Solve using partial quotients. Write the remainder as a fraction. \( 629 \div 4= \)

To solve \( 629 \div 4 \) using partial quotients, we can start by estimating how many times 4 fits into 629. Let's say we take away multiples of 4 from 629: - First, we can subtract \( 4 \times 100 = 400 \) from 629. We get \( 629 - 400 = 229 \). So, count 100. - Next, we can subtract another \( 4 \times 50 = 200 \). Now we have \( 229 - 200 = 29 \). So, add 50 to our count: 100 + 50 = 150. - Now, let's see how many times 4 goes into 29. We can subtract \( 4 \times 7 = 28 \). Thus, \( 29 - 28 = 1 \). So, add 7 to our count: 150 + 7 = 157. Now we are left with 1, which is our remainder. To express the remainder as a fraction, we note that \( \frac{1}{4} \) is our remaining part when dividing by 4. So, \( 629 \div 4 = 157 \) with a remainder of \( \frac{1}{4} \).