Basic Math and Pre-Algebra For Dummies (17 page)

So −2 − 5 = −7.

Suppose you want to calculate −2 + −4. You already know to start at −2, but where do you go from there? Here's the up and down rule for adding a negative number:

 Adding a negative number is the same as subtracting a positive number — go
down
on the number line.

By this rule, −2 + −4 is the same as −2 − 4, so start at −2, down 4:

So −2 + (−4) = −6.

Note:
The problem −2 + −4 can also be written as −2 + (−4). Some people prefer to use this convention so that two operation symbols (− and +) aren't side by side. Don't let it trip you up. The problem is the same.

 If you rewrite a subtraction problem as an addition problem — for instance, rewriting 3 − 7 as 3 + (−7) — you can use the commutative and associative properties of addition, which I discuss earlier in this chapter. Just remember to keep the negative sign attached to the number when you rearrange: (−7) + 3.

The last rule you need to know is how to subtract a negative number. For example, suppose you want to calculate 2 − (−3). Here's the up and down rule:

 Subtracting a negative number is the same as adding a positive number — go
up
on the number line.

This rule tells you that 2 − (−3) is the same as 2 + 3, so start at 2, up 3:

So 2 − (−3) = 5.

 When subtracting negative numbers, you can think of the two minus signs canceling each other out to create a positive.

Multiplication and division with negative numbers is virtually the same as with positive numbers. The presence of one or more minus signs (−) doesn't change the numerical part of the answer. The only question is whether the sign is positive or negative:

 Just remember that when you multiply or divide two numbers,

• If the numbers have the
  same sign,
  the result is always positive.
  
• If the numbers have
  opposite signs,
  the result is always negative.
  

For example,

As you can see, the numerical portion of the answer is always 6. The only question is whether the complete answer is 6 or −6. That's where the rule of same or opposite signs comes in.

 Another way of thinking of this rule is that the two negatives cancel each other out to make a positive.

Similarly, look at these four division equations:

In this case, the numerical portion of the answer is always 5. When the signs are the same, the result is positive, and when the signs are different, the result is negative.

Anything that can be counted is a
unit.
That category is a pretty large one because almost anything that you can name can be counted. You discover more about units of measurement in Chapter
15
. For now, just understand that all units can be counted, which means that you can apply the Big Four operations to units.

Adding and subtracting units isn't very different from adding and subtracting numbers. Just remember that you can add or subtract only when the units are the same. For example,

• 3 chairs + 2 chairs = 5 chairs
  

  4 oranges − 1 orange = 3 oranges
  

What happens when you try to add or subtract different units? Here's an example:

• 3 chairs + 2 tables = ?
  

The only way you can complete this addition is to make the units the same:

• 3 pieces of furniture + 2 pieces of furniture = 5 pieces of furniture
  

You can always multiply and divide units by a
number.
For example, suppose you have four chairs and but find that you need twice as many for a party. Here's how you represent this idea in math: