Flashcards and Practice Video

Understanding the Basics

When multiplying 78 by 65 using the area model, we break down each number into its place values and multiply each part separately, then sum the results.

Step-by-Step Breakdown

1. Multiply Ones Place:5×8=405 \times 8 = 405×8=40
   

2. Multiply Tens and Ones:5×70=3505 \times 70 = 3505×70=350
   

3. Multiply Tens and Ones (Swapped):60×8=48060 \times 8 = 48060×8=480
   

4. Multiply Tens Place:60×70=420060 \times 70 = 420060×70=4200
   

Adding the Partial Products

Next, we add all the partial products together:

• 404040

• 350350350

• 480480480

• 420042004200

Summing these values: 40+350+480+4200=507040 + 350 + 480 + 4200 = 507040+350+480+4200=5070

Thus, 78×65=507078 \times 65 = 507078×65=5070.

Visualizing with the Area Model

Imagine a rectangle where the length is broken into 70 and 8, and the width into 60 and 5. This rectangle is divided into four smaller rectangles, each representing a partial product of the original multiplication. By calculating the area of each smaller rectangle and summing them, you get the total area, which corresponds to the product of 78 and 65.

• 5 x 8: 404040

• 5 x 70: 350350350

• 60 x 8: 480480480

• 60 x 70: 420042004200

By understanding each step and visualizing it with the area model, you can master the multiplication of larger numbers in a more intuitive way.

Conclusion

Using the area model to multiply numbers like 78 and 65 not only simplifies the process but also helps in understanding the logic behind multiplication. Be sure to visit Khan Academy for a detailed video explanation, and don't forget to use our flashcards and practice video to reinforce your learning!