Long Division: Division of a 3-digit number with a remainder

To solve this problem, we'll divide 803 by 2 using long division, following detailed steps:

• Step 1: Divide the first digit of the dividend (8) by the divisor (2). 2 fits into 8 exactly 4 times, so the first digit of the quotient is 4.
• Step 2: Multiply the divisor (2) by this part of the quotient (4), resulting in 8. Subtract this product from 8, yielding a remainder of 0.
• Step 3: Bring down the next digit of the dividend, which is 0 (from the number 80).
• Step 4: Divide 0 by 2, which fits 0 times, adding another digit (0) to the quotient.
• Step 5: Bring down the final digit of the dividend, which is 3.
• Step 6: 2 fits into 3 a total of 1 time. This results in an additional 1 in the quotient.
• Step 7: Subtract, and this product of 1 (remainder from step) gives us the remainder, 1.

The long division yields a quotient of 401 with a remainder of 1.

Therefore, the answer to the problem is $401$ with a remainder of 1.

To solve this arithmetic problem using long division, we will divide 831 by 2.

Let's perform the steps:

• Set up 831 divided by 2.
• Look at the first digit of 831: 8. Divide 8 by 2, which equals 4. Write 4 as the first digit of the quotient.
• Multiply 4 by 2 to get 8. Subtract 8 from 8 to get 0. Bring down the next digit, which is 3.
• Now divide 3 by 2. 2 fits into 3 one time. Write 1 as the next digit of the quotient.
• Multiply 1 by 2, yield 2. Subtract 2 from 3 to get a remainder of 1. Bring down the next digit, 1, to make 11.
• Next, divide 11 by 2. 2 fits into 11 five times. Write 5 as the next digit of the quotient.
• Multiply 5 by 2, giving 10. Subtract 10 from 11 to get a remainder of 1.

The quotient is 415 and the remainder is 1.

Therefore, the solution to the problem is $415$ with a remainder of 1.

To find the solution to this division problem, we will use long division:

• Step 1: Consider the first digit of 999, which is 9. Divide 9 by 4.
• Step 2: The closest multiple of 4 that does not exceed 9 is 8 (since $4 \times 2 = 8$). Thus, the first digit of our quotient is 2.
• Step 3: Subtract 8 from 9, leaving a remainder of 1. Bring down the next digit from the dividend, which leaves us with 19.
• Step 4: Divide 19 by 4. The closest multiple of 4 is 16 ($4 \times 4 = 16$). So, the next digit of the quotient is 4.
• Step 5: Subtract 16 from 19, leaving a remainder of 3. Bring down the next digit from the dividend, giving us 39.
• Step 6: Divide 39 by 4. The closest multiple is 36 ($4 \times 9 = 36$). Thus, the final digit of the quotient is 9.
• Step 7: Subtract 36 from 39, providing a final remainder of 3.

Hence, the quotient is $249$, with a remainder of 3.

The correct answer to the problem is option 1: $249$ Rest 3.

To solve the problem, we will perform a long division of 816 by 5.

Let's go through the steps of long division:

• Step 1: Divide the first digit of the dividend: $8 \div 5 = 1$. The quotient so far is 1.
• Step 2: Multiply 1 (quotient) by 5 (divisor) to get 5.
• Step 3: Subtract 5 from 8 which gives a remainder of 3. Bring down the next digit (1) to make it 31.
• Step 4: Divide 31 by 5. $31 \div 5 = 6$ remainder 1. The quotient now is 16.
• Step 5: Multiply 6 (newest quotient digit) by 5 to get 30.
• Step 6: Subtract 30 from 31 which leaves a remainder of 1. Bring down the last digit (6) of the original number to make it 16.
• Step 7: Divide 16 by 5. $16 \div 5 = 3$ remainder 1. Add 3 to the quotient making it 163.
• Step 8: Multiplying 3 by 5, we get 15.
• Step 9: Subtract 15 from 16 to get a final remainder of 1.

This implies the complete division yields a quotient of 163 with a remainder of 1.

Therefore, the solution to the problem is $163$ with a remainder of 1.

To solve this problem using long division, follow these steps:

• Step 1: Start with the first digit of the dividend.

The dividend is 974, and the divisor is 5.
Take the first digit of the dividend, which is 9. Divide 9 by 5 to get 1 because 5 goes into 9 once.

• Step 2: Subtract and bring down the next digit.

Multiply the divisor (5) by the quotient digit (1): $5 \times 1 = 5$.
Subtract this from 9 to get a remainder of 4: $9 - 5 = 4$.
Bring down the next digit from the dividend (7), making the new number 47.

