Math with Mr. J: Mini Course on Integers

Overview

• Topics covered:
  • What integers are
  • Comparing and ordering integers
  • Adding, subtracting, multiplying, and dividing integers
• Audience: New learners or those reviewing integers.

1. What are Integers?

• Definition: Integers are whole numbers without fractional or decimal parts.
• Includes:
  • Positive numbers (e.g., 1, 2, 3, ...)
  • Negative numbers (e.g., -1, -2, -3, ...)
  • Zero (0)

Number Line Illustration

• Positive Integers: Counting up from zero (1, 2, 3, ...)
• Negative Integers: Counting down from zero (-1, -2, -3, ...)
• Zero: Separates positive and negative integers.

Examples of Integers

• Positive: 8, 37, 194
• Negative: -9, -5, -72
• Zero: 0

Non-Integers Examples

• 1/2, 4.38, 6.3, 0.45 (all contain fractions or decimals)

Integer Check

• Yes/No: Check if given numbers are integers.
  • 42: Yes
  • -8: Yes
  • -8.5: No
  • 3 1/3: No
  • 0: Yes
  • -7: Yes
  • 1/12: No
  • 996: Yes
  • 10.75: No

2. Comparing and Ordering Integers

Comparing Integers

• Visualize with a number line:
  • Right is greater: e.g., -1 is greater than -2.
  • Left is smaller: e.g., 3 is greater than -5.

Examples

1. -1 vs -2: -1 is greater.
2. -5 vs 3: 3 is greater.
3. 0 vs -4: 0 is greater.
4. 95 vs 6: 95 is less.
5. -14 vs 11: -14 is less.
6. -27 vs -29: -27 is greater.

Ordering Integers

• Organizing from least to greatest or vice versa using number lines.

Least to Greatest Example

• Order: -5, -2, -1, 0, 4

Greatest to Least Example

• Order: 5, 3, 1, -2, -3

3. Operations with Integers

Addition

1. Example 1: 12 + (-7)
   • Different signs: Subtract absolute values.
   • Answer: 5
2. Example 2: 8 + (-10)
   • Same signs: Add absolute values.
   • Answer: -18

Subtraction

1. Example 1: 5 - (-9)
   • Convert to addition: 5 + 9 = 14
2. Example 2: -3 - 20
   • Add opposite: -3 + (-20) = -23

Multiplication

1. Example 1: -7 * 4
   • Different signs: Result is negative (Answer: -28)
2. Example 2: -10 * -6
   • Same signs: Result is positive (Answer: 60)

Division

1. Example 1: -48 / -8
   • Same signs: Result is positive (Answer: 6)
2. Example 2: 36 / -4
   • Different signs: Result is negative (Answer: -9)

Conclusion

• This mini-course covers the fundamentals of working with integers.
• Important concepts include definitions, comparisons, orderings, and performing operations.
• Mastery of these concepts is essential for further mathematical understanding.