This is a link to Mike’s website and a link to an ABC News video (it is not the whole video we watched in class, but part of it).
Below are also more of Mike’s shortcuts. We looked at three of them in class. He has 10 listed on his website.
ABC News Video – (on the left side, click on “Video -> Click to Watch”)
[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 = 3,136Now, 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 = 1849Now 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 = 11,235If 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 = 42,432If 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 = 244,036If 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 = 4,331Example: 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