# Triple-Digit Multiplication

Wow. You're up to three-digit numbers for multiplication. Let's look at our possible choices and see an example for each one. Don't forget to add the zero(s) at the end of numbers when you multiply with a two- or three-digit factor. Use one zero for the tens value, two zeros for the hundreds value, etc. Check out our page on multiplying with two-digit numbers for an explanation.**Example:**

Three-digit number multiplied by a one-digit number (no carrying):

123 x 3 = ?

(1) 3 x 3 = 9 (the ones)

(2) 2 x 3 = 6 (the tens)

(3) 1 x 3 = 3 (the hundreds)

Answer: 123 x 3 = 369

**Example:**

Three-digit number multiplied by a two-digit number (no carrying):

424 x 12 = ?

Part I (424 x 2):

(1) 4 x 2 = 8

(2) 2 x 2 = 4

(3) 4 x 2 = 8

Answer: 424 x 2 = 848

Part II (424 x 1):

(1) 4 x 1 = 4

(2) 2 x 1 = 2

(3) 4 x 1 = 4

Answer: 424 x 1 = 424

Part III (848 + 4240 [we added the zero]):

848 + 4240 = 5,088

You might write it this way...

424x 12848 + 42405,088 |

**Example:**

Three-digit number multiplied by a three-digit number (no carrying):

213 x 332 = ?

Part I (213 x 2):

(1) 2 x 2 = 4

(2) 1 x 2 = 2

(3) 3 x 2 = 6

Answer: 213 x 2 = 426

Part II (213 x 3):

(1) 2 x 3 = 6

(2) 1 x 3 = 3

(3) 3 x 3 = 9

Answer: 213 x 1 = 639

Part III (213 x 3):

(1) 2 x 3 = 6

(2) 1 x 3 = 3

(3) 3 x 3 = 9

Answer: 213 x 1 = 639

Part IV (426 + 6390 + 63900 [we added the zeros]):

426 + 6390 + 63900 = 70,716

When written at one time...

213x 332426 639 0+ 6390070716 |

# Patience and Attention to Detail

Sometimes we get frustrated when doing long**multiplication**problems. It's not very exciting and it's very repetitive. But to get the correct answer, you need to stick with the

**process**. If you skip a step or make a mistake in simple addition, you will get the wrong answer. You will also probably lose some points on a test. Just be

**patient**when you're working through the three multiplication problems and carrying/regrouping values in a problem that has bigger numbers.

**Arithmetic**is easy when you know the basics, It doesn't matter what the numbers look like or how big they are.

# More Than Three Digits

You should be used to this now. The numbers will just get bigger as you learn more math. It's not a bad thing or a scary thing. Why? You don't need to worry, because you will know the basic steps to solve any multiplication problem. You can be given a number in the hundreds (100+) or a number in the trillions (1,000,000,000,000+) and you will know how to get the answer. Don't expect to solve the big number problems quickly. It will take more time, but it will not be more difficult. As always, remember to keep practicing your multiplication.# 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*