Beyond Zero: Integers & Absolute Value
Integers extend the number line to include negative numbers, zero, and positive numbers, while absolute value measures the distance of any number from zero. Together these concepts allow students to work with temperatures below zero, debts, elevations below sea level, and other real-world situations involving both positive and negative quantities.
Components of Integers & Absolute Value
This section breaks down the key concepts:
- Understanding Integers: The set of whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Comparing & Ordering Integers: Using the number line to determine which integers are greater or less.
- Absolute Value: The distance of a number from zero on the number line, always a non-negative value, written as |n|.
- Operations with Integers: Adding, subtracting, multiplying, and dividing positive and negative numbers.
Examples of Integers & Absolute Value
Understanding Integers Examples
- The temperature drops from 5°F to -3°F, meaning it is now 3 degrees below zero.
- A submarine at -200 meters is 200 meters below sea level, while a mountain peak at 3,000 meters is above sea level.
- A bank account balance of -50 dollars means the account is overdrawn by 50 dollars.
Comparing & Ordering Examples
- Compare -7 and -3: On the number line, -3 is to the right of -7, so -3 > -7.
- Order from least to greatest: 4, -1, 0, -5, 2 becomes -5, -1, 0, 2, 4.
- The coldest temperature was -12°C and the warmest was 8°C, so -12 < 8.
Absolute Value Examples
- |7| = 7 because 7 is 7 units from zero on the number line.
- |-4| = 4 because -4 is 4 units from zero, regardless of direction.
- Compare |-9| and |5|: |-9| = 9 and |5| = 5, so |-9| > |5| even though -9 < 5.
Operations with Integers Examples
- Adding -3 + 5: Start at -3 on the number line, move 5 to the right, landing on 2.
- Subtracting 4 - (-6): Subtracting a negative is the same as adding, so 4 + 6 = 10.
- Multiplying -3 × -4: A negative times a negative gives a positive, so the answer is 12.