Division in Maths
There are four mathematical operations namely, addition, subtraction, multiplication, and division. Division in Maths is considered the most difficult among the four basic mathematical operations. The division is a method of splitting a number into an equal number of parts. For example, 20 ÷ 4; it states that 20 things are split into 4 equal groups, which further implies that 5 things are there in one group. The diagram given below shows that there are 20 things which are divided into 4 equal groups and each group has 5 things.
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In this article, we will discuss division in maths, division formulas, division symbols, division examples, division rules etc.
Division Symbol
There are various division symbols that are used to represent the division in Mathematics. The most commonly used division symbol is ÷, but sometimes the backslash “/” is also used to represent the division in the form of a fraction, where the numerator value is written at the top and the denominator value at the bottom.
Example
“p divided by q”:
p÷q
Or
p/q
Dividend, Divisor, Quotient and Remainder in Division in Maths
When any number is divided by another number, we get the terms namely dividend, divisor, quotient, and remainder.
The dividend is defined as the number to be divided by another number.
A divisor is a number that divides another number without leaving any remainder.
The quotient is the result that is obtained after division.
The remainder is the number that is left after division.
The above concept can be clearly understood through the image given below:
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The division formula is:
Division Formula
Division Rules
Some of the division rules are given below:
When the digit 0 is divided by another number, the result obtained is always 0. For example, 0 ÷ 3 = 0. This sentence means that 0 chocolates are distributed among 3 girls.
When any number is divided by 0, it means that we are not dividing the number at all. For example, 3 ÷ 0 = is not possible in Mathematics. This sentence means that we have 3 chocolates but no girls to distribute the chocolates because we cannot divide any number by 0.
When any number is divided by 1, we always get the same number. For example, 3 ÷ 1 = 3. This sentence means that 3 chocolates are given to 1 girl.
When any number is divided by the same number, we always get the number as 1. For example, 3 ÷ 3 = 1. Each girl received 1 chocolate.
Numbers should always be divided in precise order. For example, 15 ÷ 3 = 5 and 3 ÷ 15 = 0.2 are two different cases. 15 chocolates divided by 3 girls is different from 3 chocolates divided by 15 girls.
The fractions such as \[\frac{1}{2}\], \[\frac{1}{3}\], \[\frac{1}{4}\], etc. are considered as division sums. For example, \[\frac{1}{4}\] is 1÷3. It means one chocolate divided by 3 girls.
Uses of Division in Real Life:
The division is used when you have to share work among people. For example, a band singing a song divides different portions of that song among the band members.
You can also use division when you make a project along with your classmates or your friends. This will give you clarity about who does a particular work and also avoid doubling the work.
The division is also used in sustainability concepts. Many countries come together to pledge for a sustainable future. They divide the target to be achieved based on their capacity.
The division is used when we have to distribute goods like fruits, chocolates, rice, vegetables among “n” number of people in our daily life. This mathematical operation plays a key role in dividing property, especially land.
Division Examples
Some of the division examples are given below:
1. Find the value of 60000 ÷ (- 10)
Solution:
60000 ÷ (-10)
= (60000 ) / (-10)
= (-60000) /(10)
= - 6000
2. Find the quotient value of 516 ÷ 12
Solution:
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Hence, the quotient value of 516 ÷12 = 43
Solved Examples
Some of the division examples with its solutions are given below:
1. Find the value of (-15625) ÷ (-125)
Solution:
(-15625) ÷ (-125)
= (-15625) / (-125)
= 15625/125
= 125
2. Divide -112 by -14.
Solution:
-112 ÷ (-14)
= (-112) /(-14)
= 112 / 14
= 8
3. Divide and find the quotient value of (-1728) ÷ 12
Solution:
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Hence, the quotient value of 1728 ÷ 12 = 144
Quiz Time
1. If 6 girls share 145 chocolates equally, how many sweets will be left?
24
0
6
1
2. (25 ÷ 5) ÷ ( 6-1)
5
1
625
25
3. What is the value of 323 ÷ 1
323
1
0
Cannot find the answer
FAQs on Division Formulas
1. Example Simple Division and Long Division.
Simple Division - The simple division in Maths is a method used to divide small numbers into equal groups or parts. It sums helps in dividing easier and simple division questions into divisible terms. The simple division example is given below:
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Long Division - The long division in Maths is a method used to divide larger numbers into small equal groups or parts. It helps in splitting the long division sums into a sequence of straightforward and easy steps. In long division, a larger number which is known as the dividend is divided by another number known as divisor which obtains the results quotient. The number which is left after division is known as the remainder. The long division example is given below:
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2. Explain the Relationship Between Multiplication and Division?
Multiplication and division are both closely related to each other. The division is basically an inverse process of multiplication. The division is a method of splitting a number into an equal number of parts while multiplication joins equal groups. For example,
3 × 5 = 15
its inverse relation( in the division form will be the following)
15 ÷ 5 = 3
15 ÷ 3 = 5
Similarly, if we divide 40 ÷ 4 = 10, its inverse relation (in the multiplication form, will be the following)
4 * 10 = 40
10 * 4 = 40
In the above example, we can see there are three numbers. It is because when we multiply two numbers (which are known as factors), the result we get is called a product of two numbers whereas if we divide two numbers we get the factors as a result.
3. How do you divide with the help of a calculator?
Division can be done manually by the long division method and short division method. Apart from manual operations, one can also do this mathematical operation on a calculator following the given process:
Let us assume you want to divide 20 with 4 on a calculator. Now enter the digit “20” on the calculator and then click on the button or option “÷” and now enter the number “4”. Press the symbol “=” to get the result. The answer would be “5”. It is very simple to calculate divisions and other mathematical operations on a calculator. Yet, the students should learn how to perform these operations manually.
In the above calculation, 20 is the dividend, 4 is the divisor, 0 is the remainder and 5 is the quotient
4. What are the rules of division?
Following are the rules of division:
When we divide the number “0” with any number, the quotient is also zero. For example, the equation 0/4= 0, which means that 0 number of things are divided among 4 members.
When we are dividing any number by zero, we are actually not dividing it with anything. Hence, it is mathematically impossible to divide anything by zero. For example, 4/0 is undefined as we can not divide 4 to 0 equal parts.
Any number divided by 1 is equal to the same number, for example, if we have to divide 4 fruits to a girl, we just give them all to the same girl. Hence, any number divided by “1” is always equal to the exact dividend.
When we divide a number with the same number, the result is 1, for example, if you have 5 fruits that are to be distributed among 5 members, we give 1 fruit to every number.