• Step 3: Repeat the division process.

Now divide 47 by 5. 5 goes into 47 nine times, so the next digit of the quotient is 9.
Multiply the divisor (5) by this quotient digit (9): $5 \times 9 = 45$.
Subtract this from 47 to get a remainder of 2: $47 - 45 = 2$.
Bring down the final digit (4), making the new number 24.

• Step 4: Divide the last number.

Finally, divide 24 by 5. 5 goes into 24 four times. The last digit of the quotient is 4.
Multiply the divisor (5) by 4: $5 \times 4 = 20$.
Subtract this from 24 to get a final remainder of 4: $24 - 20 = 4$.

Thus, the result of 974 divided by 5 is a quotient of $194$ with a remainder of $4$.

The correct choice is therefore Choice 4: $194$ with a remainder of $4$.

To solve this problem, we'll follow these steps:

• Step 1: Set up the division of $617$ by $6$.
• Step 2: Perform the long division to find the quotient and remainder.

Now, let's work through each step:

Step 1: We start by setting up the division as follows: place $6$ outside the division symbol and $617$ inside.

Step 2: Perform the division:

• Divide the first digit $6$ by $6$, which gives $1$. Thus, the first digit of the quotient is $1$. Subtract $6 \times 1 = 6$ from $6$, resulting in $0$. Bring down the next digit, which is $1$, giving us $01$.
• Since $6$ does not divide into $1$ (or $01$), we place a $0$ in the quotient and bring down the next digit, $7$, making it $17$.
• Divide $17$ by $6$, which gives $2$ as the quotient digit. Subtract $6 \times 2 = 12$ from $17$, resulting in $5$.

The quotient is $102$ and the remainder is $5$.

Therefore, the solution to the problem is $102$ with a remainder of $5$.

To solve this problem, we need to perform long division on 878 by 6 to find the quotient and remainder.

First, examine how many times 6 fits into the digits of 878 from left to right.

• Step 1: Determine how many times 6 fits into the first part of 878. 6 fits into 8 once. Below the 8, write 6, because $6 \times 1 = 6$.
• Subtract 6 from 8, which gives a remainder of 2. Bring down the next digit, 7, making the number 27.
• Step 2: Determine how many times 6 fits into 27. 6 fits into 27 four times. Below the 27, write 24, because $6 \times 4 = 24$.
• Subtract 24 from 27, which gives a remainder of 3. Bring down the last digit, 8, making the number 38.
• Step 3: Determine how many times 6 fits into 38. 6 fits into 38 six times. Below the 38, write 36, because $6 \times 6 = 36$.
• Subtract 36 from 38, which gives a final remainder of 2.

Thus, the quotient is 146 with a remainder of 2.

Therefore, the solution to the problem is $146$ with a remainder of 2.

To solve this problem, we'll use long division to divide 234 by 7 and find both the quotient and remainder:

• Step 1: Set up the long division by writing 234 inside the division bracket and 7 outside.
• Step 2: Divide the first digit, 2, by 7. Since 2 is smaller than 7, consider the first two digits, 23.
• Step 3: Determine how many times 7 fits into 23. It fits 3 times (since $7 \times 3 = 21$).
• Step 4: Subtract 21 from 23, leaving a remainder of 2.
• Step 5: Bring down the next digit of the dividend, 4, making the new number 24.
• Step 6: Determine how many times 7 fits into 24. It fits 3 times (since $7 \times 3 = 21$).
• Step 7: Subtract 21 from 24, leaving a remainder of 3.
• Step 8: No more digits left to bring down. Therefore, the division completes here.

The quotient of dividing 234 by 7 is 33, with a remainder of 3.
Thus, the solution to the problem is $33$ with a remainder of 3.

Based on the choices provided, this corresponds to choice 2, which states:
$33$ with a remainder of 3.

To solve the problem of dividing 321 by 8, we'll perform long division. Here are the steps:

• Step 1: Set up 321 as the dividend and 8 as the divisor.
• Step 2: Determine how many times 8 fits into the first digit of 321. Since 8 goes into 32 (the first two digits) four times without exceeding it, write 4 above the dividend.
• Step 3: Multiply 8 by 4 giving 32, and subtract 32 from 32, resulting in 0.
• Step 4: Bring down the next digit, 1, making the current number 1.
• Step 5: Determine how many times 8 fits into 1. It fits 0 times, placing a 0 in the quotient.
• Step 6: Since there are no more digits to bring down, 1 becomes the remainder.

Therefore, the quotient is 40 and the remainder is 1.

Thus, the solution to dividing 321 by 8 is: $\text{Quotient} = 40$, $\text{Remainder} = 1$.

