Ep 7. Intermediate Multiplication

In this episode of Secrets of Mental Math, titled "Intermediate Multiplication," host Arthur Benjamin introduces the viewer to some advanced techniques for multiplying large numbers mentally.

The episode begins with a refresher on basic multiplication, demonstrating how to multiply two-digit numbers by one-digit numbers. From there, Benjamin moves on to more complex problems, such as multiplying three-digit numbers, as well as multiplying two numbers that are both between 10 and 20.

One of the key techniques discussed in this episode is breaking down a large multiplication problem into smaller, more manageable parts. For example, if you need to multiply 567 by 24, instead of trying to do the whole problem at once, you can break it down into two simpler problems: 567 x 20 and 567 x 4. By solving these two smaller problems separately and then adding the results together, you can arrive at the answer much more easily than if you tried to tackle the entire problem at once.

Another technique demonstrated in this episode is finding "friendly numbers" to make multiplication easier. For example, if you need to multiply 643 by 8, you can see that 8 is the same as 10 - 2. So instead of multiplying by 8 directly, you can multiply by 10 (getting 6,430) and then subtract twice the original number (getting 6,430 - 1,286 = 5,144).

The episode also covers some more advanced techniques for multiplying large numbers, such as using patterns in the numbers to help break them down into smaller pieces. For example, if you need to multiply 99 by 92, you can write out the problem as (100 - 1) x (100 - 8). Then you can use the distributive property of multiplication to simplify the problem: (100 x 100) - 100 - (1 x 100) + (1 x 8). This gives you the answer, 9,108.

Throughout the episode, Benjamin emphasizes the importance of practice and repetition in mastering these mental math techniques. He encourages viewers to try out the methods he demonstrates and to keep practicing until they become comfortable with the process. With enough time and effort, anyone can learn to multiply large numbers mentally and impress their friends and family with their math skills.