Welcome! Here you can find different math tricks to help you excel in your problem solving abilities.
A lotus pond each day doubles the lotus on the surface of the pond. On August 15th, the pond was completely covered by lotus flowers. On which day was the pond covered by half of the lotus flowers?
Answer: August 14th, since the lotus doubles every day, the amount of lotus the day prior is always half of the lotus the day of.
Similar Question:
A bacteria doubles itself every hour. At 5 pm there were 8 million bacteria in a bottle. What time did it reach 1 million?
Answer: 2 pm, since the bacteria doubles every hour, every hour prior, there are 1/2^n fraction of bacteria where n is the number of hours before 5pm.
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
3/4m−2(m−1)=1/4m+5
Solve for m
In order to solve this equation, we will need to multiply each side by 4 to get 3m – 8(m – 1) = m + 20. Then from here, we will need to distribute the parenthesis to get 3m – 8m - 8 = m + 20. After this we need to combine like terms and subtract 2m from both sides. Then we will need to subtract 8 from both sides. Lastly we need to divide 12 by -6 to get m = -2.
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