Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model

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Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model
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Basics on the topic Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model

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In this multiplication using area model video, Mr. Squeaks and Imani are preparing for the Fry Festival, featuring a special guest surprise DJ! Before the show starts they need to calculate how many glow sticks and fries they have for the audience by multiplying 2-digit by 2-digit numbers. In order to help them, let’s learn how to do area model multiplication.

What is an Area Model for Multiplication

An area model is a rectangular model that can be used as a tool when multiplying 2-digit numbers by 2-digit numbers. Area model multiplication can also be used for multiplication for all types of digits, however it is mostly used to multiply larger numbers since it breaks them down and makes them easier to work with.

In the next section, you will see an example of area model multiplication 2 digit by 2 digit using a multiplication area model.

Area Model for Multiplication: How to Multiply 2 Digit by 2 Digit Numbers

Let's use an area model to help us multiply twenty-three times forty-one.

The first step is to set up the area model. Start by drawing a rectangle. Next, split it into parts based on how many place values are in each number. Twenty-three has two place values tens and ones, so split the rectangle in two parts vertically. Forty-one also has two place values tens and ones, so split the rectangle in two parts horizontally.

twenty-three-times-forty-one-area-model-four-parts-multiplication-2-digit-by-2-digit.svg

Next, label each part by writing the factors in expanded form. The value of the two in the tens place is twenty and the value of the three in the ones place is three, so label the top twenty plus three. Next the value of the four in the tens place is forty and the value of the one in the ones place is one, so label the left side with forty plus one.

twenty-three-times-fourty-one-area-model-four-parts-twenty-plus-three-on-top-fourty-plus-one-on-left-multiplication-2-digit-by-2-digit.svg

The second step is to multiply each corresponding pair to find the partial products. Partial products are the answers we get when each factor pair is multiplied.

twenty-three-times-fourty-one-area-model-four-parts-twenty-times-fourty-equals-eight-hundred-twenty-times-one-equals-one-three-times-forty-equals-one-hundred-twenty-three-times-one-equals-three-multiplication-2-digit-by-2-digit.svg

The third step is to add all the partial products.

[line 36: twenty-three-times-forty-one-area-model-four-parts-twenty-times-forty-equals-eight-hundred-twenty-times-one-equals-one-three-times-forty-equals-one-hundred-twenty-three-times-one-equals-three-eight-hundred-plus-one-hundred-twenty-plus-twenty-plus-three-multiplication-2-digit-by-2-digit]

The product of twenty-three and forty one is nine hundred forty-three.

Multiplication 2 Digit by 2 Digit Area Model Summary

When multiplying multiplying 2-digit numbers by 2-digit numbers using an area model follow these simple steps:

  • Step 1: Set up the area model by drawing a rectangle and separating it into parts based on how many place values are in each number and label each side with each factor written in expanded form
  • Step 2: Multiply each corresponding pair to find the partial products
  • Step 3: Find the sum of all the partial products

Have you practiced yet? On this website you can practice area model multiplication 2 digit by 2 digit and find an area model multiplication worksheet and area model multiplication worksheets, along with other activities, and exercises.

Transcript Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model

Mr. Squeaks and Imani are preparing for the Fry Festival. "Ohhhhhh Imani I can't wait! I wonder who the guest DJ is!?!?" "I wonder if it's DJ Aberhamster Lincoln!" Before the show starts, Mr. Squeaks and Imani need to calculate how many glow sticks and fries they have for the audience. Let's help them solve by... Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model. An area model is a rectangular model that helps us find the product of two numbers. First, we need to calculate how many glow sticks they have. There are twenty-three boxes with forty-one in each. We will use an area model to help us multiply twenty-three times forty-one. The first step is to set up the area model. Start by drawing a rectangle. Next, split it into parts based on how many place values are in each number. Twenty-three has two place values (...) TENS and ONES, so split the rectangle in two parts vertically. Forty-one also has two place values (...) TENS and ONES, so split the rectangle in two parts horizontally. Next, label each part by writing the factors in expanded form. The value of the two in the tens place is twenty and the value of the three in the ones place is three... so label the TOP twenty plus three. Next the value of the four in the tens place is forty and the value of the one in the ones place is one... so label the LEFT SIDE with forty plus one. The second step is to multiply each corresponding pair to find the partial products. Partial products are the answers we get when each factor pair is multiplied. In THIS box, (...) multiply twenty and forty... to get eight hundred. In THIS box, (...) multiply twenty and one... to get twenty. Next, multiply three and forty... to get one hundred twenty. Last, multiply three and one... to get three. The third step is to ADD all the partial products. Eight hundred plus (...) one hundred twenty plus (...) twenty plus (...) three is (...) nine hundred forty-three. They have nine hundred forty-three glow sticks! Now, we need to calculate how many fries they have. There are sixty-eight boxes with ninety-five in each, so we multiply sixty-eight times ninety-five. The first step is to set up our area model by drawing a rectangle. Since each number has two place values we separate it into four parts. Next, label each part by writing the factors in expanded form. How do we label each part? (...) Label the TOP sixty plus eight... and label the LEFT SIDE ninety plus five. What is the second step? (...) The second step is to multiply each corresponding pair to find the partial products. In THIS box, (...) multiply sixty and ninety... to get five thousand four hundred. In THIS box, (...) multiply sixty and five... to get three hundred. Next, multiply eight and ninety... to get seven hundred twenty. Last, multiply eight and five... to get forty. What is the final step? (...) The final step is to ADD all the partial products. Five thousand four hundred plus (...) seven hundred twenty plus (...) three hundred plus (...) forty (...) equals six thousand four hundred sixty. That means there are six thousand four hundred sixty fries for the festival (...) WOW! Remember (...) when multiplying two digit numbers by two digit numbers using an area model... the first step is to set up the area model by drawing a rectangle and separating it into parts based on how many place values are in each number... and label each side with each factor written in expanded form. The second step is to multiply each corresponding pair to find the partial products. The third step is to find the sum of all the partial products. Since DJ Aberhamster couldn't make it today, (...) everyone give it up for our special guest (...) DJ Imani!