Long Division Calculator

This highly accurate long division calculator performs long division with remainders quickly and easily. It divides your chosen number (the dividend) by another number (the divisor) and provides the answer as a whole number (the quotient) along with a remainder. Additionally, the result is displayed as a mixed number, which is automatically simplified to its lowest terms whenever possible.

Directions for Use

To use this division with remainders calculator, simply enter your Dividend and Divisor into the corresponding fields and click "Calculate." The tool will instantly return the long division result formatted as a quotient with a remainder, a standard mixed number, and a mixed number in its simplest form. Furthermore, it will display the step-by-step solution algorithm so you can easily follow along.

Calculation Algorithm

While you can perform long division with decimals, this guide focuses specifically on long division with remainders.

Definitions

• The dividend is the number you are dividing, which is typically the larger of the two numbers.
• The divisor is the number you are dividing by, generally the smaller of the two numbers.
• The quotient represents the whole number part of the final answer.
• The remainder is the exact amount left over after the division is complete.

For example, in the equation 168 / 15 = 11 R3: 168 is the dividend, 15 is the divisor, 11 is the quotient, and 3 is the remainder.

Long Division with Remainders Algorithm

The steps for performing long division manually are outlined below. Let’s walk through the step-by-step division process using our previous example: 168 / 15.

Step 1

• Write down the divisor and the dividend next to each other, starting with the divisor on the left.
• Separate the divisor and the dividend using a vertical line.
• Draw a horizontal line over the dividend to separate it from the upcoming quotient.

This combination of horizontal and vertical lines is commonly referred to as the division bracket or division symbol. Note that this standard division bracket is included in our calculator's interface for your convenience.

Step 2

• Divide the first digit of the dividend by the divisor. In this case, divide 1 by 15. The result of 1 divided by 15 is 0 with a remainder of 1.
• Write the whole number portion of this division above the horizontal line. In this example, you will write down 0. The digits placed above this line will ultimately form the quotient of your answer.
• Multiply this whole number part (0 in our example) by the divisor (15) and write the result (0) directly beneath the first digit of the dividend. Draw a horizontal line under this newly written number to complete Step 2.

Step 3

• Subtract the result obtained in Step 2 from the first digit of the dividend: 1 – 0 = 1. Write this answer (1) underneath the bottom horizontal line.
• Bring down the second digit of the dividend (6) and write it next to your subtraction result. In our example, this creates the new number 16.

Step 4

Now, repeat the process from Step 2 using your new number, 16.

• Divide the new number (16) by the divisor (15). The result of 16 divided by 15 is 1 with a remainder of 1.
• Write the whole number part of this calculation (1) above the top horizontal line.
• Multiply this whole number part (1) by the divisor (15) and write the result directly under the 16. Since 1 × 15 = 15, write 15. Draw a horizontal line underneath this number to conclude Step 4.

Step 5

Repeat the process from Step 3 using the new numbers.

• Subtract the result from Step 4 from your current working number: 16 – 15 = 1. Write this answer (1) below the horizontal line.
• Bring down the third digit of the dividend (8) and place it next to that answer. For our example, the resulting new number is 18.

Step 6

Repeat the process from Step 2 for the new working number, 18.

• Divide 18 by the divisor (15). 18 divided by 15 equals 1 with a remainder of 3.
• Write the 1 on top, above the horizontal line.
• Multiply 1 × 15 to get 15. Write this 15 directly underneath the 18.
• Draw a horizontal line below the 15 to complete Step 6.

Step 7

Begin repeating Step 3 with the latest numbers.

18 – 15 = 3

At this point, there are no more digits left in the dividend to bring down, and 3 is less than the divisor of 15. Therefore, the division process is complete. The final number remaining under the bottom horizontal line is the remainder. The number situated above the division bracket is the quotient.

168 / 15 = 11 R3

You can also express the final answer as a mixed number:

168 / 15 = 11 3/15

Or, reduced to its simplest form:

168 / 15 = 11 1/5

Calculation Examples

Example 1

Patrick received $150 for his birthday. He loves model railways and wants to expand his collection of trains. If each train costs $11, how many trains can Patrick buy? How much money will he have left over?

Solution

To solve this math problem, we need to perform long division with remainders. The quotient of our answer will represent the exact number of trains Patrick can purchase, while the remainder will represent the amount of unspent money he gets to keep.

150 / 11 = 13 R7.

Answer

Patrick can buy 13 trains, and he will have $7 left over.

Example 2

Jane is filling up treat bags to share with her class on her birthday. She has two large packages of gummy bears, each containing 65 pieces. If Jane wants to put exactly 8 bears into each treat bag, how many full bags can she make? If there are any left over, Jane is allowed to eat them. Will there be any extra gummy bears for Jane to enjoy, and if so, how many?

Solution

To find the answer, we will perform long division with remainders. The quotient will represent the total number of full treat bags Jane can make, and the remainder will represent the extra gummy bears she gets to eat.

First, let’s calculate the dividend for our long division equation. Since there are 2 packages with 65 gummy bears each, we multiply to find the total: 2 × 65 = 130 gummy bears.

130 / 8 = 16 R2.

Answer

Jane can successfully fill 16 treat bags, and she will have 2 leftover gummy bears to eat herself.