*Contributor: Erika Wargo. Lesson ID: 12831*

Zero doesn't seem to add up to much, does it? However, in multiplication using three-digit numbers, it "holds" a very important place! Learn the way to multiply multiple-digit numbers in simple steps!

categories

subject

Math

learning style

Visual

personality style

Otter

Grade Level

Intermediate (3-5)

Lesson Type

Skill Sharpener

Mary is working at her local flower shop. The shop has 105 flower pots with 19 flowers in each pot. How many flowers does the flower shop have in all of the pots?

Let's help Mary with her math problem.

Mary is working at her local flower shop. The shop has 105 flower pots with 19 flowers in each pot. How many flowers does the flower shop have in all of the pots?

In order to solve this problem, you could add, but multiplication is much faster.

105 x 19 =

First, set up your problem and line up the digits:

1 | 0 | 5 | |||

x | 1 | 9 | |||

Begin by multiplying the digits in the ones column: 5 x 9 = 45.

A two-digit number cannot be written in the ones place, so write the 5 in the ones place and carry the 4 to the tens place:

4 | |||||

1 | 0 | 5 | |||

x | 1 | 9 | |||

5 |

Multiply the tens place by 9: 0 x 9 = 0. Now, add the 0 + 4 = 4. Write the four in the tens place. Remember that any number times zero is zero, but the carried-over number still has to be added to the amount. Always multiply first, then add in the carried-over number:

4 | |||||

1 | 0 | 5 | |||

x | 1 | 9 | |||

4 | 5 |

Next, multiply the hundreds place: 1 x 9 = 9. Write the 9 in the hundreds place:

4 | |||||

1 | 0 | 5 | |||

x | 1 | 9 | |||

9 | 4 | 5 |

Now, you will repeat those steps and multiply the tens place in the number 19 by each number in 105.

- First, add your place holder 0 since you are now multiplying the tens place of the bottom number.
- Begin multiplying the tens place 1 by the ones place, 5: 1 x 5 = 5.
- Next, multiply the tens place of each number: 1 x 0 = 0.
- Lastly, multiply the tens place and the hundreds place: 1 x 1 = 1.

4 | |||||

1 | 0 | 5 | |||

x | 1 | 9 | |||

9 | 4 | 5 | |||

1 | 0 | 5 | 0 |

Now, add the partial products together:

4 | |||||

1 | 0 | 5 | |||

x | 1 | 9 | |||

9 | 4 | 5 | |||

+ | 1 | 0 | 5 | 0 | |

1 | 9 | 9 | 5 |

*There are **1,995** flowers in all of the plants combined.*

Another example will show how to multiply 3-digit numbers by another 3-digit number, with a zero in both numbers.

305 x 102 =

3 | 0 | 5 | |||

x | 1 | 0 | 2 | ||

Follow the same steps as above:

Multiply the ones place, 5 x 2 = 10, write the 0 and carry the 1.

Multiply the tens in 305 and the ones in 102, 0 x 2 = 0, and add the carry-over 1. 0 + 1 = 1, so write 1 in the tens place.

Multiply the hundreds in 305 and the ones in 102: 3 x 2 = 6. Write 6 in the hundreds place.

1 | |||||

3 | 0 | 5 | |||

x | 1 | 0 | 2 | ||

6 | 1 | 0 |

*It is important to write the zeros as you multiply. They are just as important as any other number and should not be skipped.

Next, multiply the tens place in 102 by each digit in 305.

What do you notice about the value of the tens place in 102? It is 0. Remember that all numbers multiplied by 0 will give you a product of 0.

Don’t forget to include your placeholder 0 in the ones place, since you are now multiplying digits in the tens place. As you can see below, the next row of our product is all zeroes:

1 | |||||

3 | 0 | 5 | |||

x | 1 | 0 | 2 | ||

6 | 1 | 0 | |||

0 | 0 | 0 | 0 |

The last step is to multiply the digit in the hundreds place in 102 by each digit in 305.

Begin with the 1 in 102 and multiply it by the ones, tens, and then hundreds place in 305.

There should now be two place-holder zeros, since we are multiplying in the hundreds place now. The place-holder zeros are very important!

1 | |||||

3 | 0 | 5 | |||

x | 1 | 0 | 2 | ||

1 | 6 | 1 | 0 | ||

0 | 0 | 0 | 0 | ||

+ | 3 | 0 | 5 | 0 | 0 |

3 | 1 | 1 | 1 | 0 |

After multiplying, add up each partial product: 305 x 102 = 31,110.

Discuss with a parent or teacher:

- What steps are followed to multiply a 3-digit number by a 1-digit number?
- What special rule is important to remember about multiplying by 0?

Now, go practice multiplying numbers in the *Got It?* section.

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