4) Use division to write \( \frac{4}{11} \) as a decimal. \( \begin{array}{l}\text { 4) How many times does } 11 \text { go into } 40 \text { ? } \\ \text { 4) } \square \text { times, with a remainder of } \square ? \\ \text { ? } \\ \begin{array}{l}1 1 \longdiv { 4 . 0 } \\ \frac{-0}{40}\end{array}\end{array} \)

To convert the fraction \( \frac{4}{11} \) into a decimal using division, we will perform long division. Here are the steps: 1. **Set up the division**: We want to divide 4.0 by 11. This means we are looking for how many times 11 goes into 40 (since we can add a decimal and a zero to 4 to make it 40). 2. **Determine how many times 11 goes into 40**: - 11 goes into 40 three times because \( 11 \times 3 = 33 \). - The remainder is \( 40 - 33 = 7 \). 3. **Write down the result so far**: - We have \( 3 \) as the first digit after the decimal point, and a remainder of \( 7 \). 4. **Bring down the next digit**: - We can bring down another 0, making it 70. 5. **Determine how many times 11 goes into 70**: - 11 goes into 70 six times because \( 11 \times 6 = 66 \). - The remainder is \( 70 - 66 = 4 \). 6. **Write down the next digit**: - We have \( 6 \) as the next digit after the decimal point, and a remainder of \( 4 \). 7. **Bring down another 0**: - We bring down another 0, making it 40 again. 8. **Repeat the process**: - We see that we are back to where we started, with \( 11 \) going into \( 40 \) three times, and the cycle will continue. Thus, the decimal representation of \( \frac{4}{11} \) is \( 0.363636... \), which can be written as \( 0.\overline{36} \). To summarize: - \( 11 \) goes into \( 40 \) **3** times, with a remainder of **7**. - \( 11 \) goes into \( 70 \) **6** times, with a remainder of **4**. - The decimal representation is \( 0.\overline{36} \).