What is Division?
Division is the method of dividing a group of things into equal parts. It is one of the four basic arithmetic operations that produce a fair-shared result. The division operation is the inverse of the multiplication operation.
Dividend ÷ Divisor = Quotient + Remainder
The divisor is the number that divides the total amount (dividend) into equal parts, which is 3.
The number that is being divided is referred to as the dividend, which is 47.
The remainder is the number that is left after the division operation, which is 2.
The result of the division operation is the quotient, which is 15.
Modeling the Problem Using Equal Groups
Division is a mathematical operation that determines the size or number of equal groups. You can make use of division to find the size of each group once you know the total number of objects and the number of equal groups.
Example: A group of four people will be served an eight-slice pizza. Determine the total number of counters in each group, the number of counters in equal groups, and the total number of counters in each group.
As the pizza contains eight slices, the number of counters will be 8.
The pizza was served to a group of four people. So, the number of groups is 4.
Number of counters in each group \( ~=~\frac{8}{4}~=~2 \)
Hence, each group will consist of two counters of pizza.
Tape Diagram or a Bar Model to form an Equation
A tape diagram is a rectangular drawing with divisions that look like a piece of tape and is used to support mathematical calculations.
Example: Jane has 10 chocolate bars. She puts an equal number of chocolates in 5 jars. How many chocolates are there in each jar?
Solution:
We have a total of 10 chocolates and 5 jars in which the chocolates have been divided equally.
So, \( \frac{10}{5}~=~2 \)
Hence, Jane has to put 2 chocolates in each jar to have an equal number of chocolates in every jar.
How to do Division Using Number Line?
The arithmetic operation of division on numbers using a number line is referred to as division on a number line.
Count back
The result of division can be counted down using the number line.
The example below will show the divisions you need to count back:
Relation between division and repeated subtraction
Division is an arithmetic operation that can be accomplished using a number line. Division is also referred to as repeated subtraction.
Example: Solve \( \frac{15}{3} \) using repeated subtraction and division relations.
Using the number line, 3 is subtracted from 15 several times.
The remainder zero is obtained by subtracting 3 from 15 five times on the number line. As a result, 3 can be subtracted from 15 a total of five times.
Therefore, 15 ÷ 3 = 5, 5 is the quotient.
How to do Division Using Arrays?
Arrays are collections of objects or images that are organized into rows and columns. Arrays can be used to represent and solve problems involving division.
Example: There are a total of 12 dots in this array and they are arranged in 3 rows.
There are 4 dots in each row. You can write a division sentence that matches the array using these numbers.
So, \(\frac{12}{3}\) = 4
Therefore, dividing 12 dots into three rows yields four dots in each row.
Solved Examples on Dividing Numbers
Example 1: Solve \( \frac{36}{6} \) using repeated subtraction and division relations.
Solution:
Using the number line, 6 is subtracted from 36 several times.
The remainder zero is obtained by subtracting 6 from 36 six times on the number line. As a result, 6 can be subtracted from 36 a total of six times.
As a result, 36 ÷ 6 = 6, 6 is the quotient.
Example 2: There are a total of 6 dots in an array and they are arranged in 3 rows:
Solution:
There are 2 dots in each row. You can write a division equation that matches the array using these numbers.
So, \( \frac{6}{3}=2 \)
Therefore, dividing 6 dots into three rows yields two dots in each row.
In the above equation, the number that is being divided is referred to as the dividend, which is 15. The divisor is the number that divides the total amount (dividend) into equal parts, which is 3, and the result of the division operation is the quotient, which is 5.
Repeated subtraction, also known as division, is a method for subtracting an equal number of items from a group. This method involves the repeated subtracting of the same number from a larger number until the remainder is zero or less than the number being subtracted.
Subtraction is the process of taking a certain amount or number away from another. Division, on the other hand, refers to separating a given value into different parts.