Add in the indicated base. $$ \begin{array}{l}432_{\text {five }} \ +323_{\text {five }}\end{array} $$ The sum is $$ \square $$ five.

Question

UpStudy AI · Accepted Answer

We are given the following addition in base five:

$$
\begin{array}{r}
432_{\text{five}} \
+ \; 323_{\text{five}}
\end{array}
$$

We'll add column by column from right to left, remembering that any sum reaching $$5$$ or more must be written in base five.

**Step 1: Units Column (rightmost digit)**

$$
2 + 3 = 5
$$

Since $$5$$ in base five is written as $$10_{\text{five}}$$, we write down $$0$$ and carry $$1$$.

**Step 2: Tens Column**

$$
3 + 2 = 5,\quad \text{plus the carried } 1 \text{ gives } 6
$$

Now, $$6$$ in base five is $$1 \times 5 + 1$$, so it is written as $$11_{\text{five}}$$. Write down $$1$$ and carry $$1$$.

**Step 3: Hundreds Column**

$$
4 + 3 = 7,\quad \text{plus the carried } 1 \text{ gives } 8
$$

Express $$8$$ in base five: $$8 = 1 \times 5 + 3$$. Write down $$3$$ and carry $$1$$.

**Step 4: Thousands Column**

There are no more digits to add, but we have a remaining carry of $$1$$. Write it down in the thousands place.

**Final Answer**

Thus, the final sum is:

$$
1310_{\text{five}}
$$

So, the sum is $$ \boxed{1310_{\text{five}}} $$.
The sum is $$1310_{\text{five}}$$.

Add in the indicated base.

The sum is five.