Math Tricks

Check out these math problems and exercise your brain!

[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