Tricks and Tips

Tips and Tricks:

X 11 Rule

  • Start on the right side of the non-11 number
  • Write down that digit
  • Group 2 digits only at a time and add (be careful with the carry!)
  • Write down the first digit

 

Example  23 x 11

·        3

·        2 + 3 = 5

·        2

·        Answer is 253

 

Example 4371

·        1

·        1 + 7 = 8

·        7 + 3 = 10 (remember to carry the one!)

·        3 + 4 plus the carry = 8

·        4

·        Answer is 48,081

 

Double and Half

 

This is for multiplication.  Double one number and take half of the other then multiply. (usually for a number ending in five, but can be used for other numbers)

 

Example 15 x 42

·        Double 15 to 30 and half 42 to 21

·        Multiply 30 x 21

·        Answer is 630

 

Example 28 x 3.5

·        Double 3.5 to 7 and half 28 to 14

·        Multiply 7 x 14

·        Answer if 98

Double Double

 

This rule is for division problems.  Double both numbers then divide

 

Example  35/2.5

  • Double 35 to 70 and double 2.5 to 5
  • Divide 70 by 5
  • Answer is 14

 

X 50 Rule

 

When multiplying by 50, take half of the other number and move the decimal point to the right 2 places

 

Example  50 x 24

  • half of 24 = 12 and move the decimal to the right 2 places
  • Answer is 1200

 

Example  50 x 21

  • Half of 21 is 10.5
  • Answer is 1050

 

X 25 Rule

 

Divide the other number by 4

Remainder of 0 – put 2 zeros at the end,        Remainder of 1 – end with 25

Remainder of 2 – end with 50,                       Remainder of 3 – end with 75

 

Example  25 x 36

·        Divide 36 by 4 = 9

·        End with 2 zeros

·        Answer is 900

 

Example  25 x 18

·        Divide 18 by 4 = 4

·        Remainder of 2 makes it end with 50

·        Answer 450

 

X 75 Rule

 

Divide by 4, Multiply by 3, add 2 zeros at the end of the answer

 

Example  75 x 24

 

  • Divide 24 by 4
  • Multiply 6 by 3= 18
  • add 2 zeros at the end
  • Answer 1800

 

X 101 Rule

 

2 digit number…Write the number down twice

 

Example  23 x 101

  • Answer is 2323

 

3 digit number…Write down the last two digits then find the sum of the first and last digit (be careful if there is a carry) and finally write down the first 2 digits.  Variation to this rule is X 202 or X 303

 

Example  234 x 101

 

  • End your answer with 34
  • Add 2 + 4 = 6 and place this in front of 34
  • Write down 23
  • Answer is 23634

 

Example 468

 

  • End your answer with 68
  • Add 4 + 8 = 12 (write the 2 and carry the 1)
  • Add 1 to 46 = 47
  • Answer is 47268

 

 

 

Add/Subtract fractions

 

Use common denominators OR Use the butterfly technique.  (Cross multiply and add or subtract sums.  This will be your numerator.  Multiply denominators and this will be your new denominator.)

 

Example   ½ + ¾

 

·        Multiply 1 x 4 + 3 x 2

·        Multiply 2 x 4

·        Answer is 10/8…this reduces to 5/8

 

Compare Fractions

 

Use the butterfly technique…but only the cross products to compare.

 

Example – Which is larger  ½ or ¾ ?

·        1 x 4 = 4 (represents the fraction ½)

·        3 x 2 = 6 (represents the fraction ¾)

·        Answer since 6 is larger than 4 then ¾ is larger

 

 

FD%

 

Percent to Fraction – put over 100 and reduce

Fraction to Percent – memorize!

Mixed number to percent – change to decimal then to percent

Mixed percent to fraction – change to improper and add 2 zeros to the denominator

Decimal to Percent – move decimal 2 places to the right

Percent to Deci