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

Question Types:
The Number Line with Signed Numbers: Only addition and subtractionThe Number Line with Signed Numbers: Complete the missing numbersThe Number Line with Signed Numbers: Identifying and defining elementsThe Number Line with Signed Numbers: Place on the axisBasic Definitions: Finding the opposite numberThe Number Line with Signed Numbers: Calculate the distance between integers on a number lineThe Number Line with Signed Numbers: Identify Numbers on a Number LineBasic Definitions: Omitting parenthesesThe Number Line with Signed Numbers: Missing formulaThe Number Line with Signed Numbers: Identify the greater value

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:

A1 - Positive and negative numbers and zero

Detailed explanation

Suggested Topics to Practice in Advance

  1. Opposite numbers
  2. Elimination of Parentheses in Real Numbers

Practice Positive and negative numbers and zero

Question 1

What is the distance between 0 and F?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Question 2

What is the distance between C and H?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Question 3

What is the distance between F and B?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Question 4

What is the distance between D and K?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Question 5

What is the distance between J and D?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Examples with solutions for Positive and negative numbers and zero

Exercise #1

What is the distance between 0 and F?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

Let's begin by marking F and 0 on the number line

We can thus determine that:

F=0 F=0

Therefore, the distance is 0 steps.

Answer

0

Exercise #2

What is the distance between C and H?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

We first mark the letter C on the number line and then proceed towards the letter H:

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Note that the distance between the two letters is 5 steps.

Answer

5

Exercise #3

What is the distance between F and B?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

One might think that as a consequence of the displacement on the axis being towards the negative domain, the result is also negative.

However it is important to keep in mind that here we are referring to the distance.

Distance can never be negative.

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

Answer

4

Exercise #4

What is the distance between D and K?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

We first mark the letter D on the number line and then proceed towards the letter K:

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555KKK

Note that the distance between the two letters is 7 steps.

Answer

7

Exercise #5

What is the distance between J and D?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

Let's begin by marking the letter J on the number line and then proceeding towards the letter D:

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555KKK

Note that the distance between the two letters is 6 steps

Answer

6

Question 1

What is the distance between A and K?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Question 2

What is the distance between I and E?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Question 3

What is the distance between D and I?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Question 4

\( 5 < -5 \)

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Question 5

\( -2 < 0 \)

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Exercise #6

What is the distance between A and K?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

One might think that because there are numbers on the axis that go into the negative domain, that the result must also negative.

However 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.

Answer

10

Exercise #7

What is the distance between I and E?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

We first mark the letter I on the number line and then proceed towards the letter E:

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555KKK

Note that the distance between the two letters is 4 steps.

Answer

4

Exercise #8

What is the distance between D and I?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

Step-by-Step Solution

Let's begin by marking the letter D on the number line and then proceeding towards the letter I:

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555KKK

Note that the distance between the two letters is 5 steps

Answer

5

Exercise #9

5 < -5

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Video Solution

Step-by-Step Solution

As per the fact that there cannot be a situation where a negative number is greater than a positive number, the answer is incorrect.

Answer

Not true

Exercise #10

-2 < 0

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Video Solution

Step-by-Step Solution

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

Answer

True

Question 1

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

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Question 2

\( -4>-3 \)

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Question 3

Every positive number is greater than zero

Question 4

The minus sign can be omitted

Question 5

\( 3.98 \) and \( +3.98 \) are two ways of writing the same number.

Exercise #11

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

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Video Solution

Step-by-Step Solution

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

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

Answer

Not true

Exercise #12

-4>-3

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Video Solution

Step-by-Step Solution

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

-4 < -3

Answer

Not true

Exercise #13

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 inevitably greater than zero.

Answer

True

Exercise #14

The minus sign can be omitted

Step-by-Step Solution

The sign cannot be omitted as it determines whether the number will be negative or positive.

Answer

Not true

Exercise #15

3.98 3.98 and +3.98 +3.98 are two ways of writing the same number.

Step-by-Step Solution

Indeed, both forms are identical since a number without a sign will be positive, as in the case of 3.98

If there is a plus sign before the number, the number is necessarily positive, as in the case of +3.98

Therefore, the answer is correct.

Answer

True

Topics learned in later sections

  1. Real line or Numerical line
  2. Addition and Subtraction of Real Numbers
  3. Multiplication and Division of Real Numbers
  4. Integers