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!.
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
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
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:
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
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
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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