Mathematical Shortcuts / Tricks for calculations.

[Subhash]

Here are few Mathematical shortcuts or tricks for easier calculation.

[1] Squaring numbers in the 50's:
Example 56 x 56:
Step 1: You start out with 25 and add the ones digit to it.
25 + 6 = 31
Step 2: Square the ones digit. 6 x 6 =36 Tack this onto the end of the answer from step 1.
Answer: 56 x 56 = 3,136

Now, if the number from step 2 is less than 10, you have to put a zero in front of it.
So, if it is 53 x 53:
Step 1: 25 + 3 = 28
Step 2: 3 x 3 = 09 (note that since 9 is smaller than 10 we have tu put a zero in front of it)
Answer: 53 x 53 = 2,809

[2] Squaring numbers that end in 5:
Example 65 x 65:
Step 1: Take the tens digit and multiply it by the number one greater than it. 6 x 7 = 42
Step 2: Tack 25 onto the end of the number from Step 1.
Answer: 65 x 65 = 4,225

[3] Multiplying two numbers that end in five that are ten apart:
Example 65 x 75
Step 1: Take the smaller tens digits (6) and multiply it by one more than the larger tens digit (7+1 = 8). 6 x 8 = 48
Step 2: Tack 75 on to the end of the number from Step 1.
Answer: 65 x 75 = 4875

[4] Multiplying two numbers that end in five that are twenty apart:
Example 65 x 85
Step 1: Multiply the smaller tens digit (6) by one greater than the larger tens digit (8 + 1 = 9) and then add 1 to that product. 6 x 9 = 54. 54 +1 = 55
Step 2: Tack 25 on to the end of the number from Step 1.
Answer: 65 x 85 = 5525

[5] Multiplying two numbers in the 90's together:
When you multiply two numbers in the 90's together, in parenthesis next to each number put how far that number is away from 100. Since 92 is 8 away from 100 and 94 is 6 away from 100, the problem 92 x 94 would look like this: 92(8) x 94(6)
Example: 93(7) x 96(4)
Step 1: Add up the numbers in parenthesis 7 + 4 = 11 and subtract that number from 100. 100 - 11 = 89
Step 2: Multiply the two numbers in parenthesis together and tack that on to the number from Step 1. 7 x 4 = 28
Answer: 93 x 96 = 8928

[6] Squaring numbers in the 40's:
Example 43 x 43:
Step 1: You start out with 15 and add the ones digit to it. 15 + 3 = 18
Step 2: You figure out how much the number you are squaring is less than 50 and square that number. 43 is 7 less than 50. 7 x 7 is 49. Tack that number onto the end of the number from step 1.
Answer: 43 x 43 = 1849

Now if the number from step 2 is less than 10, you have to put a 0 in front of it.
Example 48 x 48:
Step 1: 15 + 8 = 23
Step 2: 48 is 2 less than 50. 2 x 2 = 04
Answer: 48 x 48 = 2304


[7] Multiplying two numbers together between 100 and 109:
Example: 105 x 107
Step 1: The first digit of the answer is always 1.
Step 2: To get the next two digits of the answer, add the ones digits together. 5 + 7 = 12
Step 3: To get the final two digits of the answer, multiply the ones digits together. 5 x 7 = 35
Answer: 105 x 107 = 11,235

If the number from either step 2 or step 3 is less than 10, you have to put a zero in front of it.
Example: 102 x 104
Step 1: The first digit is always 1.
Step 2: Add the ones digits together. 2 + 4 = 06
Step 3: Multiply the ones digits together: 2 x 4 = 08
Answer: 102 x 104 = 10,608


[8] Multiplying two numbers together between 200 and 209:
Example: 204 x 208
Step 1: The first digit is always 4.
Step 2: To get the next two digits of the answer, add the ones digits together and then double it. 4 + 8 = 12, double that is 24.
Step 3: To get the final two digits of the answer, multiply the ones digits together. 4 x 8 = 32
Answer: 204 x 208 = 42,432

If the number from either step 2 or step 3 is less than 10, you must put a zero in front of it.
Example: 205 x 201
Step 1: First digit is 4.
Step 2: 5 + 1 = 6. 6 doubled is 12.
Step 3: 5 x 1 = 05
Answer: 205 x 201 = 41,205


[9] Squaring Numbers between 491 and 509:
Example: 494 x 494
Step 1: To get the first three digits of the answer, subtract the number you are squaring by 250. 494 - 250 = 244
Step 2: Tack on a zero to Step 1. So you have 2440.
Step 3: Figure out how far the number you are squaring is away from 500, and square that number and tack it onto the answer from Step 2. 494 is 6 away from 500. 6 x 6 = 36
Answer: 494 x 494 = 244,036

If the number from Step 3 is less than 10, you have to put a zero in front of it.
Example: 503 x 503
Step 1: 503 - 250 = 253
Step 2: Add a zero. You have 2530.
Step 3: 503 is 3 away from 500. 3 x 3 = 09
Answer: 503 x 503 = 253,009

[10] Multiplying two two digit numbers that end in 1:
Example: 71 x 61
Step 1: Multiply the tens digits together and tack a zero on at the end. 7 x 6 = 42. Tack on a 0 and you get 420.
Step 2: Add the tens digits together and add that sum to the number from Step 1. 7 + 6 = 13. 420 + 13 = 433
Step 3: Tack a 1 onto the end of the number from Step 2.
Answer: 71 x 61 = 4,331

Example: 31 x 51
Step 1: 3 x 5 = 15. Tack on a zero and you get 150.
Step 2: 3 + 5 = 8. 150 + 8 = 158
Step 3: Tack a 1 onto the end.
Answer: 31 x 51 = 1,581