Question

Write
11
5
​
as a decimal.
5 ones is equivalent to 50 tenths. Divide 50 tenths by 11. Then multiply and subtract to show how many tenths you have left to share.
0 .
4

1 1 5 .0

.
.

Answer 1

To convert the fraction \( \frac{11}{5} \) to a decimal, we can follow the steps in your prompt.

1. **Understanding the problem**: We need to express \( \frac{11}{5} \) in decimal form.

2. **Find how many tenths are there**:
- We know that \( 5 \) ones is equivalent to \( 50 \) tenths. Therefore, let's consider \( \frac{11}{5} \) in terms of tenths.

3. **Divide tenths by 11**:
\[
50 \text{ tenths} \div 11
\]
Let's perform the long division:

1. **How many times does 11 fit into 50?**
- \( 11 \times 4 = 44 \)
- \( 11 \times 5 = 55 \) (too much)
- So \( 11 \) fits into \( 50 \) a total of \( 4 \) times.

4. **Multiply and subtract**:
- Now, \( 11 \times 4 = 44 \)
- Subtract:
\[
50 - 44 = 6
\]
So, after dividing, we have \( 4 \) tenths with \( 6 \) tenths remaining.

5. **Bringing down the next digit**:
Since we are looking for a decimal, we can continue.

- Take the remainder \( 6 \) (as \( 6.0 \)), and consider it as \( 60 \) tenths (adding a zero to continue the division).
- \( 60 \div 11 \):
- Fits \( 5 \) times, since \( 11 \times 5 = 55 \).
- Subtract:
\[
60 - 55 = 5
\]

6. **Continue this process**:
- Bring down another \( 0 \) making it \( 50 \) again.
- From here, we see a pattern emerging:

- \( 50 \div 11 = 4 \) with a remainder of \( 6 \).
- This repeats continuously, giving you \( 0.4 \) and then another \( 5 \), back to \( 50 \).

Putting this all together, we get:
\[
\frac{11}{5} = 2.2
\]

Thus, the final answer is:
\[
\frac{11}{5} = 2.2
\]