What is negative 5 minus negative 3
The Correct Answer and Explanation is:
The correct answer is -2.
Explanation: Understanding Subtraction of Negative Numbers
The problem we are solving is: -5 – (-3)
At first glance, subtracting a negative number can seem confusing. However, there is a fundamental rule in mathematics that simplifies this process: subtracting a negative number is the same as adding its positive counterpart.
Let’s explore why this is true using two common illustrations.
1. The Number Line Method
A number line is an excellent visual tool for understanding operations with integers.
- Starting Point: First, find your starting number on the number line, which is -5.
- Understanding the Operation: The operation of subtraction normally means moving to the left on the number line (e.g., 5 – 3 means start at 5 and move 3 steps left). However, we are subtracting a negative number. The negative sign acts as a “reversal” or “opposite” direction.
- Applying the Operation: So, instead of moving 3 steps to the left (which is what subtracting 3 would do), the instruction to subtract negative 3 tells us to do the opposite: move 3 steps to the right.
Starting at -5, if we move 3 steps to the right, we land on -2.
(-5 → -4 → -3 → -2)
2. The Debt and Money Analogy
Another helpful way to think about this is in terms of money and debt.
- Imagine that a negative number represents a debt. So, -5 means you have a debt of $5.
- The operation is “minus negative 3” or – (-3). Think of this as “taking away a debt of $3.”
- If someone takes away a $3 debt from you, your financial situation has improved by $3. This is equivalent to giving you $3.
So, starting with a $5 debt (-5) and then having a $3 debt taken away is the same as adding $3 to your situation. The calculation becomes:
-5 + 3 = -2
Your original debt of $5 has been reduced, and you are now left with only a $2 debt, or -2.
Conclusion:
Both methods demonstrate the same core principle. The two consecutive negative signs (minus negative) cancel each other out and become a positive.
Therefore, the expression:
-5 – (-3)
is transformed into:
-5 + 3
Which equals -2.
