Add and subtract integers: word problems

Key notes :-

Understanding Integers

• Integers are whole numbers that can be positive, negative, or zero.
• Examples: -5, -2, 0, 3, 8, etc.
• Integers are represented on a number line, where positive integers are to the right of zero, and negative integers are to the left.

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✏️ When Do We Use Integers in Word Problems?

We use integers in word problems that involve:

• Gains and losses (e.g., money)
• Temperature increase or decrease
• Elevation rise or fall
• Scoring in games (points added or deducted)

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✅ Keywords That Show Integer Operations:

Situation	Operation	Example
Gained, Increased, Rose, Deposited	➕ Add	Gained ₹100 → +100
Lost, Decreased, Fell, Spent, Below	➖ Subtract	Lost ₹50 → –50

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Addition of Integers

• When adding two positive integers, the sum is positive:
  Example: 5+3=8
• When adding two negative integers, the sum is negative:
  Example: −4+(−6)=−10
• When adding a positive and a negative integer, subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.
  Example: 7+(−4)=3 (positive)
• Example: −7+4=−3 (negative)

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Subtraction of Integers

• Subtraction is the same as adding the opposite:
  Example: 5−3 is the same as 5+(−3)=2
• When subtracting a negative integer, it is like adding the positive equivalent:
  Example: 7−(−4)=7+4=11
• When subtracting a positive integer from a negative integer, subtract the smaller number from the larger number and keep the sign of the larger integer:
  Example: −5−3=−8

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Word Problems

Identifying key terms: Pay attention to words like gain, loss, increase, and decrease which help determine the signs (positive or negative).

Context:

• If the problem talks about a gain or increase, use positive numbers.
• If it talks about a loss or decrease, use negative numbers

📐 Steps to Solve Word Problems:

• Read the problem carefully.
• Identify the integers involved (positive or negative).
• Determine if you are adding or subtracting.
• Solve using integer rules.
• Write a final statement/answer.

📝 Practice Word Problems:

1. The temperature was –6°C. It increased by 11°C. What is the new temperature?
2. A diver is 100 m below sea level. He dives down another 80 m. Where is he now?
3. You gain 50 points in a game, then lose 65 points. What is your final score?
4. An account has ₹1,000. After spending ₹1,200, what is the balance?
5. The elevation increased by 150 m, then dropped by 210 m. What is the net change?

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✅ Answers:

1. 5°C
2. –180 m
3. –15 points
4. ₹–200
5. –60 m

Learn with an example