Division: Definition, Steps, Algorithm, Properties & Solved Questions

Division is one of the arithmetic operations in Mathematics along with addition, subtraction and multiplication. The division of a bigger number into smaller groups with the same number of elements is one of the most basic arithmetic operations of Maths. A mathematical sign consisting of a small horizontal line with a dot above and below the line denotes division. The division algorithm is an equation that establishes a relationship between all four division elements. The value of the dividend is always equal to the product of the divisor and the quotient added to the remainder in any division. Dividend = (Divisor x Quotient) + Remainder is the formula for division, also known as the Division Algorithm. 

Key Terms: Division, Arithmetic Operations, Quotient, Remainder, Dividend, Divisor, Division Algorithm, Multiplication, Subtraction, Fractions

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What is Division?

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Division is one of the four basic mathematical operations, with addition, subtraction, and multiplication being the others. The division is the process of dividing a large group into smaller groups so that each group has an equal number of elements. It is a mathematical process that is utilized for equitable grouping and sharing.

For example, how many total groups will be formed if 30 students are divided into groups of five for a sporting event? The division operation can simply be used to overcome such situations. We must divide 30 by 5 in this case. 30/5 = 6 will be the result. As a result, there will be six groups of five students each. You may double-check this value by multiplying 6 and 5, which yields the original number of 30.

The division process is essentially a series of subtraction operations. It is the multiplication operation's inverse. When dividing numbers, we break down a larger number into smaller ones so that the multiplication of the smaller ones equals the larger number. For instance, 4/2 = 2. This can be expressed as 2 x 2 = 4 as a multiplication fact.

Read More: Multiplication and Division of Integers

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Division Symbol

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A mathematical sign consisting of a small horizontal line with a dot above and below the line denotes division. The division of two numbers is represented by two basic division symbols. They are ÷ and /, respectively. 4 ÷ 2 = 2, for example, and 4/2 = 2.

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Parts of Division

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The terms related to the division process are referred to as parts of the division. Dividend, divisor, quotient, and remainder are the four parts of the division. Let's have a look at an example of the division below to see what these four elements of the division mean.

We get the values of a divisor, dividend, quotient, and remainder when we divide 24 by 2. To learn what these phrases signify, look at the table below.

Read More: Addition and Subtraction of Integers

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Division Algorithm

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The division algorithm is an equation that establishes a relationship between all four division elements. The value of the dividend is always equal to the product of the divisor and the quotient added to the remainder in any division. The general formula for division is as follows: 

Dividend = (Divisor x Quotient) + Remainder

It is called the Division Algorithm. The above formula allows us to double-check the quotient and remainder numbers acquired after division. In the above equation, we can substitute the values of the quotient, remainder, and divisor to see if the answer is the same as the dividend. If we get the dividend, we know we followed the division stages correctly. If not, it means we have a computation error that has to be fixed. 

Let's look at an example to check if it meets the above division procedure. Divide 24 by 2. 24 divided by 2 yields a quotient of 12 and a remainder of 0.

Dividend = (Divisor x Quotient) + Remainder

24 = (2 x 12) + 0

24 = 24

Hence the procedure we followed is correct.

Read More: BODMAS Rule

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How to Do Division?

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Multiplication tables can be used to achieve one-digit division. To solve 24 ÷ 6 for example, we simply need to figure out what we need to multiply by 6 to get 24 as the solution. Clearly, 6 x 4 equals 24, so 24 ÷ 6 equals 4. We can utilize the long division method to divide numbers with larger numbers. To explain it, consider the example of 65 divided by 5. To learn how to divide, follow the instructions below:

• Step 1: Make a division symbol and write divisor (5) on the left side and dividend (65) on the right side.
• Step 2: From the left, take the first digit of the dividend (6). Now, check if this digit is larger or smaller than the divisor. [If the dividend's first digit is smaller than the divisor, we consider the dividend's first two digits.]
• Step 3: Next, divide it by the divisor and write the result as the quotient on the top. The quotient of 6 ÷ 5 is 1 in this case.
• Step 4: Subtract the dividend's first digit from the product of the divisor and the digit written in the quotient (5x1), and put the difference below. The difference, in this case, is 6 - 5 = 1.
• Step 5: Reduce the dividend by the next digit (if present). The dividend's next digit is 5.
• Step 6: Continue in this manner until you get a reminder that is less than the divisor.

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Division with Remainders

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Zer (0) as the remainder is not always the case. We obtain a non-zero remainder if the dividend is not a multiple of the divisor. A division with remainders occurs when we get a non-zero remainder while multiplying two numbers. 

Consider the following scenario: 9 balloons are distributed evenly to two children, ensuring that each child has an equal number of balloons. Is it possible to do so without having any leftovers?

When you divide 9 by 2, you get 4 as the quotient and 1 as the remainder. We can divide into two groups, each with four balloons, but one balloon will be left out.

Read More: Remainder Theorem

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Properties of Division

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Let's take a look at some of the division operation's properties to assist you to grasp it even better. A few division properties are listed below:

• Division by 1: When a number is divided by one, the outcome is the number itself. To put it another way, if divisor = 1, dividend = quotient.
• Division by 0: A number's value when divided by 0 is undefined, i.e. n/0 = undefined, where n is any number.
• Division by Itself: When we divide a number by itself, the result is always 1. To put it another way, if dividend = divisor, quotient = 1.
• Divide 0 by any number: Dividing 0 by any number always yields.
• Division by 10: When dividing a number by ten, the digit at the position of the one position is always the remainder, while the following digits on the left are always the quotient.579/10 = 57.9 is an example.
• Division by 100: When we divide a number by 100, the leftover is always the number created by the ones and tens place digits, and the quotient is the number formed by the remaining digits on the left. 8709/100 = 87.09 is an example.

Read More: Multiplicative Inverse

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Things to Remember

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• The division of a bigger number into smaller groups with the same number of elements is one of math's most basic arithmetic operations
• Dividend, divisor, quotient, and the remainder are the four parts of the division.
• The division of two numbers is represented by two basic division symbols. They are ÷ and /.
• The division algorithm is an equation that establishes a relationship between all four division elements. The value of the dividend is always equal to the product of the divisor and the quotient added to the remainder in any division. Dividend = (Divisor x Quotient) + Remainder is the formula for division. It is called the Division Algorithm.
• 0 as the remainder is not always required. We obtain a non-zero remainder if the dividend is not a multiple of the divisor.
• A number's value when divided by 0 is undefined, i.e. n/0is undefined, where n is any number.
• When we divide a number by itself, the result is always 1. To put it another way, if dividend = divisor, the quotient will be 1.

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Sample Questions

Ques. Divide 1242 by 2 and calculate the quotient and remainder. Verify the answer obtained using the division algorithm. (3 Marks)

Ques. Eva's father made her some cookies. Her closest friends, Pal and Akon, planned to surprise her by paying her a surprise visit. If eve's father prepared 9 cookies, how many cookies did Eva's father give Eva, Pal, and Akon so that they were evenly distributed? To double-check your solution, use the division algorithm. (3 Marks)

Ques. Where do we use division in our everyday lives? (3 Marks)

Ques. Divide 0.8095 by 0.50. (3 Marks)

Ques. Write a detailed description of how to divide 10/4 from 6/2 step by step. (3 Marks)

Ques. What is long division? (2 Marks)

Ques. Is division and long division the same thing? (2 Marks)

Ques. Liza is the owner of two puppies. She purchased 8 chewable bones to feed them both evenly. How many bones will be given to each puppy? (3 Marks)

Ques. Divide 0.21 and 0.07 (3 Marks)

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