What is Division?
Division is a mathematical operation that is the opposite of multiplication. In division, we split a number into equal groups. Division is the repeated subtraction of numbers. Let us take a real life example and understand more about this. Suppose you have to distribute 300 candies among 30 of your friends and you want to distribute them equally. For every child to get an equal number of candies, you will have to divide 300 by the number of friends, 30. This is how division works.
What are the Parts of a Division Equation?
A division equation is written in two different ways – the sentence form and the long division form. In the long division method, basic math operations are used. A tableau is drawn to divide where the dividend is written inside it and the divisor is written outside the tableau.
Here, the dividend is the number that is being divided into equal groups. The divisor is the number of groups that the dividend is being divided by and the quotient is the answer that is arrived at after dividing. The remainder is an important part of a division equation and it is the leftover part after the division process is done. In the above example, the remainder is zero as there is no number left over.
Long Division Method
We can use the long division method to divide larger numbers. In fact, long division is especially used when you have a larger number to divide. For example 567 ÷ 3, 1091 ÷ 2, and so on. The long division method is used for 2-digit, 3-digit, and higher digit numbers for division.
What is the long division method?
Long division is a step-by-step method for dividing multi-digit numbers. In long division we apply four basic operations of arithmetic or steps such as; divide, multiply, subtract and bring down, and then repeat the process until the last digit of the given number to divide.
Steps to Solve the Long Division Method
Let us have a look at this example. Find 2782 ÷ 3.
Let’s divide 2782 by 3.
To begin, ask how many times 2 goes in 3.
Here, 2 thousands cannot be shared among 3 groups without regrouping. So, we will regroup 2 thousands as 20 hundreds and add 7 hundreds along with it.
So, let us divide the hundreds.
Now, we will divide the tens.
Now, we will divide the ones.
So, 2782 ÷ 3 will give us 927 and the remainder 1 as the answer.
Solved Examples
Example 1: Find 48 ÷ 4.
Solution:
Let’s divide 48 by 4.
We will divide the tens first.
We get the quotient as 12 and the final remainder will be 0.
Example 2: Find 905 ÷ 5.
Solution: Let’s divide 905 by 5.
So, the answer is 181 with 0 remainder.
Example 3: Find 8349 ÷ 7.
Solution:
Let’s divide 8349 by 7
First, we will divide the thousands.
Then, we will divide the hundreds.
After that, we will divide the tens.
Now, we will divide the ones.
So, the answer will be 1192 with 5 as a remainder.
Example 4: A team of 5 workers finished a task within 55 days. Each worker spends the same number of days on the task. How many days did each worker take to complete the task?
Solution:
As we have to find the number of days for each worker’s task, we will find 55 ÷ 5.
So, 55 ÷ 5 = 11. Each worker takes 11 days to finish the task.
When we use zero as a quotient, we are trying to get accurate results by the division method. A zero in the quotient can appear when the divisor is larger than the dividend or the first digit of the dividend.
The use of place values for division is important for learning the operations involved in the process. We can line up the numbers vertically, compare them and based on that we can perform other arithmetic operations. Regrouping is done for long division problems where the knowledge of place value is needed.