23

__x 15__

115 (multiply 5 by 3 to get 15, carry the one, 5 times 2 is 10 and 1 is 11)

__230__(add a zero under the 5 and multiply 1 by 3 to get 3 and 1 by 2 to get 2)

345 (add the numbers)

This method is probably the one that the majority of people learned in school.

Here's an alternate method. We will think of 23 as 20 and 3 and 15 as 10 and 5

Multiply 20 by 10 to get 200

Multiply 20 by 5 to get 100

Multiply 10 by 3 to get 30

Multiply 5 by 3 to get 15

Now we add the numbers to get 345.

Essentially we are using the distributive property twice.

20(10 + 5) + 3(10+ 5)

200 + 100 + 30 + 15 = 345

What's interesting is we can also distribute as follows and get the same answer

10(20 + 3) + 5(20 + 3)

200 + 30 + 100 + 15 = 345.

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