# Multiplying Two-Digit Numbers by Two-Digit Numbers

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Basics on the topic
**Multiplying Two-Digit Numbers by Two-Digit Numbers**

## 2-Digit by 2-Digit Multiplication

Multiplication is a mathematical operation you are probably already used to. But how do you multiply 2-digit numbers by 2-digit numbers without regrouping? Here you can learn how to multiply by double digits. After learning how to multiply 2-digit numbers, check out our double digit multiplication worksheets and practice exercises!

Multiplying by two digit numbers can be done in a few easy steps:

Step # | What to do |
---|---|

1 |
Multiply the ones placed in the bottom factor by both place values in the top factor, regrouping as needed. |

2 |
Add a placeholder, or zero. |

3 |
Multiply the tens place in the bottom factor by both place values in the top factor, regrouping as needed. |

4 |
Add the partial products to get the total. |

If you are still wondering how to do double digit multiplication, look at the example below.

## Multiplying Two Digit by Two Digit Numbers – Example

In this example, we will be multiplying by 2-digit numbers in order to find out how many sunflower seeds they have. Since there are forty-eight containers with thirty-two in each, we will find the product of forty-eight and thirty-two.

The first step is to multiply the ones place in both factors, so we multiply two times eight to get sixteen, regrouping the one to the tens place. Next multiply two times four to get eight, adding the one we regrouped to get nine.

The second step is to add the *placeholder*, or *zero*.

The third step is to multiply the tens place in the bottom factor by both place values in the top factor. We multiply three and eight to get twenty-four, and regroup the two to the tens place. Next multiply three times four to get twelve, adding the two we regrouped to get fourteen.

The last step is to add the partial products ninety-six and one thousand four hundred forty to get the final product. Forty-eight times thirty-two is one thousand five hundred thirty-six.

## Multiplying Two-Digit Numbers by Two-Digit Numbers – Summary

Remember, if someone asks you “how did you multiply 2-digit numbers by 2-digit numbers?” you can tell them to follow these easy steps:

- Multiply the ones placed in the bottom factor by both place values in the top factor, regrouping as needed.
- Add a placeholder, or zero.
- Multiply the tens place in the bottom factor by both place values in the top factor, regrouping as needed.
- Add the partial products.

Multiplying doubles takes a lot of practice. Have you practiced yet? On this website you can find a multiplying by two digit numbers worksheet, activities, and exercises.

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Transcript
**Multiplying Two-Digit Numbers by Two-Digit Numbers**

When a cool breeze whizzed through Mr. Squeaks' and Imani's home, they started to harvest some food into containers for winter. They've collected corn and sunflower seeds for their hibernation... but they need help calculating how much they have. In order to do that, we need to practice [title] "Multiplying Two-Digit Numbers by Two-Digit Numbers". They have thirteen containers with twenty-one cobs of corn in each. We need to find the product of thirteen times twenty-one. The first step is to multiply the ONES place in the bottom factor by BOTH place values in the top factor. Start by multiplying the factors in the ONES place. Which numbers are in the ONES place? (...) The bottom factor has a ONE, and the top factor has a THREE... so multiply one times three to get the product (...) three. We make sure to put the three in the ONES place, because that is the place value we multiplied. Next multiply the ONES place in the bottom factor by the TENS place in the top factor. One times one equals (...) one. We make sure to put the one in the TENS place, because that is the place value we multiplied. Now that we've multiplied the ones place by both numbers in the top factor... the second step is to add a placeholder, or a zero HERE. [zero will be added in animation to the desired spot] A placeholder is used because we are multiplying the TENS place in the bottom number next, so we write the products starting in the TENS place. Now multiply the TENS place in the bottom number by the ONES place in the top number. Two times three equals (...) six. Next multiply the two and one in the TENS place to get the product (...) two. Last, find the sum of the partial products thirteen and two hundred sixty. (...) Thirteen times twenty-one is two hundred seventy-three. [impressed]That's a lot of corn! Next, let's calculate how many sunflower seeds they have. There are forty-eight containers with thirty-two in each. The first step is to multiply the ONES place in the bottom factor by BOTH place values in the top factor. What do we get when we multiply the ONES place in both factors? (...) Two times eight is sixteen, (...) and since sixteen is a TWO DIGIT number we need to regroup... so write the six HERE and regroup the one to the tens place HERE. Next, multiply the ONES place in the bottom factor by the TENS place in the top factor. Two times four is (...) eight, and add the one we regrouped to get (...) nine. Before we move on, cross out the ONE that we regrouped (...) that way, if we need to regroup later we won't get confused. The second step is to add the placeholder HERE. Next, multiply BOTH place values in the top factor by the TENS place in the bottom factor. Three times eight is (...) twenty four... so write the four HERE and regroup the two to the tens place HERE. Next, multiply three times four (...) to get twelve... and add the two we regrouped to get (...) fourteen. The last step is to find the sum of the partial products ninety-six and one thousand four hundred forty. Mr. Squeaks and Imani have one thousand five hundred thirty-six sunflower seeds. Remember (...) when you multiply a two-digit number by a two-digit number you first... "Multiply the ONES place in the bottom factor by both place values in the top factor", regrouping as needed. The second step is to, "add a placeholder". The third step is to, "Multiply the TENS place in the bottom factor by both place values in the top factor", regrouping as needed. The last step is to find the sum of the partial products to get the final answer. After all that calculating, Mr. Squeaks realizes he has even more food than he thought... ...because Imani doesn't have a mouth to eat all that food! ...So, what does Imani eat? [animation shows him feeding her 'robot food']

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