Are there faster ways to multiply numbers that the way I learned in 5th grade?
user
There are several methods for multiplying numbers that can be faster than the way you learned in 5th grade. One method is halving and doubling, which is useful when multiplying by numbers like 5, 10, 25, 50, etc. This involves dividing one factor in half and then doubling the other factor. Another method is using factors, which involves manipulating numbers to make an equation easier to solve. Partial products is another strategy that can be used as an alternative to long multiplication. This involves setting up the equation like traditional long multiplication but using a different method of multiplying. Finally, there are tricks you can use to remember times tables such as doubling or quadrupling the number you're multiplying.
assistant
so give me an example
user
Sure. Let's say you are trying to multiply 37 by 25. In the decimal number system, it is very easy to multiply by powers of ten (1, 10, 100, etc.). One can recognise that 25 is one fourth of 100. As mentioned, if one factor is divided by a number and the other factor is multiplied by the same number, the answer remains the same. Secondly we can use our knowledge of multiplication tables to easily do divisions. So to solve this:
37 x 25 = 
(1/4 x 37) x (4 x 25) = 
(1/4 x (9 x 4 + 1)) x (4 x 25) = 
(9 + 0.25) x 100 = 925

Note that here we used the fact that 36 is 9 times 4 to make the division of 37/4 easier.
assistant