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Addition and subtraction of integers

Autor:HASH FUTURE SCHOOL (#FUTURESCHOOL), mossback90, Peter22
Tópico:Números
Understanding the Concepts & RulesBased on the video and your notes, let's summarize the key ideas for adding and subtracting integers. A. The Number Line as a Movement Tool (for both addition and subtraction)Think of the number line as your map:
  • Positive Numbers: Move to the right.
  • Negative Numbers: Move to the left.
  • Starting Point: Always begin at the first number in your problem.
B. Rules for Adding Integers
  1. Adding Numbers with the SAME Sign:
    • Rule: Add their "plain" values (their absolute values).
    • Keep the original sign.
    • Example:
      • 5+3=8 (Both positive, so add 5 and 3, keep positive)
      • −5+(−3)=−8 (Both negative, so add 5 and 3, keep negative)
  2. Adding Numbers with DIFFERENT Signs:
    • Rule: Subtract the smaller "plain" value (absolute value) from the larger "plain" value.
    • The sign of your answer will be the sign of the number that had the larger absolute value (the number "further from zero").
    • Example:
      • 5+(−3)=2 (Subtract 3 from 5, which is 2. The 5 is larger and positive, so the answer is positive.)
      • −5+3=−2 (Subtract 3 from 5, which is 2. The 5 is larger and negative, so the answer is negative.)
C. Rule for Subtracting Integers: The "Keep, Change, Change" Trick!Subtraction can be tricky, but there's a simple rule to turn it into an addition problem:
  • Rule: To subtract an integer, add its opposite.
    • This is often remembered as "Keep, Change, Change" (KCC):
      1. Keep the first number exactly the same.
      2. Change the subtraction sign ( ) to an addition sign (+ ).
      3. Change the sign of the second number to its opposite. (If it was positive, make it negative. If it was negative, make it positive).
  • Example:
    • 3−7=?
      • Keep 3, Change − to +, Change 7 to −7
      • Becomes: 3+(−7) (Now use addition rule for different signs)
      • Solution: −4
    • −5−2=?
      • Keep −5, Change − to +, Change 2 to −2
      • Becomes: −5+(−2) (Now use addition rule for same signs)
      • Solution: −7
    • 4−(−3)=?
      • Keep 4, Change − to +, Change −3 to +3
      • Becomes: 4+3 (Now use addition rule for same signs)
      • Solution: 7

    • Real-Life Application QuestionsFor each problem, first, write down the numbers as integers. Then, set up the addition or subtraction problem that applies, and finally, solve it.

    1. Temperature Fluctuation: In the morning, the temperature was . During the day, it rose by 10∘C. What was the temperature at the end of the day?
      • Set up:
      • Solution:
    2. Scuba Diving: A scuba diver is at a depth of −30 meters (30 meters below sea level). She then descends another 15 meters. What is her new depth?
      • Set up:
      • Solution:
    3. Bank Balance: Your bank account has ₹750. You make a withdrawal (take out) of ₹900. What is your new bank balance?
      • Set up:
      • Solution:
    4. Mountain & Valley: The peak of Mount Everest is approximately 8,848 meters above sea level. The deepest part of the Mariana Trench is approximately −11,000 meters (11,000 meters below sea level). What is the vertical distance (difference in elevation) between the highest point on Earth and the deepest point in the ocean?
      • Set up:
      • Solution:
    5. Game Score: In a video game, you start with 0 points. You lose 200 points on one level, then gain 350 points on the next, and then lose another 100 points on the final level. What is your total score?
      • Set up:
      • Solution:

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