Adding and Subtracting Integers in Word Problems

Adding and Subtracting Integers in Word Problems

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Adding and Subtracting Integers in Word Problems

Adding and subtracting integers in word problems isn't too different from performing these operations on integers generally. However, the difficulty with word problems often lies in understanding the problem and then translating it into a mathematical equation. Here's a step-by-step guide:

  1. Understand the Problem: Start by reading the problem carefully. Identify the integers involved and the problem's requirements.
  2. Translate the Problem: Turn the problem into a mathematical equation. Look for keywords indicating the operation to use.
  3. Perform the Operation: Once the equation is set up, perform the operation. Remember, adding two negative integers gives a negative result. Subtracting a negative from a positive is like adding the absolute values. Subtracting a positive from a negative is the same as adding two negatives.
  4. Check Your Answer: Verify your answer by putting it back into the original problem. If it doesn't make sense, you may need to review your work.

Here are a few examples:

Example 1: John has $5 in his pocket. He owes his friend $3. How much money will John have after he pays his friend?

Translation: \(5 - 3 = ?\)
Solution: John will have $2.

Example 2: A submarine is 400 feet below sea level. It then descends another 180 feet. What is its new position relative to sea level?

Translation: \(-400 - 180 = ?\)
Solution: The submarine is 580 feet below sea level.