Long Division Practice Problems with Step-by-Step Solutions

Master long division with guided practice problems. Learn the divide, multiply, subtract, bring down method through interactive exercises and detailed solutions.

📚Practice Long Division Step-by-Step
  • Divide two-digit numbers by single-digit divisors using standard notation
  • Solve three-digit by one-digit division problems with remainders
  • Master division by two-digit numbers using the DMSB method
  • Identify quotients and remainders in complex division problems
  • Apply long division notation with dividend, divisor, and quotient placement
  • Handle cases where digits are smaller than the divisor

Understanding Long Division

Complete explanation with examples

Long Division

Long division is a method used to divide large numbers by breaking down the process into a series of easier steps, dealing with one digit at a time. This technique is especially useful for dividing numbers that don’t divide evenly.

How to use Long Division?

We'll go step by step, dividing one digit at each step. We'll start with the digit on the left, write down the division result above the drawn line, and look for the remainder.
To do so, follow these steps:

  1. Divide: Determine how many times the divisor fits into the first few digits of the dividend.
  2. Multiply: Multiply the divisor by the quotient found in the first step and write the result under the dividend.
  3. Subtract: Subtract the result from the dividend to find the remainder.
  4. Bring Down: Bring down the next digit of the dividend and repeat the process.
  5. Repeat: Continue until all digits have been brought down and divided, resulting in a final quotient and possibly a remainder.

Long Division Notation

In long division, the notation is set up to clearly show the process of dividing step-by-step. The main elements include:

  1. Dividend: The number being divided. It is placed inside the long division symbol (also known as the “division bracket”).
  2. Divisor: The number by which you are dividing. This is placed outside the division bracket, on the left.
  3. Quotient: The result of the division. It is written on top of the division bracket, directly above each respective digit of the dividend as each part of the division is solved.
  4. Remainder: If the divisor does not divide the dividend evenly, you may have a remainder. This remainder is written after the quotient or represented as a decimal or fraction.

Long division example solving 453 ÷ 4 with labeled parts: dividend, divisor, quotient, and remainder, visually explaining the step-by-step process

The division bracket helps structure the process, allowing you to handle one digit of the dividend at a time. As you solve each step, you bring down the next digit from the dividend, repeating the process until no digits remain. If there’s a remainder that does not go evenly into the divisor, it can be expressed next to the quotient or as a decimal by adding a zero and continuing the division process.

Detailed explanation

Practice Long Division

Test your knowledge with 21 quizzes

5100

Examples with solutions for Long Division

Step-by-step solutions included
Exercise #1

216

Step-by-Step Solution

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: quotient=dividenddivisor \text{quotient} = \frac{\text{dividend}}{\text{divisor}} .
  • Step 3: Substitute the numbers into the formula: quotient=162 \text{quotient} = \frac{16}{2} .
  • Step 4: Perform the division: 16÷2=8 16 \div 2 = 8 .

Therefore, the solution to the problem is 8 8 .

Answer:

8 8

Video Solution
Exercise #2

525

Step-by-Step Solution

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÷5 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 5×5=25 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 5 .

Answer:

5 5

Video Solution
Exercise #3

690

Step-by-Step Solution

To solve the division problem 90÷6 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 6×15=90 6 \times 15 = 90 ). There is no remainder left over.

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

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

Answer:

15 15

Video Solution
Exercise #4

222

Step-by-Step Solution

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 11 .

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

Answer:

11 11

Video Solution
Exercise #5

360

Step-by-Step Solution

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÷3=20 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 20 . This matches choice 3 (20) in the available options.

Answer:

20 20

Video Solution

Frequently Asked Questions

What is the correct order of steps in long division?

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The long division process follows DMSB: Divide (how many times divisor fits), Multiply (divisor by quotient), Subtract (find remainder), Bring down (next digit). Repeat until all digits are processed.

How do you set up long division notation correctly?

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Place the dividend inside the division bracket, write the divisor outside on the left, and record the quotient above the bracket. Each step's result goes directly above its corresponding dividend digit.

What do you do when a dividend digit is smaller than the divisor?

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Write 0 above that digit in the quotient, then bring down the next digit to create a larger number. For example, when dividing 4 by 5, write 0 and continue with the combined digits.

How do you handle remainders in long division problems?

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After each division step, multiply the quotient by the divisor and subtract from the current working number. The final remainder (if any) can be expressed as a whole number remainder or converted to a decimal.

What's the difference between dividing by one-digit vs two-digit numbers?

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The process is identical, but two-digit divisors require more careful estimation. You may need to consider two digits of the dividend at once, and the mental math for determining how many times the divisor fits becomes more complex.

Why do we bring down digits one at a time in long division?

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Bringing down one digit at a time breaks the problem into manageable steps. This systematic approach prevents errors and makes it easier to track your work, especially with large numbers.

How can I check if my long division answer is correct?

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Multiply your quotient by the divisor, then add any remainder. The result should equal your original dividend. For example: if 93 ÷ 3 = 31, then 31 × 3 = 93 confirms the answer.

What are common mistakes students make in long division?

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Common errors include: forgetting to write 0 when a digit is smaller than the divisor, misaligning numbers in the notation, and making multiplication or subtraction errors in intermediate steps.

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