Are you worried about Division on Integers? Check here to know the complete details about the Integers Division. Like integer multiplication, the division of integers is also an important topic to solve high standard questions. Follow various properties, rules, and tricks to solve division problems. Know the several terminologies involved in this concept. Scroll to the below sections to identify important points about the division on integers.
Division of Integers – Introduction
The division is the inverse operation of multiplication. Multiplication is totalling of numbers whereas division is the distribution of numbers. Though it is the inverse operation, the rules for multiplication and division are similar. The division is used in daily life for various purposes like household, funding, trading, living expenses, etc. Division also has various properties that are used in daily life. Before going to solve division problems, you must know the definitions of various terms.
Definitions
Dividend – The number that is to be divided is called a dividend.
Divisor – The number which divides the other number is called the divisor.
Quotient – The result of the division is called the quotient.
Integers Division Rules
There are various rules to be followed while applying division for integers.
- The quotient of 2 positive integer numbers will always be a positive integer.
- The quotient of 2 negative integer numbers will always be a negative integer.
- 1 positive and 1 negative integer number gives negative integer as a quotient.
- If a positive number is divided by a positive number, then the result will be a positive number.
- If a negative number is divided by a negative number, then the result will be a positive number.
- When a positive number is divided by a negative number, the result will be a negative number.
- When a negative number is divided by a positive number, the result will be a negative number.
Properties of Division of Integers
There are 5 properties which multiplication and addition but the division of integers do not follow. They are:
- Closure Property of Division
- Commutative Property of Division
- Associative Property of Division
- Identity Property of Division
- Distributive Property of Division
Property 1: Closure Property of Division
The division of integer does not follow the actual closure property. The quotient of two integers may or may not be an integer.
If x,y, and z are integers
x/y does not belong to z ( x ÷ y ∉ Z)
Property 2: Commutative Property of Division
The division of integer does not allow commutative property also. If the numbers are swapped, the result varies.
x/y is not equal to y/x (x ÷ y ≠ y ÷ x)
Property 3: Associative Property of Division
This division does not allow associative property also.
(x÷y)÷z ≠ x÷(y÷z)
Property 4: Identity Property of Division
x÷1 = x ≠ 1÷x
Property 5: Distributive Property of Division
Division of Integers does not allow distribution property.
As mentioned above, the division of integers does not allow any of the properties whereas multiplication and addition can be possible with all the above properties.
Important Rules for Division of Integers
Rule 1:
The quotient of two positive or negative integers is a positive integer which is equal to the quotient of the corresponding absolute integer values.
- The quotient of 2 positive numbers is positive and here we divide the dividend numerical value by the divisor numerical value.
Example:
(+ 9) ÷ (+ 3) = + 3
2. The quotient of 2 negative integers is positive and here, we divide the dividend numerical value by the divisor numerical value and assign a positive (+) sign to the quotient present.
Example:
(-9)÷(- 3) = +3
Therefore, for dividing 2 integers with the same signs, we divide their values and give plus (+) sign to the quotient.
Rule 2:
A positive and a negative integer gives quotient as a negative integer and its value is equal to the quotient of the corresponding values of the integers.
Example:
(+16)÷(-4) = -4
Therefore, for dividing integers with different signs, we divide their values and give the minus(-) sign to the quotient.
Important Properties of Division of Integers
Property 1:
If an integer ‘a’ is divided by another integer ‘b’, then the integer ‘a’ is divided into ‘b’ number of equal parts.
If ‘b’ divides ‘a’ without any intimation, then ‘a’ is evenly divisible by ‘b’.
Property 2:
When an integer ‘a’ is divided by another integer ‘b’, the division algorithm is, the sum of the product of quotient and divisor & the remainder is equal to the dividend.
i.e.,
Dividend = Quotient*Divisor+Remainder
Property 3:
When an integer number is divided 1, the result that is the quotient is the number itself.
Property 4:
When an integer number is divided by itself, the result or quotient is 1.
Property 5:
When any positive or negative integer is divided by zero, the result is undefined. Therefore, division by zero is meaningless.
Property 6:
When zero is divided by a positive or negative integer, the result or quotient is zero.
Property 7:
When an integer number is divided by another integer number which is a multiple of 10 like 10, 100, 1000,10000, etc., the decimal point for the number should be moved to the left.
Solved Problems on Division of Integers
Question 1.
Allen’s score was changed to -120 points in a video game because he missed some targets. He got -15 points for each missed target. How many targets did he miss?
Solution:
As given in the question, Allen’s score was changed to -120 and he got -15 points for each missed target.
To find how many targets he missed = -120/-15 =8
He missed 8 targets and got -15 points for each missed target.
Question 2.
Lousia’s savings change by -$9 each time she goes bowling. In all, it changed by -$99 during the summer. How many times did she go bowling in the summer?
Solution:
As given in the question, Lousia changed -$99 during the summer and she changes her savings by -$9
To find how many times she went bowling = -$99/9 = 11
The solution is 11 times.
Question 3.
Elisa withdraw $20 at a time from her bank account and withdrew a total of $140. How many times did she withdraw the money?
Solution:
As per the question, Elisa withdrew a total amount of $140 (it will be negative) and she withdrew $20 at a time(it will be negative).
Therefore, to find the number of times she withdraws the money = -140/-20 = 7
The solution is 7 times.
We hope that the provided information about the Division of Integers is sufficient for your preparation. We also provide you with the solved examples and procedures in the next articles. Therefore, stay tuned to our site to get the latest updates on various information. Bookmark our page to get instant information.