# Signed Numbers (Positive and Negative) - Examples, Exercises and Solutions

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 "whole number" 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.

## Practice Signed Numbers (Positive and Negative)

### Exercise #1

a is negative number.

b is negative number.

What is the sum of a+b?

### Step-by-Step Solution

Let's check an example:

Let's say a = -1

b = -2

-1 + (-2) =

-1-2=

-3

As the example shows us, what we can also do with additional examples,

is that adding two negative numbers will always result in a negative number.

Negative

### Exercise #2

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 #3

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 #4

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 #5

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

$\frac{-0.9}{1.1}:(-4)$

### Step-by-Step Solution

Let's see if the number is negative or positive.

As you can see, in the expression the numerator is negative and the denominator is positive.

That is, the division exercise will look like this:

$\frac{-}{+}:-=$

The result of the expression will be a negative number, since we are dividing a negative number by a positive number.

Therefore, the exercise that will be obtained will look like this:

$-:-=+$

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

+

### Exercise #1

a is negative number.

b is negative number.

What is the sum of a+b?

### Step-by-Step Solution

Let's check an example:

Let's say a = -1

b = -2

-1 + (-2) =

-1-2=

-3

As the example shows us, what we can also do with additional examples,

is that adding two negative numbers will always result in a negative number.

Negative

### Exercise #2

The sum of two numbers is positive.

Therefore, the two numbers are...?

### Step-by-Step Solution

Testing through attempts:

Let's assume both numbers are positive: 1 and 2.

1+2 = 3

Positive result.

Let's assume both numbers are negative -1 and -2

-1+(-2) = -3

Negative result.

Let's assume one number is positive and the other negative: 1 and -2.

1+(-2) = -1

Negative result.

Let's test a situation where the value of the first number is greater than the second: -1 and 2.

2+(-1) = 1

Positive result.

That is, we can see that when both numbers are positive, or in certain types of cases when one number is positive and the other negative, the sum is positive.

### Exercise #3

a is a positive number.

b is a negative number.

The sum of a+b is...?

### Step-by-Step Solution

We will test this through experiments:

Let's assume that the value of the positive number is greater than the value of the negative number 1 and 2.

1+(-2) = -1

The result is negative.

We will try to make the value of the second number greater than the first 2 and 1.

2+(-1)= 1

The result is positive.

That is, we can see that the result depends on the values of the two numbers, so we cannot know from the beginning what the result will be.

It is not possible to know.

### Exercise #4

a is a positive number.

b is a negative number.

What kind of number is the sum of b and a?

### Step-by-Step Solution

We will illustrate with an example:

Let's assume that a is 1 and b is -2

1+ (-2) =
1-2 = -1

Now we define that a is 2

and b is -1

2+(-1) =
2-1 = 1

Even though the operation is negative, the number remains positive.

That is, if the absolute value of the positive number (a) is greater than that of the negative (b), the result will still be positive.

As we do not have data on this information, it is impossible to know what the sum of a+b will be.

.Impossible to know.

### Exercise #5

a and b are negative numbers.

Therefore, what kind of number is is a-b?

### Step-by-Step Solution

We test using an example:

We define that

a = -1

b = -2

Now we replace in the exercise:

-1-(-2) = -1+2 = 1

In this case, the result is positive!

We test the opposite case, where b is greater than a

We define that

a = -2

b = -1

-2-(-1) = -2+1 = -1

In this case, the result is negative!

Therefore, the correct solution to the whole question is: "It's impossible to know".

Impossible to know.

### Exercise #1

A and B are positive numbers.

Therefore, A - B results in...?

### Step-by-Step Solution

Let's define the two numbers as 1 and 2.

Now let's place them in an exercise:

2-1=1

The result is positive!

Now let's define the numbers in reverse as 2 and 1.

Let's place an equal exercise and see:

1-2=-1

The result is negative!

We can see that the solution of the exercise depends on the absolute value of the numbers, and which one is greater than the other,

Even if both numbers are positive, the subtraction operation between them can lead to a negative result.

Impossible to know

### Exercise #2

a is a negative number.

b is a positive number.

Therefore, a - b is....?

### Step-by-Step Solution

We test using an example:

We define that

a = -1

b = 2

Now we replace in the exercise:

-1-(2) = -1-2 = -3

In this case, the result is negative!

We test a case where the value of b is less than a

We define that

a = -2

b = 1

-2-(1) = -2-1 = -3

In this case, the result is again negative.

Since it is not possible to produce a case where a is greater than b (because a negative number is always less than a positive number),

The result will always be the same: "negative", and that's the solution!

Negative

### Exercise #3

$-27-(-7)+(-6)+2-11=$

### Step-by-Step Solution

First, we solve the multiplication exercise, that is where there is a plus or minus sign before another sign.

$-27+7-6+2-11=$

Now we solve as a common exercise from left to right:

$-27+7=-20$

$-20-6=-26$

$-26+2=-24$

$-24-11=-35$

$-35$

### Exercise #4

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

$(-16)\cdot(-5)=$

Positive

### Exercise #5

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

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