Propagation and Division of Integers
The multiplication and division of integers are deuce of the basic operations performed on integers. Multiplication of integers is the unchanged as the repetitive addition which means adding an integer a specific number of multiplication. For example, 4 × 3 means adding 4 three multiplication, i.e 4 + 4 + 4 = 12. Division of integers means equal grouping or dividing an whole number into a special routine of groups. For example, -6 ÷ 2 substance dividing -6 into 2 equal parts, which results in -3. Let us learn more about the multiplication and division of integers in this article.
| 1. | What is Generation and Division of Integers? |
| 2. | Multiplication of Integers |
| 3. | Division of Integers |
| 4. | Times and Division of Integers Examples |
| 5. | Properties of Multiplication and Division of Integers |
| 6. | FAQs along Multiplication and Division of Integers |
What is Multiplication and Part of Integers?
The four basic arithmetic operations associated with integers are:
- Addition of integers
- Subtraction of integers
- Multiplication of integers
- Division of integers
Multiplication and sectionalisation of integers are the almost of the essence arithmetic operations used much. Let us learn the multiplication and air division of integers in detail.
Multiplication of Integers
Multiplication of integers is the process of repetitious addition including confident and negative numbers or we can simply say integers. When we occur to the case multiplication of integers, the following cases must make up taken into calculate:
- Multiplying 2 cocksure numbers
- Multiplying 2 negative numbers pool
- Multiplying 1 positive and 1 electronegative total
When you multiply integers with two positive signs, Positive x Positive = Affirmatory = 2 × 5 = 10.
When you multiply integers with two dissident signs, Negative x Dismissive = Positive = –2 × –3 = 6.
When you breed integers with one unfavorable sign and one positive sign, Negative x Positive = Negative = –2 × 5 = –10.
The following table will help you remember rules for multiplying integers:
| Types of Integers | Result | Object lesson |
|---|---|---|
| Both Integers Formal | Sure | 2 × 5 = 10 |
| Both Integers Negative | Positive | –2 × –3 = 6 |
| 1 Positive and 1 Negative | Negative | –2 × 5 = –10 |
Example: Anna grub 4 cookies per day. How many cookies does she dine in 5 days? ⇒ 5 × 4 = 20 cookies.
Multiplication of Integers Rules and Stairs
Multiplication of integers is very similar to normal generation. However, since integers deal with some negative and incontrovertible numbers, we birth certain rules or conditions to remember while multiplying integers arsenic we saw in the previous section. Let us calculate at the steps for multiplying integers.
- Pace 1: Determine the absolute prize of the numbers.
- Footprint 2: Find the product of the absolute values.
- Stone's throw 3: Once the product is obtained, fix the sign of the number according to the rules or conditions.
Let us take an example to understand the steps better. Multiply - 7 × 8.
Step 1: Make up one's mind the absolute time value of - 7 and 8.
|-7| = 7 and |8| = 8.
Step 2: Get hold the product of the absolute value numbers 7 and 8.
7 × 8 = 56
Step 3: Determine the sign away of the product reported to the multiplication of integers rules. According to the multiplication of integer rule, if a bad amoun is multiplied with a positive number, so the product is a negative number.
Therefore, - 7 × 8 = - 56.
Division of Integers
Division of integers involves the group of items. It includes both undeniable numbers and negative numbers. Just like multiplication, the division of integers too involves the homophonic cases.
- Dividing 2 positive numbers
- Dividing 2 negative numbers
- Dividing 1 positive and 1 negative keep down
When you divide integers with two positive signs, Positive ÷ Certain = Positive → 16 ÷ 8 = 2.
When you part integers with two negative signs, Negative ÷ Perverse = Positive → –16 ÷ –8 = 2.
When you divide integers with one negative augury and combined positive sign, Negative ÷ Plus = Negative → –16 ÷ 8 = –2.
The following table will avail you commend rules for dividing integers:
| Types of Integers | Result | Example |
|---|---|---|
| Both Integers Positive | Incontrovertible | 16 ÷ 8 = 2 |
| Some Integers Negative | Prescribed | –16 ÷ –8 = 2 |
| 1 Positive and 1 Negative | Negative | –16 ÷ 8 = –2 |
To sum it every last up and to make everything easy, the 2 well-nig important things to remember when you are multiplying integers or dividing integers are:
- When the signs are different, the answer is always Gram-negative.
- When the signs are the same, the respond is always positive.
Generation and Segmentation of Integers Examples
Few examples of multiplication and variance of integers are shown in the table given below:
| Multiplication | Division |
|---|---|
| 4 × 2 = 8 | 15 ÷ 3 = 5 |
| 4 × -2 = -8 | 15 ÷ –3 = –5 |
| -4 × 2 = -8 | –15 ÷ 3 = –5 |
| -4 × -2 = 8 | –15 ÷ –3 = 5 |
Properties of Multiplication and Class of Integers
Generation and division of integers properties help U.S. to identify the relationship between two or more integers when they are linked aside multiplication or division surgical operation between them. There are a few properties associated with the multiplication and division of integers.
Properties related to multiplication and air division of integers are listed below:
- Settlement Property
- Independent Dimension
- Associative Attribute
- Distributive Property
- Identity Property
Let's understand from each one prop in sexual congress to the division and times of integers in particular.
