Add and subtract integers: word problems

Key notes :-

1. 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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2. 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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3. 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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4. 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

Learn with an example