# Multiplication of Integers Definition, Properties | How to Multiply Integers?

Wanna solve challenging Integer Multiplication Problems? Here is the best guide for you. In the below sections, we have mentioned the important rules and examples on Multiplication of Integers. Get a clear idea of types and rules present in Integer Multiplication and know the easy methods to solve problems. Learn about Multiplication of Integers Definitions, Step by Step Procedure to Multiply Integers, Properties, in the coming modules.

## What is Multiplication of Integers?

Integers multiplication is defined as the repeated addition of integers. The rules for multiplication and division are almost similar. Integer multiplication includes 3 cases:

• Multiplication between two positive integers
• The multiplication between two negative integers
• Multiplication between one positive integer and negative integers

### Key Points about Multiplication of Integers

Have a glance at the important points to be taken into consideration while multiplying integers.

• A positive integer multiplied by a negative integer is negative.
• A negative integer multiplied by a negative integer is positive.
• Multiplication is commutative whereas division is not.
• When simplifying, calculate the operations of multiplication in order from left to right.

### Procedure for Multiplication of Integers

Go through the simple and easy guidelines listed below on How to Multiply Integers. They are as such

1. First of all, read the problem and make sure all the ideas and words are understood.
2. Identify the problem to be solved.
3. Note down the phrase which gives the information for the problem.
4. Translate the given information to an expression.
5. Simplify the given expression.
6. Apply the formulae to the problem and solve it.

### Rules for Multiplication of Integers

While Performing the Integer Multiplication keep the below mentioned instructions or rules in mind so that you can solve the problems easily. They are along the lines

• Product of 2 positive integer numbers is an integer number
• Product of 2 negative integer numbers is an integer number
• The addition of 2 positive integer numbers is an integer number
• The addition of 2 negative integer numbers is an integer number
• Sum of an integer number and its inverse equals zero
• Product of an integer number and its reciprocal equals 1

### Solved Examples on Product of Integers

Question 1.

Simplify -5*5?

Solution:

From the given question,

The first number is negative and the second number is positive, so the result must be negative.

5*5 = 25

As the result must be negative.

Therefore, Multiplying -5*5 we get the result as-25.

Question 2.

Simplify -20*-50?

Solution:

From the given question, -20*-50

Hence, both the numbers are negative, the multiplication of two negative numbers will be positive, so the result will be positive.

Therefore, -20*-50 = 1000

Therefore, Multiplying -20*-50 we get the result as 1000.

Question 3.

Simplify 7*0?

Solution:

Any integer multiplied by zero results in zero.

7*0=0

Thus, 7*0 becomes 0.

Question 4.

Simplify the following

a. 4.(5.2)

b. (4.5).2

Solution:

The value of the expression is 40. Changing the group of integers or numbers won’t change the result.

Therefore 4.(5.2) = (4.5).2 = 40.

Question 5.

Simplify 3(-2)(-5)(-1)?

Solution:

From the given question,

3(-2)(-5)(-1)

Multiply 2 numbers as follows:

3(-2)*(-5)(-1)

(-6)(-5)(-1)

30(-1)

-30

As multiplication is commutative, the order of multiplication does not affect the final result. We must work left to right to obtain the correct result.

Therefore, 3(-2)(-5)(-1) is -30.

### Properties of Multiplication of Integers

Multiplication of Integers has various properties and each property has a specific rule. All of them are given below.

1. Closure Property for Multiplication
2. Commutative Property for Multiplication
3. Distributive Property for Multiplication
4. Associativity Property for Multiplication
5. Multiplication by zero
6. Multiplicative Identity

### Points to Remember Regarding Integer Multiplication Properties

1. Closure Property of multiplication states that the product of two integer values will be an integer.
2. Commutative property of multiplication states that swapping of two integer numbers will not change the value of the final result.
3. Associative property of multiplication states that the way of the grouping of integer values together does not affect the final result.
4. Distributive property of multiplication states the distribution ability of one operation value over other mathematical values within the bracket.
5. Multiplication by zero states that the product of any positive or negative integer by zero is zero.
6. Multiplicative Integer states that when we multiply any integer with one, the final result will be integer itself.

### Example Questions on Integer Multiplication

Question 1.

The tank contains a capacity of 30,000 litres and 1,000 litres are taken every day from it. Find the amount of water in the tank 3 days ago?

Solution:

As per the given question, the water in the tank changes by -1000 every day. Therefore, we need to subtract 3 times to calculate the water amount before 3 days, so the change is

-3*-1000=+3000

The complete calculation is :

30,000+(-3*-1000) = 30,000+3,000 = 33,000

Therefore, before 3 days the amount of water in the tank was 33,000 litres.

The solution is 33,000 litres.

Question 2.

Flora made 6 deposits of $7 each from the bank account. What is the overall change in the account? Solution: As given in the question, 6 deposits of$7 are made from each bank account.

Therefore 6(7) = 42

The solution is $42. Question 3. The temperature dropped by 2 degrees F every hour for 6 hours. What was the total number of degrees the temperature changed in the 6 hours? Solution: As given in the question, the temperature is dropped by 2 degrees for 6 hours. i.e., -2*6 = -12 Therefore, the solution is -12. Question 4. The price of one share of Acme company declined$5 per day or 4 days in a row. How much did the price of one share change in total after the 4 days?

Solution:

As given in the question, $5 is declined. Therefore it is negative Time will always be positive. Therefore, -5*4 = -20 The solution is$-20.

Question 5.

A mountain climber climbed up a cliff 50 feet at a time. He did this 5 times in one day. What is the overall change in his elevation?

Solution:

As given in the question, The climber climbed up 50 feet. Therefore, it is positive.

He did it 5 times a day.

Hence, 50*5 = 250

The solution is 250 feet.

Question 6.

The price of the jeans was reduced $6 per week for 7 weeks. By how much the price of jeans changed over the 7 weeks? Solution: As given in the question, the price is reduced. Therefore, it is negative. It was reduced for 7 weeks. Hence, (-6)*7 = -42 The solution is -42$.

Hope the above-given article clears all your doubts regarding Multiplication of Integers. Refer all the mentioned problems to know the various models. Bookmark our site to get all the notifications regarding various competitive exam topics and concepts. In case of any doubts, you can contact us through the below comment section.

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