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:

A1 - Positive and negative numbers and zero

Suggested Topics to Practice in Advance

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

Practice Positive and negative numbers and zero

examples with solutions for positive and negative numbers and zero

Exercise #1

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

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.

Answer

4

Exercise #2

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

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.

Answer

10

Exercise #3

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

Video Solution

Answer

True.

Exercise #4

-2 < 0

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

Video Solution

Answer

True

Exercise #5

3=3 -3=-3

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

Video Solution

Answer

True

examples with solutions for positive and negative numbers and zero

Exercise #1

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

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

Video Solution

Answer

Not true

Exercise #2

-4>-3

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

Video Solution

Answer

Not true

Exercise #3

5 < -5

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

Video Solution

Answer

Not true

Exercise #4

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

Video Solution

Answer

No

Exercise #5

What is the opposite number of 5 5

Video Solution

Answer

5 -5

examples with solutions for positive and negative numbers and zero

Exercise #1

What is the opposite number of 87 87

Video Solution

Answer

87 -87

Exercise #2

What is the opposite number of 0.7 0.7

Video Solution

Answer

0.7 -0.7

Exercise #3

What is the opposite number of 7 -7

Video Solution

Answer

7 7

Exercise #4

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

Answer

5

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

Answer

6

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