Negative Numbers Subtraction: When is a - b < 0?

a and b are negative numbers.

a - b is a negative number.

Choose the correct answer.

To solve this problem, we'll follow these steps:

• Step 1: Identify and understand the condition $a - b < 0$.
• Step 2: Evaluate each option where both numbers are negative.
• Step 3: Check to see which one yields a negative result for $a - b$.

Now, let's work through each step:

Step 1: The problem gives us $a$ and $b$ are negative numbers, and $a - b$ must also be negative, meaning $a < b$.

Step 2: Examine the given choices:

• Choice 1: $a = -5, b = 5$: Since $b$ is positive, this pair doesn't meet the condition.
• Choice 2: $a = -5, b = -6$: Calculate $a - b = -5 - (-6) = -5 + 6 = 1$, which is positive.
• Choice 3: $a = -3, b = -1$: Calculate $a - b = -3 - (-1) = -3 + 1 = -2$, which is negative.
• Choice 4: $a = -3, b = -4$: Calculate $a - b = -3 - (-4) = -3 + 4 = 1$, which is positive.

Step 3: Based on calculations above, the only pair that results in a negative $a - b$ is Choice 3: $a = -3, b = -1$. Therefore, $a = -3, b = -1$ is the correct answer.