Law of closure Property of Multiplication of Integers
The closure belongings states that the hardening is closed for any primary mathematical operation. Integers are closed subordinate addition, subtraction, and multiplication. All the same, they are non closed under division.
| Military operation | Example |
|---|---|
| a × b is an integer | 2 × –6= –12 |
| a ÷ b non always an integer | –3/4 is a fraction |
Multiplication of Integers Commutative Holding
According to the independent property, interchanging the positions of operands in an operation does not touch the result. The addition and multiplication of integers survey the commutative property, while the division of integers does not hold this property.
| Operation | Example |
|---|---|
| a × b = b × a | 5 × (–6) and (–6) × 5 = –30 |
| a ÷ b ≠ b ÷ a | 15 ÷ 3 = 5 but 3 ÷ 15 = 1/5 |
Associative Property of Multiplication of Integers
According to the associable property, changing the grouping of integers does not alter the result of the operation. The associative property applies to the addition and times of two integers but not in the case of the division of integers.
| Operation | Example |
|---|---|
| (a × b) × c = a × (b × c) | (5 × –3) × 2 = –30 5 × (–3 × 2) = –30 |
| (a ÷ b) ÷ c ≠ a ÷ (b ÷ c) | (20 ÷ 5) ÷ 2 = 2 but 20 ÷ (5 ÷ 2)= 8 |
Disseminative Property of Multiplication of Integers
Distributive property states that for any construction of the configuration a (b + c), which means a × (b + c), operand a can be distributed among operands b and c arsenic (a × b + a × c) i.e., a × (b + c) = a × b + a × c. Times of integers is distributive finished addition and subtraction. The distributive property does non hold true for the division of integers.
| Military operation | Example |
|---|---|
| a × (b + c) = (a × b) + (a × c) | 4 × (–3 + 6) =12 (4 × –3) + (4 × 6) = 12 |
| a × (b – c) = (a × b) – (a × c) | 2 × (5 – 3) = 4 (2 × 5) – (2 × 3) = 4 |
Identity element Property of Multiplication of Integers
In the case of the multiplication of integers, 1 is the increasing indistinguishability. Thither is no identicalness element in the case of the division of integers.
| Identity Under Addition is 0 | Identity Under Multiplication is 1 |
|---|---|
| For any whole number a, a + 0 = 0 + a = a | For any integer a, 1 × a = a × 1 = a |
| For example, 8 + 0 = 0 + 8 = 8 | For example, (– 4) × 1 = 1 × (– 4) = – 4 |
Multiplication and Division of Integers Tips and Tricks:
- There is neither the smallest whole number nor the biggest integer.
- The smallest positive integer is 1 and the sterling negative integer is -1.
- PEMDAS rule applies for operations connected integers. "Operations" are some of the following: Brackets, Squares, Powers, Square Roots, Division, Multiplication, Addition, and Subtraction.
Related Articles:
Check these exciting articles incidental to the concept of multiplication and segmentation of integers.
- Multiplying Integers Worksheet
- Multiplying and Nonbearing Integers Worksheet
- Dividing Integers Calculator
- Multiplying Integers Calculator
Examples of Part and Generation of Integers
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Division and Multiplication of Integers Practice Questions
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FAQs connected Multiplication and Division of Integers
What is Multiplication of Integers?
Multiplication of integers is the repetitious add-on of numbers which means that a number is added to itself a specific number of times. E.g., 4 × 2, which agency 4 is added two multiplication. This implies, 4 + 4 = 4 × 2 = 8.
What are the Properties of Multiplication of Integers with Examples?
The properties of multiplication of integers are given below:
- Closure property → -2 × 3 = -6, where -2, 3, and -6 are integers.
- Associative property → (2 × 3) × (-9) = 2 × (3 × -9) = -54.
- Independent property → -4 × -7 = -7 × -4 = 28.
- Immanent property → 3 × (-4 + 2) = (3 × -4) + (3 × 2) = -6.
- Identity → 3 × 1 = 1 × 3 = 3. 1 is the identity factor.
What are the Rules for Multiplication and Division of Integers?
The basic rules for air division and multiplication of integers are presented downstairs:
- Times or division of two numbers with the same sign results in a positive number.
- Propagation Beaver State division of two numbers with opposite signs results in a unsupportive number.
What are the Properties of Variance of Integers?
The properties of the division of integers are given down the stairs:
- If we watershed 0 by whatsoever non-zero integer, the answer will e'er be 0. It can be mathematically expressed every bit 0 ÷ a = 0.
- Whatever integer divided by itself results in 1. This implies, a ÷ a = 1.
- When an whole number is sectioned by another integer, then it satisfies the division algorithmic program which says 'dividend = divisor × quotient + remainder'.
- When an integer is divided by 1, the result is e'er the integer itself. For example, -5 ÷ 1 = -5.
What is the Predominate of Division of Integers?
The rules for the division of integers are given below:
- Positive ÷ positive = positive
- Negative ÷ negative = affirmative
- Negative ÷ positive = negative
How exercise you Multiply Integers?
While multiplying integers, follow this trick to easy get the answer:
- Multiply without the negative sign.
- If both the integers are dissenting or both are positive, the product bequeath be positive.
- If ane integer is supportive and the other is counter, the product will be negative.
How do you Multiply Multiple Integers?
If there are to a higher degree two integers, then follow these simple steps to multiply them:
- Multiply without the negative sign.
- The sign of the final answer stern atomic number 4 determined by the number of negative signs.
- If the total number of negative signs is straight, the final answer leave be positive.
- If the total number of negative signs is odd, the final answer will be negative.
What are the Four Rules for Multiplying Integers?
Four rules of multiplying integers are stated below:
- Predominate 1: Positive × Overconfident = Positive
- Rule 2: Prescribed × Negative = Negative
- Rule 3: Negative × Positive = Negative
- Pattern 4: Negative × Negative = Positive
How brawl you Manifold a Positive and Negative Integer?
When we have two integers, one positive and one negative, follow these needle-shaped stairs to stupefy their product:
- Manifold without the negative sign.
- Sum the disconfirming sign to the answer to get the final exam resolve.
what are the rules in multiplying and dividing integers
Source: https://www.cuemath.com/numbers/multiplication-and-division-of-integers/
