Division is a mathematical operation used to separate a group of objects into equal parts. In this lesson, we will explore the basics of division, including terminology, methods, and examples.

## Terminology

There are several terms associated with division that you should be familiar with:

- Dividend: The number being divided.
- Divisor: The number that is dividing the dividend.
- Quotient: The result of the division.

## Methods of Division

There are several methods used to perform division, including long division, short division, and repeated subtraction. Here, we will focus on long division, which is the most common method.

**Long Division:**

- Write the dividend and divisor in a long division format.
- Determine how many times the divisor can go into the first digit of the dividend. Write this number above the digit.
- Multiply the divisor by this number, and write the result under the first digit of the dividend.
- Subtract this result from the first digit of the dividend.
- Bring down the next digit of the dividend next to the remainder from the previous step.
- Repeat steps 2-5 until all digits of the dividend have been used.
- The final result is the quotient.

let’s use the long division method to divide 635 by 5.

Step 1: Set Up the Problem

First, we need to set up the division problem. We write the dividend, 635, inside the division bracket, and the divisor, 5, outside the bracket, as shown below:

5

——

635

Step 2: Find the Quotient

Next, we need to find the quotient. We ask ourselves: how many times does 5 go into 6? The answer is 1, so we write 1 above the division bracket, on top of the 6. Then, we multiply the quotient, 1, by the divisor, 5, and write the result, 5, below the first digit of the dividend, 6. Finally, we subtract 5 from 6 to get 1, and bring down the next digit of the dividend, which is 3.

5

——

635

-5

—

1

Step 3: Repeat the Process

Now, we need to repeat the process. We ask ourselves: how many times does 5 go into 13? The answer is 2, so we write 2 above the division bracket, on top of the 3. Then, we multiply the quotient, 2, by the divisor, 5, and write the result, 10, below the 13. Finally, we subtract 10 from 13 to get 3, and bring down the next digit of the dividend, which is 5.

5

——

635

-5 0

—-

13

-10

—-

3

Step 4: Repeat the Process

We repeat the process again. We ask ourselves: how many times does 5 go into 35? The answer is 7, so we write 7 above the division bracket, on top of the 5. Then, we multiply the quotient, 7, by the divisor, 5, and write the result, 35, below the 35. Finally, we subtract 35 from 35 to get 0, which means we have no remainder.

5

——

635

-5 0

—-

13

-10

—-

3

– 0

—-

0

Step 5: Write the Answer

We have successfully divided 635 by 5 using long division. The quotient is 127, and there is no remainder. Therefore, the answer is:

635 ÷ 5 = 127