Some amazing mathematics tricks

• Multiply a number that terminates with 5 together other pair number:
  e.g.: 32 x 45.
  You can divide the even number by two and multiply the number that terminates with 5, obtaining other equivalent multiplication: 16 x 90, what can simplify the mental calculation because you can focus atention at the simple multiplication 16 x 9.

• Multiply a number by 11:
  e.g. 123 x 11.
  You can just realize a simple sum like 123 plus 1230 (you can think it like a 123 that was shifted to left and concatened a zero after the 3)

• Divisibility by 3:
  e.g. 12455 is divisible by 3?
  You can know this fastly just adding the digits and verifying if this number is divisible by 3 (1+2+4+5+5 = 17, then that isn’t divisible). This method can be used with to discover if a number is divisible by 9.

• Divisibility by 11:
  e.g. 32431 is divisible by 11?
  You can know this fastly just adding the digits with even position and subtract this sum from the sum of digits with odd position. 2+3 = 5, 3+ 4 + 1 = 8, 8 - 3 = 5. If the result number can be divided by 11, the initial number can be divided by 11. (in this case, the number isn’t divisible by 11)

• Calculating percentages
  e.g. How calculate 5% of 120?
  You can substitute simple calculations of percentage by simple division calculations.
  1% = divide by 100 the number
  2% = divide by 50 the number
  5% = divide by 20 the number
  10% = divide by 10 the number
  20% = divide by 5 the number
  25% = divide by 4 the number
  50% = divide by 2 the number

So, 5% of 120 is just 120/20 = 6.

Other calculus can be done to estimate the value but no your exact value, e.g., 16% you can divide by 6 but you will obtain a inexactly result (16% of 60 is 9,6 but with the method I said you will obtain 10)

• Adding fractions
  e.g. 1/4 + 3/5
  

The method is just multiply the denominator among (4 by 5) them and after multiply the denominators in a “cross mode” (1 by 5 and 4 by 3). The result you will obtain is the result below