We learned in the previous article about the number line AND we also talked about positive and negative numbers. In this article we move on and call them integers.

## The term "integer" refers to any number to the left of which there is a plus sign (+) or minus sign (-).

• The plus sign ($+$ ) indicates that the number is positive (greater than zero). The minus sign (-) means that the number is negative (less than zero).
• When a number appears without one of these two signs, it means that the number is positive.
• Exception: The number $0$ . Zero is the only number that is neither positive nor negative. It is possible to write "$+0$" or "$-0$", but in this case the signs will have no meaning.

## Examples with solutions for Signed Numbers (Positive and Negative)

### Exercise #1

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

### Step-by-Step Solution

It's important to remember: when we multiply a negative by a negative, the result is positive!

You can use this guide:

Positive

### Exercise #2

Will the result of the exercise below be positive or negative?

$5\cdot(-\frac{1}{2})=$

### Step-by-Step Solution

Let's remember the rule:

$(+x)\times(-x)=-x$

Therefore, the sign of the exercise result will be negative:

$+5\times-\frac{1}{2}=-2\frac{1}{2}$

Negative

### Exercise #3

What will be the sign of the result of the next exercise?

$(-4)\cdot12=$

### Step-by-Step Solution

Let's remember the rule:

$(+x)\times(-x)=-x$

Therefore, the sign of the exercise result will be negative:

$-4\times+12=-48$

Negative

### Exercise #4

What will be the sign of the result of the next exercise?

$(-6)\cdot5=$

### Step-by-Step Solution

Remember the law:

$(+x)\times(-x)=-x$

For the sum of the angles of a triangle is always:

$-6\times+5=-30$

Negative

### Exercise #5

What will be the sign of the result of the next exercise?

$2\cdot(-2)=$

### Step-by-Step Solution

To solve the exercise you need to remember an important rule: Multiplying a positive number by a negative number results in a negative number.

$(−)×(+)=(−)$
Therefore, if we multiply negative 2 by 2 the result will be negative 4.

That is, the result is negative.

$+2\times-2=-4$

Negative

### Exercise #6

What will be the sign of the result of the next exercise?

$(-3)\cdot(-4)=$

### Step-by-Step Solution

Let's remember the rule:

$(-x)\times(-x)=+x$

Therefore, the sign of the exercise result will be positive:

$-3\times-4=+12$

Positive

### Exercise #7

What will be the sign of the result of the next exercise?

$(-2)\cdot(-\frac{1}{2})=$

### Step-by-Step Solution

Let's recall the law:

$(-x)\times(-x)=+x$

Therefore, the sign of the exercise result will be positive:

$-2\times-\frac{1}{2}=+1$

Positive

### Exercise #8

What will be the sign of the result of the next exercise?

$6\cdot3=$

### Step-by-Step Solution

Let's remember the rule:

$(+x)\times(+x)=+x$

Therefore, the sign of the exercise result will be positive:

$+6\times+3=+18$

Positive

### Exercise #9

What will be the sign of the result of the exercise?

$(+3\frac{1}{4}):(+\frac{2}{5})$

### Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

$+:+=$

Since we are dividing a positive number by a positive number, our result will necessarily be positive.

+

### Exercise #10

What will be the sign of the result of the exercise?

$(+7.5):(+3)$

### Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

$+:+=$

Since we are dividing a positive number by a positive number, the result will necessarily be a positive number.

+

### Exercise #11

Fill in the missing number:

$10\cdot?=-100$

### Step-by-Step Solution

Let's remember the law:

$(-x)\times(+x)=-x$

Let's think about which number we need to multiply by 10 to get 100:

$10\times10=100$

Now let's put the numbers together with the appropriate sign as written in the law above, and we'll get:

$+10\times(-10)=-100$

$-10$

### Exercise #12

Fill in the missing number:

$(-6)\cdot?=-12$

### Step-by-Step Solution

Let's remember the law:

$(-x)\times(+x)=-x$

Let's think about which number we need to multiply by 6 to get 12:

$6\times2=12$

Now let's put the numbers together with the appropriate sign as written in the law above, and we'll get:

$-6\times(+2)=-12$

$2$

### Exercise #13

Fill in the missing number:

$2\cdot?=-8$

### Step-by-Step Solution

Let's remember the law:

$(-x)\times(+x)=-x$

Let's think about which number we need to multiply by 2 to get 8:

$2\times4=8$

Now let's put the numbers together with the appropriate sign as written in the law above, and we'll get:

$+2\times(-4)=-8$

$-4$

### Exercise #14

Fill in the missing number:

$(-2)\cdot?=-4$

### Step-by-Step Solution

Let's remember the law:

$(-x)\times(+x)=-x$

Let's think about which number we need to multiply by 2 to get 4:

$2\times2=4$

Now let's put the numbers together with the appropriate sign as written in the law above, and we'll get:

$-2\times(+2)=-4$

$2$

### Exercise #15

Fill in the missing number:

$(-3)\cdot?=-9$

### Step-by-Step Solution

Let's remember the law:

$(-x)\times(+x)=-x$

Let's think about which number we need to multiply by 3 to get 9:

$3\times3=9$

Now let's put the numbers together with the appropriate sign as written in the law above, and we'll get:

$-3\times(+3)=-9$

$3$