Add in the indicated base. $$ \begin{array}{l}311_{ ext {five }} \ +344_{ ext {five }}\end{array} $$ The sum is $$ \square $$ five .

Question

Add in the indicated base. $$ \begin{array}{l}311_{	ext {five }} \ +344_{	ext {five }}\end{array} $$ The sum is $$ \square $$ five .

UpStudy AI · Accepted Answer

We want to add 
$$
311_{\text{five}} \quad \text{and} \quad 344_{\text{five}},
$$
performing the addition in base five.

1. **Rightmost Column (Units Place):**

Add $$1$$ (from $$311$$) and $$4$$ (from $$344$$):
   $$
   1 + 4 = 5.
   $$
   In base five, $$5$$ is represented as $$10_{\text{five}}$$. Write down $$0$$ and carry over $$1$$.

2. **Next Column (Fives Place):**

Add $$1$$ (from $$311$$), $$4$$ (from $$344$$), and the carried $$1$$:
   $$
   1 + 4 + 1 = 6.
   $$
   In base five, $$6 = 11_{\text{five}}$$. Write down $$1$$ and carry over $$1$$.

3. **Next Column (Twenty-Fives Place):**

Add $$3$$ (from $$311$$), $$3$$ (from $$344$$), and the carried $$1$$:
   $$
   3 + 3 + 1 = 7.
   $$
   In base five, $$7 = 12_{\text{five}}$$. Write down $$2$$ and carry over $$1$$.

4. **Process the Carry:**

Since there are no more digits, simply write the carried $$1$$ in the next column (the one representing $$5^3 = 125$$).

Thus, the digits from left to right are the carried $$1$$, then $$2$$, then $$1$$, and finally $$0$$. This gives:
$$
1210_{\text{five}}.
$$

The sum is $$ \boxed{1210_{\text{five}}} $$.
The sum is $$1210_{\text{five}}$$.

Add in the indicated base.

The sum is five .

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Add in the indicated base. The sum is five .