5. Use the partial quotients method to find \( 1,032 \div 43 \)

To solve \( 1,032 \div 43 \) using the partial quotients method, we will follow these steps: 1. **Estimate how many times 43 can fit into 1,032.** We can start by estimating with multiples of 43. 2. **Subtract the product from the dividend (1,032) and repeat.** We will continue this process until the remainder is less than 43. Let's go through the steps: ### Step 1: Initial Estimate - We can start by estimating how many times 43 fits into 1,032. - A good starting point is to try \( 20 \times 43 \). Calculating \( 20 \times 43 \): \[ 20 \times 43 = 860 \] ### Step 2: Subtract and Repeat Now, we subtract 860 from 1,032: \[ 1,032 - 860 = 172 \] Next, we see how many times 43 fits into 172. We can try \( 4 \times 43 \). Calculating \( 4 \times 43 \): \[ 4 \times 43 = 172 \] Now, we subtract 172 from 172: \[ 172 - 172 = 0 \] ### Step 3: Combine the Quotients Now we can combine our estimates: - From the first step, we had \( 20 \). - From the second step, we had \( 4 \). Adding these together gives us: \[ 20 + 4 = 24 \] ### Conclusion Thus, the result of \( 1,032 \div 43 \) using the partial quotients method is: \[ \boxed{24} \]