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

Question

a and b are negative numbers.

a - b is a negative number.

Choose the correct answer.

Step-by-Step Solution

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

  • Step 1: Identify and understand the condition ab<0 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 ab a - b .

Now, let's work through each step:

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

Step 2: Examine the given choices:

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

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

Answer

a=3,b=1 a=-3,b=-1