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Math Tricks!

Duo Pisces

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Home
Apps
Privacy Policy
About Us
Past Weekly Math Problems
Math Tricks!
More
  • Home
  • Apps
  • Privacy Policy
  • About Us
  • Past Weekly Math Problems
  • Math Tricks!
  • Home
  • Apps
  • Privacy Policy
  • About Us
  • Past Weekly Math Problems
  • Math Tricks!

Math Tricks!

Welcome! Here you can find different math tricks to help you excel in your problem solving abilities. We come out with a new trick every week!.

(a + b)(a - b) = a^2 - b^2

14 x 16 = ?

Solution:

14 x 16 = (15 - 1)(15 + 1) = 15^2 - 1

15^2 = 225

14 x 16 = 225 - 1 = 224

Examples:

24 x 26 = (25 - 1)(25 + 1) = 625 - 1 = 624

Sum of Arithmetic Sequences

1 + 2 + 3 + . . . + 97 + 98 + 99 = ?

Solution:

1. 1 + 2 + 3 + . . . + 99 = (1 + 99) + (2 + 98) + . . . + (49 + 51) + 50

2. 100 x 49 + 50 = 4950

Therefore: 1 + 2 + 3 + . . . + 98 + 99 = 4950

Examples:

2 + 4 + 6 + 8 = (2 + 8) + (4 + 6) = 10x2 = 20

To find the sum of arithmetic sequences you can add the first and last terms together and then multiply it by the amount of terms divided by two

Pythagorean Triples

33^2 + 56^2 = n^2

Solution:

33^2 + 56^2 = 1089 + 3136 = 4225 = 65^2

Therefore: If you see a right triangle with side lengths of 33 and 65, then you know the last side will be 65.

Pythagorean Triples can be used to quickly calculate the remaining side of a right triangle if you know already know 2 sides. Other pairs are: 

  • (3,4,5) 
  • (5,12,13) 
  • (7,24,25) 
  • (9,40,41)

45's Rule

45*45 = ?

Step by Step Calculation: 

1) 4*(4 + 1) = 20

2) 20*100 + 25 = 2025


Therefore: 45*45 = 2025

To Summarize:

n5*n5 = n(n+1)*100 + 25

For Example:

25*25 = 2*3*100 + 25 = 625

105*105 = 10*11*100 + 25 = 11,025

Operation Orders

146 + 8*6 - 145 = ?

Step by Step Calculation: 

1) Rewrite as (8*6) + (146 - 145)

2) 146 - 145 = 1

8*6=  48

Therefore: 1 + 48 = 49

To Summarize:

You can rewrite equations as separate smaller equations which can then be solved much easier than the whole thing.

For Example:

87 + 6*4 - 37 + 63

(6*4) + (87-37+63) = ?

24 + 113 = 137

Muliplication of Sevens Rule

27x7=? 

Step by Step Calculation: 

1) 27x(10-3) 

2) 270-81=189

Therefore: 27x7=189

To Summarize:

nx7=nx(10-7)=nx10-nx3


For Example:

45x7=45x(10-3)=450-135=315

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