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eBook - ePub
Fast mental calculation tricks
About this book
Who wouldn't like to master math naturally, being able to do perform mental calculation without the help of a calculator?
If you had to calculate the square of 115 in a few seconds what would you answer? Or the product 238x5, or even the square of 76?
With this guide you will become masters of fast mental calculation, you will surprise your friends with your skills and you will be astonished when you discover that reaching apparently impossible goals can be achieved with very little effort.
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Yes, you can access Fast mental calculation tricks by EasyMath in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.
Information
Multiply by 1,5
How do you easily multiply a number by 1,5?
The answer is very simple, just observe that multiplying by 1,5 is equivalent to calculate the half of the triple, or it can be obtained by adding its half to the starting number. Some examples that make use of the first technique are:
12 x 1,5 = (12 x 3) : 2 = 36 : 2 = 18
17 x 1,5 = (17 x 3) : 2 = (10 x 3 + 7 x 3) : 2 = (30 + 21) : 2 = 51 : 2 = (50 + 1) : 2 = 25 + 0,5 = 25,5
74 x 1,5 = (74 x 3) : 2 = (70 x 3 + 4 x 3) : 2 = (210 + 12) : 2 = 222 : 2 = 111
99 x 1,5 = (99 x 3) : 2 = (100 x 3 - 1 x 3) : 2 = (300 - 3) : 2 = 150 - 1,5 = 148,5
The same calculations performed with the second technique:
12 x 1,5 = 12 + (12 : 2) = 12 + 6 = 18
17 x 1,5 = 17 + (17 : 2) = 17 + (10 : 2 + 7 : 2) = 17 + 5 + 3,5 = 22 + 3,5 = 25,5
74 x 1,5 = 74 + (74 : 2) = 74 + (70 : 2 + 4 : 2) = 74 + 35 + 2 = 70 + 30 + 4 + 5 + 2 = 111
99 x 1,5 = 99 + (99 : 2) = 99 + (100 : 2 - 1 : 2) = 99 + 50 - 0,5 = 100 - 1 + 50 - 0,5 = 150 - 1,5 = 148,5
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Multiply by multiples of 10
Suppose we want to calculate the product of a number and a multiple of 10, for example
12 x 30
where 30 is multiple of 10, in fact
30 = 3 x 10
we can write
12 x 30 = (12 x 3) x 10 = 36 x 10 = 360
We observe that the product between a number and n times 10 can be obtained just calculating the product of the number by n and then multiply the result by 10.
Other explanatory examples:
8 x 50 = (8 x 5) x 10 = 40 x 10 = 400
9 x 90 = (9 x 9) x 10 = 81 x 10 = 810
15 x 40 = (15 x 4) x 10 = (15 x 2 x 2) x 10 = (30 x 2) x 10 = 60 x 10 = 600
24 x 70 = (24 x 7) x 10 = (20 x 7 + 4 x 7) x 10 = (2 x 7 x 10 + 28) x 10 = (14 x 10 + 28) x 10 = (140 + 28) x 10 = 168 x 10 = 1680
81 x 20 = (81 x 2) x 10 = (80 x 2 + 1 x 2) x 10 = (160 + 2) x 10 = 162 x 10 = 1620
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Multiply by 11, 21, 31, …
Let's see other examples of fast calculations. To multiply a number by 11 just multiply it by 10 and add the number itself, in fact 11 = 10 + 1. Let's see some examples:
23 x 11 = (23 x 10) + 23 = 230 + 23 = 253
40 x 11 = (40 x 10) + 40 = 400 + 40 = 440
88 x 11 = (88 x 10) + 88 = 880 + 88 = 900 - 20 + 80 + 8 = 980 - 20 + 8 = 960 + 8 = 968
145 x 11 = (145 x 10) + 145 = 1450 + 145 = 1450 + 100 + 40 + 5 = 1550 + 40 + 5 = 1590 + 5 = 1595
Similarly, to multiply a number by 21 just multiply it by 20 and add the number itself, in fact 21 = 20 + 1, where, in turn, 20 = 2 x 10.
Examples:
23 x 21 = (23 x 20) + 23 = (23 x 2) x 10 + 23 = 46 x 10 + 23 = 460 + 23 = 483
56 x 21 = (56 x 20) + 56 = (56 x 2) x 10 + 56 = (50 x 2 + 6 x 2) x 10 + 56 = (100 + 12) x 10 + 56 = 1120 + 56 = 1120 + 50 + 6 = 1170 + 6 = 1176
83 x 21 = (83 x 20) + 83 = (83 x 2) x 10 + 83 = (80 x 2 + 3 x 2) x 10 + 83 = (160 + 6) x 10 + 83 = 1660 + 83 = 1660 + 80 + 3 = 1740 + 3 = 1743
The multiplication of a number by 31 (and, similarly, by 41, 51, 61 and so on) ca...
Table of contents
- Preliminary remarks
- Some examples
- Add 10, 100, 1000
- Subtract 10, 100, 1000
- Multiply by 10, 100, 1000
- Divide by 10, 100, 1000
- Add two numbers
- Subtract two numbers
- Double of a number
- Half of a number
- Quadruple a number and associated calculations
- Multiply by 5
- Divide by 5
- Multiply by 1,5
- Multiply by multiples of 10
- Multiply by 11, 21, 31, …
- Multiply by 9, 19, 29, …
- Factorization
- Square of a number
- Units in a product