How do you multiply a negative number with a positive fraction?

It is easiest to think about the signs of the numbers separately from their values (as though the numbers were positive):

First consider the signs:

• Multiplying positive by positive => result is positive
• Multiplying positive by negative => result is negative
• Multiplying negative by positive => result is negative
• Multiplying negative by negative => result is positive

Or to summarise:

• If the numbers are the same sign (both positive or both negative) the result is positive.
• If the numbers are of opposite signs (one positive, one negative) the result is negative.

Then multiply the values of the two numbers together (multiply them as though both were positive) and put the sign on the result as decided above.

eg to multiply -24 by 3:

1. negative times positive => result negative (different signs)
2. 24 x 3 = 72
3. sign found in step 1 to be negative, so -24 x 3 = -72

eg to multiply -15 by -1/3

1. negative times negative => result positive (same signs)
2. 15 x 1/3 = 5
3. sign found in step 1 to be positive, so -15 x -1/3 = 5

eg to multiply 12 by -1/4

1. positive times negative => result negative (different signs)
2. 12 x 1/4 = 3
3. sign found in step 1 to be negative, so 12 x -1/4 = -3.