how do you do the shortcut method in 
multiplication and division?

In division, numerator is called Dividend and denominator is called Divisor.

Method 1: Division using the factors of the divisor

This method is also called Double Division.

Here you can directly divide 75 by 15 and the answer would be 5. But, to understand this method, we are not doing like that.
Now, factories divisor.

So we can write 15 as 5 × 3.

Now we can divide 75 by 3 which gives us 25.
         
Now we can divide 25 by 5 and that gives 5 as answer.
So the answer is 5.

Method 2: Division By Parts

Write 75 as 45 + 30

So we can write

         = 

So the answer is 5.

Method 3: Division by 10.

Just move the decimal point one place to the left side.

         
So the answer is 1.256

Method 4: Division by 100

Just move the decimal point two places to the left side.

        
So the answer is 0.1256

Method 5: Division by 5

Divide the dividend by 100 and multiply by 20.

         
So the answer is 40

Method 6: Division by 50

Divide the dividend by 100 and multiply it by 2.

         
So the answer is 4.

Method 7: Division by 25

Divide the dividend by 100 and multiply it by 4.

         
So the answer is 8