.

product of the numbers (without their signs) is 24. The answer is –24.

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      Dividing Signed Numbers

      The rules for assigning the sign of the answer when dividing signed numbers are exactly the same as those for multiplying signed numbers (see “Multiplying Signed Numbers” earlier in this chapter.) The rules do differ, though, because you have to divide, not multiply.

      

When you divide signed numbers, just count the number of negative signs in the problem — in the numerator, in the denominator, and perhaps in front of the problem. If you have an even number of negative signs, the answer is positive. If you have an odd number of negative signs, the answer is negative.

      

Q.

      A. There are two negative signs in the problem, which is even, so the answer is positive. The answer is +4.

      Q.

      A. There are three negative signs in the problem, which is odd, so the answer is negative. The answer is –9.

      Q.

      A. There are two negative signs — one of them in front of the fraction — so the answer is positive. The answer is +11.

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Working with Nothing: Zero and Signed Numbers

      What role does 0 play in the signed-number show? What does 0 do to the signs of the answers? Well, when you’re doing addition or subtraction, what 0 does depends on where it is in the problem. When you multiply or divide, 0 tends to just wipe out the numbers and leave you with nothing.

Here are some general guidelines about 0:

       Adding zero: is just a. Zero doesn’t change the value of a. (This is also true for .)

       Subtracting zero: When doing subtraction with 0, order matters. Is 0 being subtracted or are you subtracting from 0?. When you subtract 0 from a number, you don’t change it.. Use the rule for subtracting signed numbers: Change the operation from subtraction to addition and change the sign of the second number, giving you .

       Multiplying by 0: . Twice nothing is nothing; three times nothing is nothing; multiply by nothing and you get nothing; likewise, .

       Dividing 0 by a number: . Take you and your friends: If none of you has anything, dividing that nothing into shares just means that each share has nothing.Note: You can’t use 0 as a divisor. Numbers can’t be divided by 0; not even 0 can be divided by 0. The answers just don’t exist.

      So, working with 0 isn’t too tricky. You follow normal addition and subtraction rules, and just keep in mind that multiplying and dividing with 0 (0 being divided) leaves you with nothing — literally.

      Q. Perform the operation:

      A. . Adding 0 to any number doesn’t change the number – even when the number is negative!

      Q. Perform the operations:

      A. 0. You want to pay attention to the whole problem. The first operations result in a huge number, but the final result is 0. That’s what 0 does best!

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Practice Questions Answers and Explanations

      1 4.6. The number 4.6 is to the right of 0 on the number line, and is to the left of 0. And, of course, a positive number will be larger than a negative number.

      2 0. Even though 0 isn’t positive (or negative), it’s to the right of , so 0 is larger.

      3 . To make the comparison easier, rewrite as , so it has the same number of decimal places as . The number is closer to 0 (on the left of 0), so it is larger.

      4 . The two negative numbers