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Adding and Subtracting with Negatives

Chapter 25

Adding and Subtracting with Negatives Concept Explanation:

Adding and subtracting with negative numbers is crucial for mathematical fluency. The basic rules include:

  1. Adding a Negative Number: This is the same as subtracting the positive equivalent. For example,  5 + (-3) = 5 - 3 = 2 .
  2. Subtracting a Negative Number: This is the same as adding the positive equivalent. For example,  5 - (-3) = 5 + 3 = 8 .

Common Mistakes:

  1. Sign Confusion: Many students confuse adding and subtracting negative numbers; it’s essential to remember the rules.
  2. Neglecting Parentheses: When dealing with expressions, ensure that parentheses are properly used to indicate negative numbers.

Helpful Tips:

  • Number Line Visualization: Use a number line to visualize the addition or subtraction of negative numbers.
  • Practice with Word Problems: Real-life contexts can make the concept easier to grasp.

Hard Questions:

Q1: Calculate  7 + (-2) .

Step-by-Step Solution:

  1. Since you are adding a negative number, subtract instead:

 7 + (-2) = 7 - 2 = 5

Answer:

  • The result is  5 .

Q2: Calculate  10 - (-4) .

Step-by-Step Solution:

  1. Subtracting a negative is the same as adding:

 10 - (-4) = 10 + 4 = 14

Answer:

  • The result is  14 .

Q3: Calculate  -3 + (-5) .

Step-by-Step Solution:

  1. Add the two negative numbers:

 -3 + (-5) = -8

Answer:

  • The result is  -8 .

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