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# Multiplying multi-digit numbers

Sal shows lots of examples for how to multiply  2- and 3-digit numbers using "standard algorithm". Created by Sal Khan.

## Want to join the conversation?

• why did math start
• The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. ... If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived.
• Why do we use multiplication? And why do we use division?
• @will.wettstein we use division and multiplication in everyday life like if you are a banker or a cashier
• Am I supposed to multiply 3 digits by 2 (or 3) digits in my head?
• You can, but I suggest you stick with paper and pencil for while and put the calculator away. Calulators will give you answers, but you will learn much faster without it. If you want to see different ways of manipulating numbers, google Vedic maths.
• I hate the fact that I go in circles and I never get passed this.
• There is a Vedic math trick for multiplying any multi-digit numbers, called vertical and crosswise.

For example, let’s use this trick on the last problem in the lesson, 523 x 798.

Multiply the first digits: 5 x 7 = 35. This represents 35 ten-thousands.

Cross multiply the first two digits by the first two digits: (5x9)+(2x7) = 45+14 = 59. This represents 59 thousands. So we have a running total of 350+59 = 409 thousands so far.

Cross multiply the first three digits by the first three digits: (5x8)+(2x9)+(3x7) = 40+18+21 = 79. This represents 79 hundreds. So we have a running total of 4,090+79 = 4,169 hundreds so far.

Cross multiply the last two digits by the last two digits: (2x8)+(3x9) = 16+27 = 43. This represents 43 tens. So we have a running total of 41,690+43 = 41,733 tens so far.

Finally, multiply the last digits: 3x8 = 24. This represents 24 ones. So we get a final total of 417,330+24 = 417,354.

So 523 x 798 = 417,354.

If you google Vedic math, you might find some more cool arithmetic tricks!

Have a blessed, wonderful day!
• always keep trying one day maybe you can help someone like how you need help (o゜▽゜)o☆
• why does this take so long and is there a faster way to do it?
• Yes, there are faster ways of multiplying multi-digit numbers. Try looking up Vedic multiplication. There is a general method called vertical and crosswise, which is much faster than the usual method when the numbers have several digits. There are also fast Vedic multiplication tricks for special cases, for example when both factors are near the same power of 10.
• Is there in inverse operation to subtraction?
• Yes. If subtraction is the inverse operation to addition, then addition is the inverse operation to subtraction. It's pretty simple if you think about it!