According to the given choices, the correct choice is: $40$ with a remainder of 1

To solve this problem, we'll perform long division of 974 by 8. Here are the detailed steps:

• Step 1: Set up the division
  Write 974 under the division bar and 8 outside.
• Step 2: Divide
  Start with the leftmost digit, which is 9.
  8 goes into 9 one time ($8 \times 1 = 8$).
  Subtract 8 from 9 to get a remainder of 1.
• Step 3: Bring down the next digit
  Bring down 7, the next digit of 974, to make it 17.
  8 goes into 17 two times ($8 \times 2 = 16$).
  Subtract 16 from 17 to get a remainder of 1.
• Step 4: Bring down the last digit
  Bring down the last digit, which is 4, making it 14.
  8 goes into 14 one time ($8 \times 1 = 8$).
  Subtract 8 from 14 to get a remainder of 6.

Putting it all together, the quotient is 121, and the final remainder is 6.

Therefore, the solution to the problem is $121$ with a remainder of 6.

Among the choices given, the correct one is choice 4: $121$ with a remainder of 6.

To solve this problem, we will use the long division method on $631 \div 9$.

• Step 1: Observe the dividend $631$ and divisor $9$.

• Step 2: Start division with the leftmost digit of the dividend:

  • $9$ into the first significant digit $6$ gives a quotient of $0$ (as 9 > 6 ).

  • Extend to the next digit for $63$. Divide $63 \div 9 = 7$, since $9 \times 7 = 63$.

  • Subtract: $63 - 63 = 0$. Now, bring down the next digit $1$.

  • With the current remainder $1$, dividing $1 \div 9$ gives zero quotient, remainder stays $1$.

• Final Step: Overall, $631 \div 9 = 70$ with a remainder of $1$ as $9 \times 70 + 1 = 631$.

Therefore, the solution to the problem is $70$ with a remainder of $1$.

To solve this problem, we'll follow these steps:

• Step 1: Use long division to divide 722 by 9.

• Step 2: Calculate the quotient and remainder during division.

• Step 3: Verify against the given multiple-choice options.

Now, let's work through each step:

Step 1: Begin with the long division of 722 by 9.

Step 2: Breakdown the division:
- 9 goes into 72 eight times (because $9 \times 8 = 72$). - Subtract $72$ from $72$, leaving $0$.
- Bring down the next digit $2$.
- 9 goes into 2 zero times.
- This gives a quotient of $80$ and a remainder of $2$, since $80 \times 9 + 2 = 722$.

Step 3: Verify with choices:
- Compare the quotient $80$ and remainder $2$ against the options provided.
- The correct choice is: $80$ with a remainder of $2$.

Thus, the answer is that $9$ goes into $722$, leaving a quotient of $\mathbf{80}$ and a remainder of $\mathbf{2}$.

To solve this problem, we need to divide 979 by 9 using long division.

The steps are as follows:

• Step 1: Divide the first digit. 9 divided by 9 is 1. Write 1 as the first digit of the quotient.
• Step 2: Multiply 1 by 9 and subtract from 9. This leaves 0. Bring down the next digit, 7.
• Step 3: Now divide 7 by 9. The result is 0 (because 7 is less than 9). Write 0 as the next digit of the quotient.
• Step 4: Bring down the next digit, which is 9, making it 79.
• Step 5: Divide 79 by 9. This gives 8 since 9 times 8 is 72.
• Step 6: Multiply 8 by 9 giving 72, and subtract from 79 leaving a remainder of 7.

The quotient of the division is 108 with a remainder of 7.

Therefore, the solution to the problem is $108$ with a remainder of 7.

Let's solve this division problem using the long division method.

• We need to divide $988$ by $9$.
• Begin by considering the first digit $9$ in $988$. Since $9$ goes into $9$ exactly once, we write down $1$ above the division line, creating a current quotient of $1$.
• Multiply $1 \times 9 = 9$, and subtract from $9$, leaving $0$.
• Bring down the next digit $8$, making the number $8$.
• Determine how many times $9$ fits into $8$. It fits $0$ times, so write down $0$ as the next digit in the quotient.
• Bring down the last digit $8$, now making the number $88$.
• Now see how many times $9$ fits into $88$. $9$ fits $9$ times (since $9 \times 9 = 81$.
• Write $9$ above the line as the final digit of the quotient, giving us $109$.
• Subtract $9 \times 9 = 81$ from $88$ to find the remainder: $88 - 81 = 7$.

Therefore, the quotient is $109$ with a remainder of $7$.

Referring to the answer choices, the correct choice is: $109$ with a remainder of 7.