Squaring a 2-digit number ending in 2

Steps
take a 2-digit number ending in 2.
the last digit will be ___4.
multiply the first digit by 4: the second number will be the next to the last digit: __X4.
square the first digit and add the number carried from the previous step: XX__.

Example
if the number is 52, the last digit is ___4.
4 x 5 = 20 : __04.
5 x 5 = 25, 25 + 2 = 27 (add carry): 2704.
so 52 x 52 = 2704.

SQUARING a 2-DIGIT NUMBER ENDING IN 1

STEPS

take a-2 digit number ending in 1.
substract 1 from the number.
square the difference.
add the difference twice to its square.
add 1.

EXAMPLE

If the number is 41, substract 1 : 41-1=40.
40 x 40 = 1600 ( square the difference ).
1600 + 40 + 40 =1680 ( add the difference twice to its square ).
1680 + 1 = 1681 ( add 1 ).
so 41 x 41 = 1681

Dividing a 2-digit number by 1 1/7

STEPS

1. Select a 2-digit number.
2. Multiply it by 7.
3. Divide the product by 8.

Example:

1. The number chosen to divide by 1 1/7 is 26.
2. Multiply by 7: 7 × 26 = 140 + 42 = 182
3. Divide by 8: 182/8 = 22 3/4
4. So 26 divided by 1 1/7 = 22 3/4.

See the pattern?

1. The number chosen to divide by 1 1/7 is 61.
2. Multiply by 7: 7 × 61 = 427
3. Divide by 8: 427/8 = 53 3/8
4. So 61 divided by 1 1/7 = 53 3/8