Math Antics - Long Division

Introduction

This tutorial will guide you through the process of long division, a fundamental math skill used to divide larger numbers. Long division breaks the division process into manageable steps, making it easier to understand and calculate. Whether you're helping a student or brushing up on your math skills, this guide will provide clear instructions to master long division.

Step 1: Understand the Components of Long Division

Before diving into the long division process, familiarize yourself with the key components:

• Dividend: The number you are dividing (e.g., 456).
• Divisor: The number you are dividing by (e.g., 12).
• Quotient: The result of the division.
• Remainder: What is left over after division if the numbers do not divide evenly.

Step 2: Set Up the Long Division Problem

To begin, set up your long division problem:

1. Write the dividend (the number being divided) under the long division symbol.
2. Write the divisor (the number you are dividing by) outside of the long division symbol.

For example, if you're dividing 456 by 12, it will look like this:

   ____
12 | 456

Step 3: Divide the First Digit

1. Look at the first digit of the dividend. Determine how many times the divisor can fit into that digit.
2. If the divisor is larger than the first digit, include the next digit from the dividend.

For example:

• In 456, the first digit is 4. Since 12 doesn’t fit into 4, look at the first two digits (45).
• Determine how many times 12 fits into 45, which is 3 times.

Step 4: Multiply and Subtract

1. Multiply the divisor by the quotient obtained in the previous step.
2. Write this product below the selected digits of the dividend.
3. Subtract this product from the digits you used to find the quotient.

Continuing from our example:

• 3 x 12 = 36
• Place 36 below 45 and subtract: 45 - 36 = 9.

   __3__
12 | 456
      -36
      ----
        9

Step 5: Bring Down the Next Digit

1. Bring down the next digit from the dividend (which is 6 in this case) next to the remainder you just calculated.

Now you have:

   __3__
12 | 456
      -36
      ----
        96

Step 6: Repeat the Division Process

1. Repeat the process with the new number (96).
2. Determine how many times the divisor fits into 96.
3. Multiply, write the product, and subtract again.

For our example:

• 12 fits into 96 exactly 8 times.
• 8 x 12 = 96, so you write that below 96 and subtract: 96 - 96 = 0.

   __38__
12 | 456
      -36
      ----
        96
      -96
      ----
         0

Conclusion

You've completed the long division process! The quotient of 456 divided by 12 is 38, with no remainder. To practice, try dividing different pairs of numbers using the same steps. Understanding long division can significantly enhance your mathematical skills and confidence. Keep practicing, and you'll become proficient in no time!