Long Division Steps Explained (With Examples)

Long division might seem intimidating at first, with its unique setup and multiple steps. However, once you understand the process, it becomes a powerful tool for solving complex math problems. Whether you're a student tackling it for the first time, a parent helping with homework, or just someone looking for a quick refresher, this guide is for you.

This post will break down long division into simple, manageable steps. We will walk through the entire process, from setting up the problem to finding the final answer, complete with clear examples. By the end, you'll have the confidence to solve long division problems accurately and efficiently.

Understanding the Basics of Long Division

Before diving into the steps, let's get familiar with the key terms and symbols used in a long division problem. Knowing these components is the first step to mastering the process.

• Dividend: The number being divided. It's the larger number that you are breaking into smaller, equal groups.

• Divisor: The number you are dividing by. It tells you how many groups you need to create.

• Quotient: The answer to the division problem. It represents the number of items in each group.

• Remainder: The amount "left over" after the division is complete. This occurs when the dividend cannot be perfectly divided by the divisor.

The problem is typically set up using a special symbol that looks like a right parenthesis attached to a horizontal line. The divisor is placed to the left of the symbol, and the dividend is placed underneath the horizontal line.

A Step-by-Step Guide to Long Division

Long division can be boiled down to a simple, repeatable cycle of steps. A common acronym to remember the order is DMSB: Divide, Multiply, Subtract, and Bring down. Let's explore each step in detail.

Step 1: Set Up the Problem

Write the dividend inside the long division symbol and the divisor to the left of it. Make sure your numbers are aligned neatly to avoid confusion later.

Step 2: Divide

Start with the first digit of the dividend (or the first two digits if the first digit is smaller than the divisor). Ask yourself, "How many times does the divisor go into this number?" Write this answer (part of the quotient) on top of the division symbol, directly above the digit you were dividing.

Step 3: Multiply

Multiply the number you just wrote in the quotient by the divisor. Place the result directly below the part of the dividend you were working with.

Step 4: Subtract

Subtract the result from Step 3 from the number directly above it. Write the difference below the line.

Step 5: Bring Down

Bring down the next digit from the dividend and write it next to the result of your subtraction. This creates a new number for you to work with.

Step 6: Repeat (or Find the Remainder)

Repeat the DMSB cycle (Divide, Multiply, Subtract, Bring down) with the new number you formed in Step 5. Continue this process until there are no more digits to bring down from the dividend. If the final subtraction leaves a number other than zero, that number is your remainder.

Long Division Examples

Let's see the steps in action with a few examples.

Example 1: Simple Division (125 ÷ 5)

Here, our dividend is 125 and our divisor is 5.

1. Divide: 5 goes into 12 two times. Write "2" above the 2 in 125.

2. Multiply: 2 × 5 = 10. Write "10" below 12.

3. Subtract: 12 – 10 = 2.

4. Bring down: Bring down the 5, creating the new number 25.

5. Repeat:

6. Divide: 5 goes into 25 five times. Write "5" in the quotient next to the 2.

   • Multiply: 5 × 5 = 25. Write "25" below 25.

   • Subtract: 25 – 25 = 0.

There are no more numbers to bring down, and our final subtraction is 0.So, 125 ÷ 5 = 25.

Example 2: Complex Division (578 ÷ 14)

Now, let's try a problem with a two-digit divisor.

1. Divide: 14 cannot go into 5, so we look at 57. 14 goes into 57 four times (since 14 × 4 = 56). Write "4" above the 7.

2. Multiply: 4 × 14 = 56. Write "56" below 57.

3. Subtract: 57 – 56 = 1.

4. Bring down: Bring down the 8 to make the new number 18.

5. Repeat:

6. Divide: 14 goes into 18 one time. Write "1" in the quotient next to the 4.

   • Multiply: 1 × 14 = 14. Write "14" below 18.

   • Subtract: 18 – 14 = 4.

There are no more numbers to bring down. The leftover 4 is our remainder.So, 578 ÷ 14 = 41 with a remainder of 4 (or 41 R 4).

Example 3: Division with a Remainder (936 ÷ 4)

Let's work through one more, this time focusing on the remainder.

1. Divide: 4 goes into 9 two times. Write "2" above the 9.

2. Multiply: 2 × 4 = 8. Write "8" below 9.

3. Subtract: 9 - 8 = 1.

4. Bring down: Bring down the 3 to make 13.

5. Repeat (1): 4 goes into 13 three times. Write "3" in the quotient. 3 × 4 = 12. 13 - 12 = 1.

6. Repeat (2): Bring down the 6 to make 16. 4 goes into 16 four times. Write "4" in the quotient. 4 x 4 = 16. 16 - 16 = 0.

Wait, it seems 936 is perfectly divisible by 4. Let's adjust the example to 937 ÷ 4 to demonstrate a remainder.

1. Steps 1-5 remain the same until we bring down the 7 to make 17.

2. Repeat (2): 4 goes into 17 four times. Write "4" in the quotient. 4 × 4 = 16. 17 - 16 = 1.

There are no more digits to bring down, so our remainder is 1.So, 937 ÷ 4 = 234 with a remainder of 1.

Tips for Accurate Long Division

• Estimate First: Before you start, try to guess the answer. For 578 ÷ 14, you could round 14 to 15. How many 15s are in 57? About 3 or 4. This gives you a reasonable starting point.

• Check Your Work: To verify your answer, multiply the quotient by the divisor and add the remainder (if there is one). The result should equal the dividend. For 578 ÷ 14 = 41 R 4, the check is (41 × 14) + 4 = 574 + 4 = 578. It matches!

• Stay Neat: Keep your columns aligned. Misaligned numbers are a major source of errors.
  

Common Mistakes to Avoid

1. Misaligning Numbers: Placing a number in the wrong column can throw off your entire calculation.

2. Forgetting to Bring Down: Always remember to bring down the next digit after each subtraction step.

3. Multiplication or Subtraction Errors: Double-check your basic arithmetic at each step. A small error can lead to a big mistake.
   

Real-World Applications of Long Division

Long division isn't just for math class. We use its principles all the time.

• Splitting Bills: Dividing a restaurant bill among friends.

• Party Planning: Figuring out how many packs of supplies you need for a certain number of guests.

• Travel: Calculating average speed (miles per hour) on a road trip.

Master Long Division and More

Understanding long division is a fundamental math skill that opens the door to more advanced topics like fractions and algebra. By following the DMSB cycle—Divide, Multiply, Subtract, Bring down—you can tackle any long division problem with confidence. Practice is key, so don't be afraid to work through problems until the process feels natural.

Need more help with long division or other math topics? At Tutor-ology, our expert tutors provide personalized, one-on-one instruction to help students excel. For a limited time, you can save 30% on all our courses, bringing the cost to just $7 per hour! Give your child the academic advantage they deserve.

Click here to learn more and register now!