Math shortcut from my instructor.

[Bill Cummings]

I hope the way I type this makes sense.
My apprentice teacher, decades ago, taught us how to find half of uneven fraction measurement in our heads. (No calculator or paper/pencil.)
Example:
Find half of 13 and 3/8" (inch.)
1) Drop back to the next even number which would be 12 then find half which would be 6".
2) Add the three and the eight together to get 11 for the top number of your new fraction. (The numerator.)
3) Double the bottom number of the fraction which would now be 16. (The denominator)
4) There you have it. --- half of 13-3/8 is 6-11/16.
Practice, on paper, finding half of several fraction that start with an uneven number until see that this works.
(Uneven numbers like 3, 5, 7, 9, 11, 13, 15, and so on ---- (Good Luck.)

[Bill Cummings]

Math shortcut
To find the square of a number that ends in five and do it in your head without calculator, pencil or paper.
When you set out to find the square of a number that ends in 5 like 25, 35, 45, 55 and so on remember
the last two numbers in your answer will always be 25.
Let's start with finding the square of 35.
Normally on paper it would be 35 X 35 = 1225.
Doing it in your head the last two numbers in the answer remember is always 25
That was the 5 x 5 = 25 (that took care of the two 5's in the one's column.
For the two numbers in the tens column 3 X 3 we change one of the three's to 0ne number larger which
would be 4. Now multiply 3 X 4 and get 12 now put the 25 to the right of 12 (1225) this is the answer.
TRY:
45 squared. That would be: (45 X 45) Get the fives out of the way 5x5 = 25
Now you are left with the two 4's.
Change one of the 4's to a 5 and multiply 4 X 5 = 20 now put the 25 on the end and get 2025.
Look how clever you are now!