Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model—Let's Practice
- What Is Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model?
- Solving Multiplication Problems Using an Area Model – Examples
- Understanding Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model – Guided Practice
- Using Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model – Application
- Solving Multiplication Problems Using an Area Model – Summary
- Solving Multiplication Problems Using an Area Model – Frequently Asked Questions
Basics on the topic Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model—Let's Practice
Understanding Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model – Introduction
We're diving into the world of multiplying two-digit numbers by two-digit numbers using area models. This method helps us visualize multiplication and break it down into simpler steps. Get ready because we're going to practice this together!
What Is Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model?
Multiplying two-digit numbers by two-digit numbers using area models involves breaking down the multiplication problem into smaller, more manageable parts and using an area model to visualize the process. This method helps us see how the numbers are multiplied and combined.
Here are the steps to tackle multiplication using an area model:
| Step # | Action |
|---|---|
| 1 | Set up the area model by labeling the top and left side with each factor written in expanded form. |
| 2 | Multiply each part separately. |
| 3 | Add the partial products together. |
| 4 | Check your answer to ensure it makes sense with the problem. |
Let's practice understanding this method with a few examples.
Solving Multiplication Problems Using an Area Model – Examples
Example 1:
Problem: Use an area model to solve $ 51 × 79$ .
Steps to Solve the Problem:
| Step # | Action | Description |
|---|---|---|
| 1 | Set up the area model by labeling the top and left side with each factor written in expanded form. | 50 + 1 and 70 + 9 |
| 2 | Multiply $ 50 × 70$ . | 3,500 |
| 3 | Multiply $ 50 × 9$ . | 450 |
| 4 | Multiply $ 1 × 70$ . | 70 |
| 5 | Multiply $ 1 × 9$ . | 9 |
| 6 | Add the partial products. | 3,500 + 450 + 70 + 9 |
| 7 | Combine the results. | 4,029 |
Solution: The product is 4,029.
Example 2:
Problem: Use an area model to solve $ 23 × 86$ .
Steps to Solve the Problem:
| Step # | Action | Description |
|---|---|---|
| 1 | Set up the area model by labeling the top and left side with each factor written in expanded form. | 20 + 3 and 80 + 6 |
| 2 | Multiply $ 20 × 80$ . | 1,600 |
| 3 | Multiply $ 20 × 6$ . | 120 |
| 4 | Multiply $ 3 × 80$ . | 240 |
| 5 | Multiply $ 3 × 6$ . | 18 |
| 6 | Add the partial products. | 1,600 + 120 + 240 + 18 |
| 7 | Combine the results. | 1,978 |
Solution: The product is 1,978.
Understanding Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model – Guided Practice
Take a look at these numbers: Use an area model to solve $ 34 × 52$ .
In number sentence form: 34 × 52 = 1,768
Using Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model – Application
Now it's your turn. Solve these problems on your own.
Use an area model to solve $ 45 × 67$ .
In number sentence form: 45 × 67 = 3,015
Solving Multiplication Problems Using an Area Model – Summary
Key Learnings from this Text:
- Solving problems using an area model can be achieved by following these steps:
| Step # | Action |
|---|---|
| 1 | Set up the area model by labeling the top and left side with each factor written in expanded form. |
| 2 | Multiply each part separately. |
| 3 | Add the partial products together. |
| 4 | Check your answer to ensure it makes sense with the problem. |
- Mastering the use of an area model for multiplying two-digit numbers is an important foundational math skill.
Keep practicing these steps, and you'll become a pro at using an area model to multiply two-digit numbers! Check out more fun math challenges and exercises on our website to continue sharpening your skills.
Solving Multiplication Problems Using an Area Model – Frequently Asked Questions
Transcript Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model—Let's Practice
Razzi says get these items ready (...) Because today we're going to practice... Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model. It's time to begin! Use an area model to solve... fifty-one times seventy-nine. Pause the video to work on the problem (...) and press play when you are ready to see the solution! First, set up the area model by labeling the top and left side with each factor written in expanded form. Then multiply, (...) fifty times seventy (...) which equals three thousand five hundred... fifty times nine (...) which equals four hundred fifty... one times seventy (...) which equals seventy... and one times nine (...) which equals nine. Last add the partial products. Did you also get four thousand twenty-nine? Let's tackle the next problem! Use an area model to solve... twenty-three times eighty-six. Pause the video to work on the problem (...) and press play when you are ready to see the solution! First, set up the area model by labeling the top and left side with each factor written in expanded form. Then multiply, (...) twenty times eighty (...) which equals one thousand six hundred... twenty times six (...) which equals one hundred twenty... three times eighty (...) which equals two hundred forty... and three times six (...) which equals eighteen. Last add the partial products. Did you also get one thousand nine hundred seventy-eight? Razzi had so much fun practicing with you today! See you next time!
Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model—Let's Practice exercise
-
Which option is the correct expanded form of 97?
HintsRemember, expanded form will show each digit expanded into its actual value.
Take a look at this example of the number 23 written in expanded form!
SolutionThe correct way to write the number 97 in expanded form is 90 + 7! To do that we separated the number into the tens digit and the ones digit.
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Solve 24 x 12.
HintsRemember the steps to solve the problem!
1) Set up the area model by labeling the top and left side with each factor written in expanded form.
2) Multiply each square in the area model.
3) Add the products together.
Here is the correct area model for this problem to help.
SolutionThe correct answer is 288! In this image, we see all of the multiplication problems done correctly. Then once we add up all the answers (200 + 40 + 40 + 8), we get the correct answer.
-
Solve 86 x 54.
HintsRemember the steps to solve the problem!
1) Set up the area model by labeling the top and left side with each factor written in expanded form.
2) Multiply each square in the area model.
3) Add the products together!
Here is the correct area model for this problem to help.
SolutionThe correct answer is 4,644! In this image, we see all of the multiplication problems done correctly. Then once we add up all the answers (4,000 + 300 + 320 + 24), we get the correct answer!
-
79 x 67
HintsRemember the steps to solve the problem!
1) Set up the area model by labeling the top and left side with each factor written in expanded form.
2) Multiply each square in the area model.
3) Add the products together!
Here is the correct area model for this problem to help!
SolutionThe correct answer is 5,293! In this photo, we see all of the multiplication problems done correctly. Then once we add up all the answers (4200 + 540 + 490 + 63), we get the correct answer!
-
Solve 45 x 21.
HintsRemember the steps to solve the problem!
1) Set up the area model by labeling the top and left side with each factor written in expanded form.
2) Multiply each square in the area model.
3) Add the products together!
Your area model should look like in the picture!
SolutionThe correct answer is 945! In this image, we see all of the multiplication problems done correctly. Then once we add up all the answers (800 + 100 + 40 + 5), we get the correct answer!
-
98 x 86
HintsRemember the steps to solve the problem!
1) Set up the area model by labeling the top and left side with each factor written in expanded form.
2) Multiply each square in the area model.
3) Add the products together!
The first step of the area problem has been set up correctly in the picture!
SolutionThe correct answer is 8,428! In this image, we see all of the multiplication problems done correctly. Then once we add up all the answers (7,200 + 640 + 540 + 48), we get the correct answer!
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Multiplying Two-Digit Numbers by Two-Digit Numbers
Multiplying Two-digit Numbers by Two-digit Numbers — Let's Practice!
Multiplying 2-Digit Numbers by Multiplies of 10
Multiplying Tens, Hundreds and Thousands
Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model
Multiplying Two-Digit Numbers by Two-Digit Numbers Using an Area Model—Let's Practice
