Understanding integers

Key Notes:

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Scenario 2: Temperature Changes

Situation: The temperature in a city changes from 5°C to -3°C overnight.

Explanation:

• Initial Temperature: +5°C
• Final Temperature: -3°C
• Change in Temperature: −3−5=−8

Result: The temperature dropped by 8°C.

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Scenario 3: Elevation Above and Below Sea Level

Situation: A submarine dives 200 meters below sea level, then rises 150 meters.

Explanation:

• Initial Position: 0 meters (sea level)
• Dive: -200 meters
• Rise: +150 meters
• Final Position: −200+150 = −50

Result: The submarine is 50 meters below sea level.

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Scenario 4: Business Profits and Losses

Situation: A business makes a profit of $1,000 in January but incurs a loss of $600 in February.

Explanation:

• January Profit: +1,000/-
• February Loss: -600 /-
• Net Profit/Loss: 1000+(−600)=400

Result: The business has a net profit of 400/- over the two months.

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Scenario 5: Points in a Game

Situation: In a game, a player scores +10 points in the first round and loses 15 points in the second round.

Explanation:

• First Round: +10 points
• Second Round: -15 points
• Total Points: 10+(−15)=−5

Result: The player has a total of -5 points after two rounds.

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Scenario 6: Balancing a Checkbook

Situation: John writes a check for $75 and later deposits $100 into his account.

Explanation:

• Initial Balance: $0
• Check Written: -$75
• Deposit: +$100
• Final Balance: −75+100=25

Result: John’s account balance is $25.

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Scenario 7: Stock Market

Situation: A stock’s price increases by $5 on Monday and decreases by $8 on Tuesday.

Explanation:

• Monday Increase: +$5
• Tuesday Decrease: -$8
• Net Change: 5+(−8)=−3

Result: The stock’s price has a net decrease of $3.

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Scenario 8: Tracking Weight Loss and Gain

Situation: Alex gains 3 kg over the holidays and loses 5 kg after exercising.

Explanation:

• Weight Gain: +3 kg
• Weight Loss: -5 kg
• Net Weight Change: 3+(−5)=−2

Result: Alex has a net weight loss of 2 kg.

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Scenario 9: Balancing an Equation

Situation: To balance the equation x+5=2x + 5 = 2x+5=2, solve for xxx.

Explanation:

• Subtract 5 from both sides: x+5−5=2−5
• Simplify: x=−3

Result: xxx equals -3, indicating a value that makes the equation true.

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Scenario 10: Travel Distance

Situation: A car travels 100 km north (positive direction) and then 150 km south (negative direction).

Explanation:

• Northward Travel: +100 km
• Southward Travel: -150 km
• Net Distance: 100+(−150)=−50

Result: The car is 50 km south of its starting point.

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Key Takeaways:

• Positive integers represent gains, increases, or movements in a positive direction.
• Negative integers represent losses, decreases, or movements in a negative direction.
• Understanding how to add, subtract, and interpret positive and negative integers helps in various real-life scenarios, from financial planning to tracking physical changes.