The method to solve an exercise with real numbers, when it involves multiplication and division, is very similar to the one we use when we have to add or subtract real numbers, with the difference that, in this case, we must make use of the multiplication and division table that we learned in elementary school.

When we have two real numbers with the same sign (plus or minus) we distinguish two cases:

• The product (result of the multiplication) of two positive numbers will be positive. The quotient (result of the division) of two positive numbers will be positive.
$(+2) \times (+1)= +2$
$(+2) :(+1)= +2$
• The product of two negative numbers will be positive. The quotient of two negative numbers will be positive.
$(-2) \times (-1)= +2$
$(-2) :(-1)= +2$
• When we have two numbers with different signs, that is, one with the plus sign and the other with the minus sign, the result of the multiplication or division will always be negative.
$(+2) \times (-1)= -2$
$(-2) :(+1)= -2$

## Examples with solutions for Multiplication and Division of Signed Mumbers

### 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

Complete the following exercise:

$5\cdot0=$

### Step-by-Step Solution

Let's recall the law:

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

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

$+5\times+0=+0$

0

### Exercise #10

Complete the following exercise:

$2\cdot10=$

### Step-by-Step Solution

Let's remember the rule:

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

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

$+2\times+10=+20$

20

### Exercise #11

Complete the following exercise:

$7\cdot3=$

### Step-by-Step Solution

Let's remember the rule:

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

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

$+7\times+3=+21$

21

### Exercise #12

Complete the following exercise:

$8\cdot2=$

### Step-by-Step Solution

Let's recall the law:

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

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

$+8\times+2=+16$

16

### Exercise #13

Complete the following exercise:

$1000\cdot0=$

### Step-by-Step Solution

Let's remember the rule:

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

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

$+1000\times+0=+0$

0

### Exercise #14

Complete the following exercise:

$5\cdot10=$

### Step-by-Step Solution

Let's remember the rule:

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

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

$+5\times+10=+50$

50

### Exercise #15

Complete the following exercise:

$100\cdot2=$

### Step-by-Step Solution

Let's remember the rule:

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

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

$+100\times+2=+200$