Operations with Integers: A Comprehensive Worksheet Guide
This guide provides a detailed explanation of operations with integers, covering addition, subtraction, multiplication, and division. We'll delve into the rules governing these operations and provide examples to solidify your understanding. This information can be used to create a comprehensive worksheet, tailored to various skill levels.
What are Integers?
Integers are whole numbers, including zero, and their negative counterparts. They can be represented on a number line, stretching infinitely in both positive and negative directions. Examples of integers include: -3, -2, -1, 0, 1, 2, 3, and so on.
1. Addition of Integers
When adding integers, consider the signs:
-
Same Signs: Add the absolute values and keep the common sign. For example: 5 + 3 = 8; -5 + (-3) = -8.
-
Different Signs: Subtract the smaller absolute value from the larger absolute value. The sign of the result is the same as the number with the larger absolute value. For example: 5 + (-3) = 2; -5 + 3 = -2.
Example Worksheet Questions (Addition):
- -7 + 12 = ?
- -9 + (-4) = ?
- 15 + (-8) = ?
- -6 + 6 = ?
- -23 + 15 + 7 = ?
2. Subtraction of Integers
Subtraction of integers can be simplified by converting it into addition:
- Change the subtraction sign to addition and change the sign of the second number. For example: 5 - 3 = 5 + (-3) = 2; -5 - 3 = -5 + (-3) = -8; 5 - (-3) = 5 + 3 = 8; -5 - (-3) = -5 + 3 = -2.
Example Worksheet Questions (Subtraction):
- 11 - 5 = ?
- -8 - 3 = ?
- -6 - (-9) = ?
- 14 - (-7) = ?
- -15 - 10 + 5 = ?
3. Multiplication of Integers
Multiplying integers follows these rules:
-
Same Signs: The product is positive. For example: 5 x 3 = 15; (-5) x (-3) = 15.
-
Different Signs: The product is negative. For example: 5 x (-3) = -15; (-5) x 3 = -15.
Example Worksheet Questions (Multiplication):
- 6 x (-4) = ?
- (-7) x (-2) = ?
- (-3) x 8 = ?
- 5 x (-1) x (-3) = ?
- (-2) x (-2) x (-2) = ?
4. Division of Integers
Division of integers follows the same sign rules as multiplication:
-
Same Signs: The quotient is positive. For example: 15 ÷ 3 = 5; (-15) ÷ (-3) = 5.
-
Different Signs: The quotient is negative. For example: 15 ÷ (-3) = -5; (-15) ÷ 3 = -5.
Example Worksheet Questions (Division):
- 20 ÷ (-4) = ?
- (-18) ÷ (-6) = ?
- (-25) ÷ 5 = ?
- 0 ÷ (-9) = ?
- (-36) ÷ (-4) ÷ 3 = ?
5. Order of Operations (PEMDAS/BODMAS)
Remember to follow the order of operations when solving problems with multiple operations:
- Parentheses/ Brackets
- Exponents/ Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Example Worksheet Questions (Order of Operations):
- -3 + 5 x (-2) = ?
- (4 - 8) ÷ (-2) + 6 = ?
- -2 x (-5) + 10 ÷ (-5) - 3 = ?
This comprehensive guide provides a solid foundation for creating a worksheet on integer operations. Remember to vary the difficulty level and include a mix of problem types to adequately assess understanding. You can easily adapt these examples and create a PDF using a word processor or spreadsheet software.
