Long Division - Examples, Exercises and Solutions

To solve the division problem $90 \div 6$, follow these steps:

• Step 1: Identify the numbers involved, where 90 is the dividend and 6 is the divisor.
• Step 2: Divide 90 by 6 using long division.
• Step 3: Determine how many times 6 fits into 90 without exceeding it.

Let's perform the division:

90 divided by 6 equals 15, as 6 fits perfectly into 90 fifteen times (since $6 \times 15 = 90$). There is no remainder left over.

Given the multiple-choice options, the correct choice is: $15$.

This means that 6 goes into 90 exactly 15 times, matching Option 1 of the given choices.

To solve the problem of dividing 25 by 5, we follow these steps:

• Step 1: Identify the dividend and the divisor. In this case, the dividend is 25 and the divisor is 5.
• Step 2: Perform the division $25 \div 5$.

Now, let's execute the division:

Step 1: Divide 25 by 5. We ask ourselves how many times does 5 fit into 25.

Step 2: 5 goes into 25 exactly 5 times because $5 \times 5 = 25$ and there's no remainder.

Thus, we find that the quotient is 5.

Therefore, the answer to the problem is $5$.

To solve the problem of dividing 65 by 5, follow these steps:

• Step 1: Identify the dividend, which is 65, and the divisor, which is 5.
• Step 2: Perform the division operation $65 \div 5$.
• Step 3: Calculate the quotient by determining how many times 5 goes into 65 evenly.

Now, let's execute the division:
Step 1: We recognize that 65 is the number to be divided, and 5 is the divisor.
Step 2: Apply division: $65 \div 5 = 13$.
Since 65 divided by 5 yields a quotient of 13 without any remainder, we have found our solution.

Thus, the answer to the division problem is $13$.

To solve the problem $39 \div 3$, we will apply long division:

• Step 1: Set up the division problem.
  Write 39 inside the division bracket and 3 outside as the divisor.
• Step 2: Divide the first digit of the dividend by the divisor.
  Determine how many times 3 fits into 3 (the first digit of 39):
  3 fits into 3 exactly 1 time. Write 1 above the line.
• Step 3: Multiply and subtract.
  Multiply 3 (divisor) by the result from the previous step (1), giving 3.
  Subtract 3 from 3, resulting in 0.
• Step 4: Bring down the next digit of the dividend.
  Bring down 9 (the next digit from 39). The new number to consider is 9.
• Step 5: Divide the result by the divisor.
  Determine how many times 3 fits into 9: 3 fits into 9 exactly 3 times. Write 3 above the line.
• Step 6: Multiply and subtract again.
  Multiply 3 by 3, which gives 9. Subtract 9 from 9, resulting in 0.

The division process is complete with no remainder. The quotient is 13.

The final answer is $\boxed{13}$.

To solve this division problem, we will divide the number 48 by 4 and find the quotient.

The expression for this calculation is:

$\frac{48}{4}$

Let's perform the division:

• We start with the number 48.
• We divide 48 by 4. The question we are asking is: "How many times does 4 go into 48?"
• By calculating, we find that 4 fits into 48 exactly 12 times.

The steps can be broken down as follows:

• 4 goes into the first digit of 48 (4), 1 time.
• The remainder from this division is 0, bring down the next digit, which is 8.
• 4 goes into 8, 2 times (as 4 × 2 = 8).
• There is no remainder, confirming the division is complete.

Thus, the quotient of 48 divided by 4 is:

$12$

Therefore, the correct answer is 12, which corresponds to choice 4.

To solve this division problem, we will proceed as follows:

• Identify the dividend, which is 50, and the divisor, which is 5.
• Use the division formula: $\frac{\text{dividend}}{\text{divisor}} = \text{quotient}$.
• Calculate the quotient by dividing 50 by 5.

Let's carry out the calculation step:

The division is $\frac{50}{5} = 10$.

Therefore, the quotient of 50 divided by 5 is $10$.

The correct choice from the given options is: Choice 2: $10$.

To solve this problem, let's carry out the division:

• Step 1: Confirm the numbers involved. We are dividing 38 by 2, where 38 is the dividend and 2 is the divisor.
• Step 2: Perform the division using long division or directly calculate $38 \div 2$.
• Step 3: Start dividing: 2 goes into 3 one time (since 2 fits into 3 once), leaving a remainder of 1.
• Step 4: Bring down the next digit from the dividend. The sequence now is: how many times does 2 go into 18?
• Step 5: 2 fits into 18 nine times exactly without any remainder.

Thus, $38 \div 2 = 19$.

Therefore, the solution to this problem is $19$.

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

• Step 1: Identify the numbers involved: 60 (dividend) and 3 (divisor).
• Step 2: Perform the division operation to find the quotient.

Let's work through these steps:

Step 1: In this problem, we need to divide 60 by 3.
Step 2: Using basic division, we calculate:

$60 \div 3 = 20$

How we calculated this:
- Divide the tens digit, 6 by 3, which equals 2. Note that 2 as the first digit of the quotient corresponds to twenty since this operation considers the tens place.
- Multiply 2 by 3 to get 6, which subtracted from the original 6 leaves 0.
- Bring down the 0 in the units place.
- Now, divide 0 by 3. This results in 0.
- So, the units place of our quotient is also 0, confirming our answer is 20.

