Scenario: Hiking & Financial Planning - Apply all rational number operations to solve complex real-world problems!
A hiker starts at sea level (0 meters). During the day, they:
What is their final position relative to the starting point?
Calculation: 0 + 250 + (-180) + (-75) = -5 meters
The hiker ends up 5 meters below the starting point.
Step 1: Start at sea level: 0 meters
Step 2: Morning climb: 0 + 250 = 250 meters
Step 3: Afternoon descent: 250 + (-180) = 70 meters
Step 4: Evening descent: 70 + (-75) = -5 meters
Sarah has $120 in her savings account. She spends $150 on a purchase, then deposits $80 from her paycheck. What is her final account balance?
Calculation: 120 + (-150) + 80 = 50 dollars
Sarah's final account balance is $50.
Method 1: Sequential calculation
120 - 150 + 80 = -30 + 80 = 50
Method 2: Group positive and negative amounts
(120 + 80) + (-150) = 200 - 150 = 50
Group positive and negative numbers separately, then combine.
Example: 5 + (-3) + 8 + (-2) = (5 + 8) + (-3 + -2) = 13 + (-5) = 8
Look for numbers that add to convenient values (like 10, 100).
Example: 7 + 3 + 5 = (7 + 3) + 5 = 10 + 5 = 15
Always check your answer:
An elevator starts at the 5th floor, goes up 8 floors, down 12 floors, up 3 floors, and down 7 floors. What floor does it end on?
Your calculation:
A stock starts at $50. It gains $3, loses $8, gains $5, and loses $2. What is the final price? What is the total change from the starting price?
Your calculation:
The temperature at 6 AM was -5°C. It rose 8°C by noon, dropped 3°C by 6 PM, and dropped another 6°C by midnight. What was the temperature at midnight? What was the total change from 6 AM to midnight?
Your calculation: