area model for 29 times 34
To create the area model for 29 times 34, we will make a rectangle with sides that represent the two numbers being multiplied.
First, draw a rectangle and label the sides with the two numbers.
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| |
| |
| |
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The first number, 29, will be represented by the length of the rectangle, and the second number, 34, will be represented by the width of the rectangle.
Next, divide the length of the rectangle (29) into tens and ones.
29 can be decomposed into 20 + 9.
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| 20 9 |
| |
| |
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Now, divide the width of the rectangle (34) into tens and ones.
34 can be decomposed into 30 + 4.
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| 20 10 9 |
| 30 4 |
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Finally, find the area of each section by multiplying the tens and ones in each section.
The left section represents 20 times 30, which is 600.
The middle section represents 10 times 30, which is 300.
The right section represents 9 times 30, which is 270.
The bottom section represents 20 times 4, which is 80.
The top section represents 9 times 4, which is 36.
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| 20 10 9 |
| 30 4 |
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The total area of the rectangle is found by adding the products of each section: 600 + 300 + 270 + 80 + 36 = 1286.
Therefore, the area model for 29 times 34 is:
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| 20 10 9 |
| 30 4 |
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Total Area: 1286
To represent the multiplication of 29 by 34 using the area model, follow these steps:
Step 1: Draw a rectangle and label its length and width with the factors of the multiplication, 29 and 34.
```
34
----------
29|
----------
```
Step 2: Divide the rectangle into four smaller sections by drawing a horizontal line and a vertical line.
```
34
----------
29|
--|------
|
----------
```
Step 3: Label the sections with the corresponding products of the factors.
```
34
----------
29| 870
--|------
|
----------
```
Step 4: Complete the area model by multiplying the remaining sections.
```
34
----------
29| 870
--|------
| 1166
----------
```
Step 5: Calculate the final product by adding up all the products from the area model:
870 + 1166 = 2036
Therefore, the product of 29 multiplied by 34 is 2036.
To understand the area model for multiplying numbers, let's break down the calculation of 29 times 34 step by step.
Step 1: Write the numbers
Write the first number, 29, vertically along the left side, and write the second number, 34, horizontally along the top.
| | 3 | 4 |
|---|---|---|
| 2 | | |
| 9 | | |
Step 2: Divide each number into its digits
Separate both numbers into their respective digits.
| | 3 | 4 |
|---|---|---|
| 2 | | |
| 9 | | |
Step 3: Multiply each digit
Multiply each digit of the top number by the corresponding digit of the bottom number. Start from the rightmost digit of the bottom number and work your way to the left.
| | 3 | 4 |
|---------|---|---|
| 2 | 6 | 8 |
| 9 | 2 | 6 |
Step 4: Add the partial products
Add the partial products diagonally to form the final product.
| | 3 | 4 |
|---------|---|---|
| 2 | 6 | 8 |
| 9 | 2 | 6 |
|---------|---|---|
| | 9 | 8 | 6 |
Step 5: Determine the final answer
The final answer is 29 times 34 equals 986.
So, using the area model, we can see that 29 times 34 is equal to 986.