Therefore, the solution to the problem is $20$. This matches choice 3 (20) in the available options.

To solve this problem, we'll perform a simple division calculation:

• Step 1: Identify the numbers involved in the division. We have a dividend of 16 and a divisor of 2.
• Step 2: Use the division formula: $\text{quotient} = \frac{\text{dividend}}{\text{divisor}}$.
• Step 3: Substitute the numbers into the formula: $\text{quotient} = \frac{16}{2}$.
• Step 4: Perform the division: $16 \div 2 = 8$.

Therefore, the solution to the problem is $8$.

To solve this problem, we'll use the simple division approach:

• Step 1: Identify the dividend and divisor. Here, the dividend is 14, and the divisor is 7.
• Step 2: Apply the formula for division, $\frac{14}{7}$.
• Step 3: Calculate the division.

Now, let's work through each step:
Step 1: The given problem provides the dividend (14) and the divisor (7).
Step 2: Using the formula for division, divide the dividend by the divisor: $\frac{14}{7}$.
Step 3: Performing the calculation gives us a quotient of 2.

Therefore, the solution to the problem is $2$, matching choice 3 in the provided options.

To solve this problem, we will divide 22 by 2 to find the quotient.

Step-by-step solution:

• Step 1: Set up the division of 22 by 2.
• Step 2: Divide the first digit of 22, which is 2, by 2. This gives us 1, with no remainder.
• Step 3: Bring down the next digit, 2, making it 2 again.
• Step 4: Divide 2 by 2, which gives us another 1.
• Step 5: There are no more digits to bring down, and no remainder is left.

Therefore, the quotient when dividing 22 by 2 is $11$.

Comparing this with the provided multiple-choice options, the correct choice is option 3: $11$.

To determine the result of dividing 184 by 8, we use long division:

1. **Set up the division**: Write 184 under the division bracket with 8 outside.
2. **Analyze the first digit**: 8 goes into 18, the first two digits of 184, a total of 2 times since $8 \times 2 = 16$.
3. **Subtract 16 from 18**: We get a remainder of 2. Bring down the next digit 4, giving us 24.
4. **Divide again**: 8 goes into 24 exactly 3 times because $8 \times 3 = 24$.
5. **Subtract**: Subtracting gives zero remainder.

Thus, the quotient is 23, confirming that $184 \div 8 = 23$ without any remainder. The operation has been checked accurately by multiplying 23 by 8, which yields 184.

Therefore, the solution to the division problem is $23$. This matches the correct choice provided in the list of options.

To solve the division of $100$ by $5$ using long division, we follow these steps:

• Step 1: Divide the leftmost digit of the dividend $1$ by the divisor $5$. Since $1$ is smaller than $5$, we look at the first two digits of the dividend $10$.
• Step 2: Divide $10$ by $5$ to get $2$. Write $2$ above the dividend.
• Step 3: Multiply $2$ by $5$, giving us $10$. Subtract $10$ from $10$ to get $0$.
• Step 4: Bring down the next digit $0$. Divide this $0$ by $5$, which gives us $0$. Write $0$ next to the $2$.
• Step 5: Multiply this $0$ by $5$, which also gives $0$. Subtract $0$ from $0$ to get $0$ again.

The quotient of this division is $20$. Therefore, the result of dividing $100$ by $5$ is $20$.

To solve the problem of dividing 306 by 2 using long division, we will follow these steps:

• Step 1: Set up the expression as $306 \div 2$.
• Step 2: Begin the division with the hundreds digit.
• Step 3: Move to the tens digit and then finally to the units digit.

Let's proceed with these steps:

Step 1: Start with the hundreds place. Divide 3 (from 306) by 2. The quotient is 1, and we write it atop. Multiply 1 by 2, which gives 2, and subtract it from 3, leaving a remainder of 1. Bring down the next digit (0).

Step 2: Divide 10 by 2. The quotient is 5. Write 5 atop the division bar. Multiply 5 by 2, resulting in 10. Subtract 10 from 10, leaving no remainder. Bring down the next digit (6).

Step 3: Divide 6 by 2. The quotient is 3. Write 3 directly next to the previous quotient digits (1 and 5) on top. Multiply 3 by 2, which gives 6. Subtract this from 6, which yields 0, showing no remainder.

Thus, by performing long division, we find that:

The solution to the division $306 \div 2$ is $\mathbf{153}$.

To solve the problem of dividing 518 by 7, we'll perform long division:

1. Start with the first digit of the dividend, which is 5, in the hundreds place.

• $7$ does not go into $5$, so proceed to the next digit to make it 51.

2. Determine how many times $7$ goes into $51$ completely:

• $7 \times 7 = 49$, which is closest to 51 without exceeding it.
• Write $7$ as part of the quotient.
• Subtract $49$ from $51$, which leaves a remainder of $2$.

3. Bring down the next digit from the dividend, which is $8$, making the new number $28$.

4. Determine how many times $7$ goes into $28$ completely:

• $7 \times 4 = 28$, which equals 28.
• Write $4$ as the next digit of the quotient.
• Subtract $28$ from $28$, which leaves a remainder of $0$.

Since we reach a remainder of 0 after using all digits of the dividend, the division is exact. Therefore, the result is:

$74$. Thus, the correct answer is choice 3.