# Positive and negative numbers and zero - Examples, Exercises and Solutions

Positive, negative numbers and zero are a fundamental topic in algebra, it is very easy to understand it by drawing a number line in which zero is located in the middle.

• Zero is our reference point.
• The positive numbers are the same numbers we use to this day and are located to the right of zero. Now that we are beginning to study the subject of positive and negative numbers, we will see a sign before the positive ones, the plus sign (+), to make it clear that it is a positive number, but, later, after we understand the subject well, we will suppress it.
• Negative numbers are those that are located on the left side of zero and have a minus sign (-). Unlike positive numbers, the minus sign will always appear next to negative numbers to indicate that they are actually negative numbers.

We will illustrate this on the number line:

## examples with solutions for positive and negative numbers and zero

### Exercise #1

What is the distance between F and B?

### Step-by-Step Solution

It is true that because the displacement on the axis is towards the negative domain, one might think that the result is also negative.

But it is important to keep in mind that here we are asking about the distance.

Distance can never be negative.

Even if the displacement is towards the negative domain, the distance is an existing value.

4

### Exercise #2

What is the distance between A and K?

### Step-by-Step Solution

It is true that because there are numbers on the axis that go into the negative domain, one might think that the result is also negative.

But it is important to keep in mind that here we are asking about distance.

Distance can never be negative.

Even if we move towards or from the domain of negativity, distance is an existing value (absolute value).

We can think of it as if we were counting the number of steps, and it doesn't matter if we start from five or minus five, both are 5 steps away from zero.

10

5 < -5

### Step-by-Step Solution

Since there cannot be a situation where a negative number is greater than a positive number, the answer is incorrect.

Not true

-2 < 0

### Step-by-Step Solution

Since every negative number is necessarily less than zero, the answer is indeed correct

True

### Exercise #5

4\frac{1}{2} < -5

### Step-by-Step Solution

The answer is incorrect because a negative number cannot be greater than a positive number:

4\frac{1}{2} > -5

Not true

-4>-3

### Step-by-Step Solution

The answer is incorrect because neative 3 is greater than negative 4:

-4 < -3

Not true

### Exercise #7

Every positive number is greater than zero

### Step-by-Step Solution

The answer is indeed correct, any positive number to the right of zero is necessarily greater than zero.

True

### Exercise #8

Fill in the corresponding sign

$+3?0$

### Step-by-Step Solution

Since the number 3 comes after the number 0, it is necessarily greater:

3 > 0

>

### Exercise #9

Fill in the corresponding sign

$17?+17$

### Step-by-Step Solution

Since both numbers are positive and identical, they are equal to each other:

$17=+17$

$=$

K < A

### Step-by-Step Solution

Let's locate the numerical representation of the point on the number line:

$K=5$

$A=-5$

Now let's place:

5 < -5

It appears that the answer is not correct.

Not true

-4>A

### Step-by-Step Solution

Let's locate the numerical representation of the letter on the number line:

$A=-5$

Now let's place:

-4 > -5

It appears that the answer is indeed correct.

True

B>A

### Step-by-Step Solution

Let's locate the numerical representation of the letter on the number line:

$B=-4$

$A=-5$

Now let's place:

-4 > -5

It appears that the answer is indeed correct.

True

### Exercise #13

What are the missing numbers?

### Step-by-Step Solution

Let's look at the numbers from left to right:

$-6,-4,-2$

We notice that the common operation is:

$+2$

$-6+2=-4$

$-4+2=-2$

Therefore, the next sequence will be:

$-2+2=0$

$0+2=2$

0,2

### Exercise #14

Fill in the corresponding sign

$0?-3.9$

### Step-by-Step Solution

Since the number -3.9 is further from zero, it must be smaller, therefore:

0 > -3.9

> 

### Exercise #15

Fill in the missing number

### Step-by-Step Solution

Let's look at the numbers from left to right:

$0,\frac{1}{2},1,1\frac{1}{2}$

We notice that the common operation is:

$+\frac{1}{2}$

$0+\frac{1}{2}=\frac{1}{2}$

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

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

Therefore, the next sequence will be:

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

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

$2\frac{1}{2}+\frac{1}{2}=3$

$2,2\frac{1}{2},3$
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