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102 LearnersLast updated on September 1, 2025
Subtraction of Two Negative Integers
The mathematical operation of finding the difference between two negative integers involves understanding how to handle negative values within subtraction. This operation is key in simplifying calculations and solving problems that involve negative numbers.
What is Subtraction of Two Negative Integers?
Subtracting two negative integers involves finding the difference between them, which can be understood as adding the additive inverse of the second integer to the first.
When handling negative integers, it is critical to pay attention to the signs.
The result of subtracting two negative integers can be positive, negative, or zero, depending on the values and their order.
How to Subtract Two Negative Integers?
When subtracting two negative integers, follow these steps:
1. Identify the integers: Recognize both integers and their signs.
2. Change the operation: Convert the subtraction of a negative integer to the addition of its positive equivalent.
3. Perform addition: Add the numbers as if they were positive, then apply the sign of the larger absolute value integer to the result.
Methods to Subtract Two Negative Integers
The following are common methods for subtracting two negative integers:
Method 1: Direct Method
Step 1: Rewrite the expression by changing the subtraction of a negative integer to addition.
Step 2: Add the absolute values of both integers.
Step 3: Use the sign of the integer with the larger absolute value for the result.
Method 2: Number Line Method
Step 1: Represent both integers on a number line.
Step 2: Count the spaces between the two integers.
Step 3: Determine the direction (left or right) based on the integers’ positions.
Properties of Subtraction of Two Negative Integers
Subtraction of negative integers follows certain properties:
1. Subtraction is not commutative: Changing the order changes the result. (-A) - (-B) ≠ (-B) - (-A)
2. Subtraction is not associative: Grouping changes the result. [(-A) - (-B)] - (-C) ≠ (-A) - [(-B) - (-C)]
3. Subtraction of a negative is addition: (-A) - (-B) = (-A) + B
4. Subtracting zero changes nothing: (-A) - 0 = -A
Tips and Tricks for Subtracting Two Negative Integers
Here are some tips and tricks to efficiently subtract two negative integers:
1. Remember to change the operation to addition when subtracting a negative.
2. Use a number line for better visualization, especially for beginners.
3. Focus on the absolute values to determine the sign of the result.
4. Practice with different integer pairs to build confidence.
Misinterpreting signs
Students often confuse subtraction and addition when dealing with negative signs. Always change the subtraction of a negative number to addition.
Mistake 1
Ignoring absolute values
Forget to consider the absolute values of integers when determining the result’s sign, which can lead to incorrect answers.
Mistake 2
Miscalculating on a number line
When using a number line, ensure accurate counting of spaces and understanding of direction to avoid mistakes.
Mistake 3
Overlooking simplification
Simplification involves rewriting the expression in a straightforward manner. Always simplify the expression first.
Mistake 4
Omitting zero as a placeholder
If needed, use zero as a placeholder to maintain alignment and ensure correct operations.
Mistake 5
Examples of Subtraction of Two Negative Integers
Subtract -5 from -3
2
Problem 1
Use the direct method, (-3) - (-5) = -3 + 5 = 2
Subtract -8 from -12
Explanation
-4
Problem 2
(-12) - (-8) = -12 + 8 = -4
Subtract -15 from -7
Explanation
8
Problem 3
(-7) - (-15) = -7 + 15 = 8
Subtract -20 from -25
Explanation
-5
Problem 4
(-25) - (-20) = -25 + 20 = -5
Subtract -3 from -10
Explanation
-7
Yes, subtracting a negative integer is the same as adding its positive equivalent.
1.Is subtraction commutative with negative integers?
2.How do we determine the sign of the result?
3.What happens when subtracting zero from a negative integer?
4.What method is best for beginners?
Common Mistakes and How to Avoid Them in Subtracting Two Negative Integers
Subtracting negative integers can be tricky, leading to common errors. Being aware of these mistakes can help avoid them.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
