We are subtracting a larger number from a smaller number.
We must re-stack the numbers (larger on top) and make an addition problem. . **

. . $\displaystyle \begin{array}{cc} - & FAD\,2 \\ + & AFCE \\ \hline \end{array}\;\;\text{(base 16)}$

Then there are two ways to proceed:

[1] Perform the subtraction in base 16: . $\displaystyle \begin{array}{cc} - & FAD2 \\ + & AFCE \\ \hline {\color{blue}-} & {\color{blue}4\,B\,0\,4} \end{array}$

[2] Convert to base 10 and subtract: .$\displaystyle \begin{array}{cc} - & 64,\!210 \\ + & 45,\!006 \\ \hline - & 19,\!204\end{array}$

Then convert the answer to base 16: .$\displaystyle -19,\!204 \;=\;{\color{blue}-4\,B\,0\,4}\;\;\text{(base 16)}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**

Consider the subtraction: .$\displaystyle 25 - 50$

We know that the answer is: .$\displaystyle -25$

But just try to subtract like this: .$\displaystyle \begin{array}{cc} & 25 \\ -& 50 \\ \hline \end{array}$

Did you get a silly answer, like $\displaystyle -35$ ?

3. ## thanks

i got it now.