The Number Line with Signed Numbers - 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 axisThe Number Line with Signed Numbers: Calculate the distance between integers on a number lineThe Number Line with Signed Numbers: Identify Numbers on a Number LineThe Number Line with Signed Numbers: Missing formulaThe Number Line with Signed Numbers: Identify the greater value

The real line looks like this: a horizontal line in which small equidistant vertical lines are inserted.

Real number line

A1 - Real number line

Characteristics of the number line:

  • Below each vertical line a whole number is inserted in ascending order from left to right.
  • The distance between two consecutive numbers is called a "segment".

The operations of addition and subtraction can be seen as a horizontal movement on the number line.

  • When adding, we move to the right.
  • When subtracting, we move to the left.
Detailed explanation

Suggested Topics to Practice in Advance

  1. Opposite numbers
  2. Elimination of Parentheses in Real Numbers
  3. Positive and negative numbers and zero

Practice The Number Line with Signed Numbers

Question 1

All negative numbers appear on the number line to the left of the number 0.

Question 2

Does the number \( -6 \) appear on the number line to the right of number \( 2\text{?} \)

Question 3

Every positive number is greater than zero

Question 4

\( -2 < 0 \)

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Question 5

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

Examples with solutions for The Number Line with Signed Numbers

Exercise #1

All negative numbers appear on the number line to the left of the number 0.

Video Solution

Step-by-Step Solution

If we draw a number line, we can see that to the right of zero are positive numbers, and to the left of zero are negative numbers:

-4-4-4555-3-3-3-2-2-2-1-1-1000111222333444

Therefore, the answer is correct.

Answer

True.

Exercise #2

Does the number −6 -6 appear on the number line to the right of number 2? 2\text{?}

Video Solution

Step-by-Step Solution

If we draw a number line, we can see that the number minus 6 is located to the left of the number 2:


-4-4-4555-3-3-3-2-2-2-1-1-1000111222333444-5-5-5-6-6-6Therefore, the answer is not correct.

Answer

No

Exercise #3

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 #4

-2 < 0

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Video Solution

Step-by-Step Solution

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

Answer

True

Exercise #5

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

Question 1

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

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Question 2

\( -4>-3 \)

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Question 3

\( 5 < -5 \)

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Question 4

The minus sign can be omitted

Question 5

What is the distance between 0 and F?

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Exercise #6

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

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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 #7

-4>-3

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Video Solution

Step-by-Step Solution

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

-4 < -3

Answer

Not true

Exercise #8

5 < -5

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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 #9

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 #10

What is the distance between 0 and F?

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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

Question 1

What is the distance between A and K?

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Question 2

What is the distance between C and H?

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Question 3

What is the distance between D and I?

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Question 4

What is the distance between D and K?

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Question 5

What is the distance between F and B?

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Exercise #11

What is the distance between A and K?

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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 #12

What is the distance between C and H?

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Video Solution

Step-by-Step Solution

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

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

Answer

5

Exercise #13

What is the distance between D and I?

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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:

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Note that the distance between the two letters is 5 steps

Answer

5

Exercise #14

What is the distance between D and K?

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Video Solution

Step-by-Step Solution

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

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

Answer

7

Exercise #15

What is the distance between F and B?

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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

Topics learned in later sections

  1. Addition and Subtraction of Real Numbers
  2. Multiplication and Division of Real Numbers
  3. Integers