Positive and Negative Numbers Practice Worksheet

Understanding Positive and Negative Numbers

When dealing with numbers, it’s essential to understand the concept of positive and negative numbers. These numbers are used to represent quantities that have opposite directions or values. In this practice worksheet, we’ll explore the basics of positive and negative numbers, their operations, and provide exercises to help you master the concept.

What are Positive and Negative Numbers?

Positive Numbers: A positive number is a number that is greater than zero. It can be a whole number, a fraction, or a decimal. For example:

• Whole numbers: 1, 2, 3,…
• Fractions: ¹⁄₂, ²⁄₃, ³⁄₄,…
• Decimals: 0.5, 1.2, 3.4,…

Negative Numbers: A negative number is a number that is less than zero. It can also be a whole number, a fraction, or a decimal. For example:

• Whole numbers: -1, -2, -3,…
• Fractions: -¹⁄₂, -²⁄₃, -³⁄₄,…
• Decimals: -0.5, -1.2, -3.4,…

Operations with Positive and Negative Numbers

When performing operations with positive and negative numbers, it’s crucial to follow specific rules:

• Addition: When adding two numbers with the same sign (both positive or both negative), you add their absolute values and keep the same sign.
  • 2 + 3 = 5
  • (-2) + (-3) = -5
• Subtraction: When subtracting two numbers with the same sign, you subtract the absolute values and keep the same sign.
  • 5 - 3 = 2
  • (-5) - (-3) = -2
• Multiplication: When multiplying two numbers with the same sign, the result is always positive.
  • 2 × 3 = 6
  • (-2) × (-3) = 6
• Division: When dividing two numbers with the same sign, the result is always positive.
  • 6 ÷ 2 = 3
  • (-6) ÷ (-2) = 3

However, when performing operations with numbers that have opposite signs, the rules change:

• Addition: When adding two numbers with opposite signs, you subtract the absolute values and keep the sign of the number with the larger absolute value.
  • 2 + (-3) = -1
  • (-2) + 3 = 1
• Subtraction: When subtracting two numbers with opposite signs, you add the absolute values and keep the sign of the number being subtracted from.
  • 5 - (-3) = 8
  • (-5) - 3 = -8
• Multiplication: When multiplying two numbers with opposite signs, the result is always negative.
  • 2 × (-3) = -6
  • (-2) × 3 = -6
• Division: When dividing two numbers with opposite signs, the result is always negative.
  • 6 ÷ (-2) = -3
  • (-6) ÷ 2 = -3

Practice Exercises

Now it’s time to practice! Try to solve the following exercises:

Section 1: Addition and Subtraction

1. 2 + 3 =?
2. (-2) + (-3) =?
3. 5 - 2 =?
4. (-5) - (-2) =?
5. 3 + (-2) =?
6. (-1) + 4 =?
7. 2 - (-3) =?
8. (-4) - 1 =?

Section 2: Multiplication and Division

1. 2 × 3 =?
2. (-2) × (-3) =?
3. 6 ÷ 2 =?
4. (-6) ÷ (-2) =?
5. 2 × (-3) =?
6. (-2) × 3 =?
7. 6 ÷ (-2) =?
8. (-6) ÷ 2 =?

Section 3: Mixed Operations

1. 2 + 3 × (-2) =?
2. (-1) + 2 - 3 =?
3. 4 - 2 × (-1) =?
4. (-3) + 2 - (-1) =?
5. 2 × (-3) + 4 =?
6. (-2) × 3 - 1 =?
7. 3 + (-2) × 2 =?
8. (-1) + 4 ÷ (-2) =?

Answers

Section 1: Addition and Subtraction

1. 5
2. -5
3. 3
4. -3
5. 1
6. 3
7. 5
8. -5

Section 2: Multiplication and Division

1. 6
2. 6
3. 3
4. 3
5. -6
6. -6
7. -3
8. -3

Section 3: Mixed Operations

1. -4
2. -2
3. 6
4. -2
5. -2
6. -7
7. -1
8. -3

Important Notes

• When performing operations with positive and negative numbers, make sure to follow the rules outlined above.
• Pay attention to the signs of the numbers and how they affect the result.
• Practice regularly to become more comfortable with working with positive and negative numbers.

In conclusion, understanding positive and negative numbers is crucial for performing various mathematical operations. By following the rules outlined in this practice worksheet, you’ll become more confident in working with these numbers. Remember to practice regularly to reinforce your knowledge.