# Multiplying More Than Two Factors

You knew it was going to happen. Some teacher or workbook was going to start assigning problems with more than two values to multiply. You're in luck. Because multiplication works like addition, you can use some shortcuts here. Let's start by looking at simple problems first. Remember to move in order and hit every number when you're multiplying.2 x 2 = 4

8 x 6 = 48

2 x 4 x 60 = 480 (2x4=8 and then 8x60=480)

6 x 9 x 10 x 5 = 2,700 (6x9=54, then 54x10=540, and then 540x5=2,700)

The answers (products) can get large very quickly when you are multiplying. While "100 + 100" equals two hundred (200), "100 x 100" equals ten thousand (10,000). Take every problem one step at a time. Or try grouping if it's faster.

# Any Order You Want

We just mentioned that multiplication is like addition in many ways. One of the cool things about multiplication is that you can move numbers around. You can multiply in any order you want. All of the options give you the same answer. The Commutative Law of Multiplication allows you to do this.10 x 5 x 6 x 12 x 4 = 14,400

12 x 10 x 6 x 5 x 4 = 14,400

Since the order doesn't matter, you can group numbers together that are easier to multiply. Using the above example, we tried this to make the problem go faster:

10 x 5 x 6 x 12 x 4 = ?

Step 1:

10 x 12 = 120

5 x 6 = 30

The 4 was left over. So 120 x 30 x 4 = ?

Step 2:

30 x 4 = 120

Save the other 120. So 120 x 120 = ?

Step 3:

120 x 120 = 14,400

You didn't see a

**pattern**in our original factors did you? After you broke it down, the multiplication became a lot easier. It was also easier to check our work along the way instead of doing multiplication that might have included "72 x 4". The more practice you have, the easier it will become.

# Grouping Factors

You can rearrange and regroup if you have a multiplication problem with many factors. You can move factors and parentheses around. Remember that all of the operations have to be multiplication for this to work.**Example:**

(5 x 3 x 15) x (2 x 3) = ?

**Steps to Solve:**

Step 1: Since it is all multiplication, let's get rid of the parentheses.

5 x 3 x 15 x 2 x 3=?

Step 2: Let's rearrange the factors.

2 x 3 x 3 x 5 x 15=?

Step 3: Put some parentheses back in so it's easier to visualize our multiplication.

(2 x 3 x 3) x (5 x 15) = ?

Step 4: The order of operations says to work on the inside of the parentheses first.

(18) x (75) = ?

Step 5: Finish the multiplication with the two-digit factors and carrying.

**Answer:**

(5 x 3 x 15) x (2 x 3) = 1,350

# 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*