When we read the signs of sales, -20%, -25%, -10%… we are not always able to understand how much it is discount. In truth, it is not that difficult: there are gods tricks that allow us to calculate certain percentages quite easily, at least enough for the uses that can be done in everyday life. We will see some that we consider particularly useful, but also some of the most popular ones on social media which, as we will explain, are not magical, but simple mathematical precautions.
Percentage calculation: the multiplication of the dozens
When it comes to calculating percentages in which both the total and the percentage I am multiples of 10 Enough multiply the tens. Let’s see examples:
- To calculate 40% of 70 just multiply 4 × 7 = 28.
- To calculate 60% of 130 just multiply 6 × 13 = 78.
If only one of the two numbers is multiple of 10 the calculation is slightly complicated but it is always quite easy:
- To calculate 62% of 30 just multiply 6.2 × 3 = 18.6
The most famous trick: the inverted percentages
One of the tricks that most depopulated on social networks is that of Inverted percentages: do you want to calculate 22% of 50? Just calculate 50% of 22, which is half, or 21, and you’re done, try to believe!
This trick works well when you have to calculate the percentage of a totalin this case 50, which corresponds to an easy percentage to calculate: it does not work instead with other numbers, for example if to calculate 37% of 83 we try to calculate 83% of 37 we are faced with the same type of difficulty. However, there are different percentages that are easy to calculate enough on the fly, like 25% of the figure above which is often found in the discounts.
Calculate the discounts with the hamlets of the whole: 50%, 10% or 200%
The percentages of discounts often correspond to particular fractions of the total quite easy to calculate:
- The 25% corresponds to ¼ of the totalso enough divide by 4 or halve the total twice: 25% of 60 will therefore be 60: 4 = 15;
- The 75% corresponds to ¾ of the totalbut that’s what remains after a 25% discount, so we can first calculate 25% and then subtract it from the total: 75% of 60 will therefore be 60-15 (25% of 60 that we calculated above);
- The 20% corresponds to ⅕ of the total and enough divide by 5: for example 20% of 36 are calculating 36: 5 = 6.2
The easiest percentages to calculate: 50%, 10% or 200%
The easier percentages To calculate are those that correspond to divisions, or easy multiplications, we see some examples:
- To calculate the 50% Enough half divide: e.g. I find 50% of 70 by calculating 70: 2 = 35;
- To calculate the 10% Enough divide for 10or moves the comma to the left: to calculate 10% of 213 we see the number as 213.0 and move the comma of a position on the left obtaining 21.3;
- To calculate the1% Enough divide by 100or moves the comma to the left of two positions: to calculate the 1% of 87 we move the comma of two positions on the left obtaining 0.87;
- To calculate the 200% Enough doubleso the 200% of 60 will be 120.
The superpowers of 10% and 1%: divide the calculation
We saw that calculating the 10% and the1% of a number is very easy, this allows us to calculate many Other percentages in mind. To do this you have to look at each number as a combination of 10 and 1, for example:
- To calculate the 9% We can remind us of 70 = 10-1 for which we calculate 10% of 70, which is 7, and subtract 1% of 70, which is 0.7 thus obtaining that 9% of 70 is: 7-0.7 = 6.3;
- To calculate the 5% We calculate 10% of a number and then halve, so 5% of 64 will be half of 6.4 or 3.2.
Because these tricks work: the properties of operations
All these tricks are based on mathematical properties of operations and of fractionsthings that normally learn in elementary or middle school. By way of example we explain two, that of the multiplication of the dozens and that of Inverted percentages.
When we used the trick of the multiplication of the dozens To calculate 40% of 70, it was a matter of finding the
number x which is at 70 as much as 40 is 100
that in mathematics it can be expressed with the proportion
X: 70 = 40: 100.
This proportion is resolved by multiplying 70 × 40 and then dividing by 100, or
x = (70 × 40): 100
that we can write like fraction as in the figure below. The hamlets, however, can be simplifyand we can erase the zeros of 70 and 40 with the two zeros of the 100: in the end it will remain only to multiply 7 × 4 that does 28!
Finally, to find 22% of 50 we used the trick of Inverted percentages: We calculated 50% of 22, for which it was enough to halve. Even these two percentages can be written as fractions (see figure above), and the only difference between the two is that in one case 50 × 22 must be calculated and 22 × 50 in the other, but
By changing the order of the factors the result does not change
So the result will be the same: here we have reversed the percentagewithout magic, using only the commutative property of multiplication!
