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