To understand Integers correctly you need to understand the rules for multiplying and dividing integers three rules:

In general math, repeated addition of the same numeric term over and over can be expressed in terms of multiplication. For example, suppose you are in a room with 4 rows of chairs, and in each row, there are 5 chairs. You could compute the total number of chairs by adding the number of chairs in each row:

5 + 5 + 5 + 5 = 20

Or you could multiply 4 times 5 (sometimes written as 4 x 5 or 4 • 5), or (4)(5) = 20

In general, if a term x occurs repeatedly n times in a sum expression, we can reduce the expression to:

n.x = x + x + x +…+ x (total n times)

## 1. Rules for Multiplying and Dividing Integers:

## Multiplying two positive numbers

Multiply both numbers to give the result **positive**

In general, you learned to multiply positive numbers to obtain their result; thus, for example, **7 x 3 is 21.**

## Dividing two positive Integers

Dividing two positive integers yields a result **positive**.

Divide positive numbers to obtain their result; thus, for example, **21 / 3 is 7.**

## 2. Rules for Multiplying and Dividing Integers: Two negative numbers

### Multiplying two negative numbers

Multiply both numbers to give the result **positive**

Multiplying two negative numbers say -7 x -3, do the normal multiplication which is 7 x 3 = 21, and then multiply their signs. Here negative x negative number gives positive

so -7 x -3 = 21

### Dividing two negative numbers

Dividing two negative integers yields a **positive **result.

Dividing two negative numbers say -21 / -3, do the normal division which 21 / 3 = 7, and then divide their signs. Here negative/negative number gives positive

## 3. Multiplying and Dividing one positive and other negative numbers

### Multiplying a positive and a negative number

Multiplying a positive and a negative number give the resulting **negative**

Here, when you multiply positive and negative numbers say -7 x 3, do the normal multiplication which is 7 x 3 = 21, and then multiply their signs. Here negative x positive number gives negative.

So -7 x 3 = – 21

### Dividing one positive and other negative number

Dividing positive and negative integers yields a **negative **result.

So, when you divide one positive and other negative numbers say 21 / -3, do the normal division which 21 / 3 = 7 and then divide their signs. Here positive/negative number or a negative number/ positive number gives a negative.

So, 21 / -3 = -7

## Conclusion:

**– x + = –**

**+ x – = –**

**– x – = +**

**+ x + = +**

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