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Maths Formulas

Division Formula

The division is a core skill of mathematics.  It involves calculating the fraction someone is owed or should receive. For example when splitting a check or dividing the costs of a trip. It is a mathematical challenge you are likely to encounter on an almost daily basis. In this article, we will discuss the division formula with examples. Let us discuss it in detail.

Division Formula

Concept of Division

There are four basic operations of mathematics, which are Addition, Subtraction, Multiplication, and Division. The division is the process of breaking a number up into an equal number of parts. The division is an arithmetic operation used in Maths. It splits the number of items into different groups.

For example, 20 divided by 4: If we take 20 apples and put them into four equal-sized groups, there will be 5 apples in each group.

Division Formula

Method of Division 

The mathematical expression 3 × 5 represents three groups with five items in each group. To get the product, students can build a model of three groups with five items in each group. We can also use repeated addition to find the product. They can add 3 five times like: 3 + 3 + 3 + 3 + 3 = 15.

It must be noted that multiplication will undo the division and vice versa. In other words, since \(3 \times 5 = 15, then 15 \div 5 = 3.\)

Since division and multiplication are inverse operations of each other. Then students can use models similar to the models used in multiplication, to divide. In the expression \(15 \div 3\), you begin with fifteen items and want to know how many groups you can make with three items in each group. The answer, or quotient, is the number of groups. Let us look at an example.

\(15 \div 3 = 5\)

As we know that multiplication is a form of repeated addition. Similarly, the division is a form of repeated subtraction. For example, \(15 \div 3\) asks you to repeatedly subtract 3 from 15 until you reach zero:

  • 15 – 3 = 12
  • 12 – 3 = 9
  • 9 – 3 = 6
  • 6 – 3 = 3
  • 3 – 3 = 0.

This process required 3 to be subtracted 5 consecutive times, so again we see that

\(15 \div 3 = 5.\)

The number which is divided is the dividend. And the number in which the dividend is being divided is the divisor. The answer to a division problem is the quotient. Example signs for “a divided by b”:

  • \(a \div b\) &
  • \(\frac{a}{b}\)

So the Division formula is:

  • \(Dividend \div Divisor=Quotient\) OR
  • \(\frac {Dividend}{Divisor} = Quotient\)

Special Cases

During the Division, some special cases are:

  • Dividing by 1: When any number is divided by 1, then the answer remains the same. Thus, if the divisor is 1 then the quotient equals the dividend.
  • Dividing by 0: No number can be divided by zero. Its answer is undefined.
  • Dividend equals Divisor: If the dividend and the divisor both are the same number, but not zero, then the answer will always be 1.

Solved Examples for Division Formula

Q.1: Solve \(221 \div 13.\)


Here, Dividend = 221

Divisor = 13

Then, applying the simple division method we will get the quotient.

Therefore \(221 \div 13=17\)

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