# Less than Zero

In the world of numbers, you will usually work with whole numbers. Those are the numbers that are zero and greater on a number line. There are no parts of numbers to worry about with whole or**natural numbers**. When you start to work with integers, you will start using numbers that are less than zero. For example, you might have -3, -25, or -147. When you divide positive and negative numbers, you don't worry about the signs until you are done with the problem. Just set them aside while you work on your problem. The rules are the same as the ones you learned for multiplication.

# It's All About Being Negative

When you are done with a division problem that has positive and negative values, you don't care how many positive values there are. You only need to pay attention to the number of negative values. Negative numbers have the power of negation. They can change signs of quotients. After you count them up, you need to figure out if you have an odd or an even number of negative signs. If it is even, you have a positive answer. If you have an odd number of negative values, your quotient will be negative.**Problem:**

Positive or Negative Quotients?

56 ÷ 47÷ (-58) ÷ (-12) = ? (Positive: Even number of negative factors)

(-15) ÷ (-15) ÷ 98 ÷ (-3) = ? (Negative: Odd number of negative factors)

That's kind of it. We'll do an easier example to show you the process, but you really only need to do the division and then count the number of negative values.

**Example:**

50 ÷ 2 ÷ (-5) = ?

**Steps to Solve:**

(1) Write out the problem without the signs.

50 ÷ 2 ÷ 5 = ?

(2) Solve the division problems.

50 ÷ 2 = 25

25 ÷ 5 = 5

So...

50 ÷ 2 ÷ 5 = 5

(3) Count the number of negative factors in the original problem :1.

(4) Since the number of negative values is odd, the final answer is negative.

**Answer:**

50 ÷ 2 ÷ (-5) = -5

**Example (with decimals):**

8.4 ÷ (-1.2) ÷ 3.5 = ?

**Steps to Solve:**

(1) Write out the problem without the signs.

8.4 ÷ 1.2 ÷ 3.5 = ?

(2) Solve the division problems. (You need to count the decimal places in this example).

8.4 ÷ 1.2 = 7

7 ÷ 3.5 = 2

So...

8.4 ÷ 1.2 ÷ 3.5 = 2

(3) Count the number of negative factors: 1

(4) Since the number of negative factors is odd, the final answer is negative.

**Answer:**

8.4 ÷ (-1.2) ÷ 3.5 = -2

If you solved the last example on your own, you did a lot of division steps.

• Divided two-digit numbers.

• Came up with a quotient of two decimals.

• Figured out if the quotient was positive or negative.

Good work! If you didn't get the right answer, get a piece of scratch paper and try to work it out again. It will be worth the effort so that you understand all of the steps in the process.

## Related Activities

One and Two-Digit Division Quiz (With Remainders)
- Play Activity |
One and Two-Digit Division Quiz (No Remainders)
- Play Activity |

# Useful Reference Materials

**Wikipedia:**

*https://en.wikipedia.org/wiki/Arithmetic*

**Encyclopædia Britannica:**

*http://www.britannica.com/topic/arithmetic*

**Encyclopedia.com:**

*http://www.encyclopedia.com/topic/arithmetic.aspx*