# How to calculate the percentage of the amount of the simplest ways

Every person in his life almost every day is faced with the concept of interest. And this concerns not only obtaining a percentage value from one number, but also solving the problem, how to calculate the percentage of the sum of numbers. In everyday life and everyday life, many do not pay attention to it, nevertheless, all these calculations are incorporated in us from the school bench.

## What is the percentage

As for the concept of interest, it can be explained in the simplest way, without going into the fundamentals of mathematical calculations. In fact, percentage represents some part of something else. It does not matter in which indicator the correspondence of percentage to the main source will be expressed. The main thing is to understand that such a representation can be in the form of the percent itself (%) or in the form of a fraction, which ultimately determines the ratio of the percentage part to the original variant.

## The use of interest in practice

How to calculate interest, each of us knows more from the school course of mathematics. In everyday life, we are confronted with percentages almost every minute. Any housewife, preparing a dish, uses a recipe in which the percentage is presented. The simplest example: take half a glass of milk ... This is the mathematical interpretation of what constitutes a certain part in relation to the whole.

Absolutely all calculations are based on 100 percent (100%) or unit (1), if the calculation will be made using fractions. From this and repelled when calculating any component of the initial indicator.

The same applies to the question of how to calculate the percentage of the amount, when the initial (100 percent) indicator is not one number, but several. Calculation options here can be quite a lot. Consider the most basic.

## Calculate percent by proportion

Now we will not take into account the calculation of interest using the same tables of office programs such as Excel, which do this in automatic mode when specifying the appropriate formula.

In some cases, a calculator is used, where you can set the calculation of such actions. But it is not about that now.

Consider the most common methods of calculation, familiar to us from the school course of mathematics.

The simplest and most common way is to solve proportions.

In this case, the initial number is set as 100 percent (say, some arbitrary number “a”), and its part (say, “b”) - as unknown “x”. In math it looks like this:

*a = 100%;*

*b = x.*

Based on the rules of proportion, you can calculate the unknown number x. For this, the so-called cross method is used. In other words, you need to multiply b by 100 and divide by a. Exactly the same rule applies if, in the case of drawing up a proportion, change b and x in places when the percentage is known, but you need to calculate the part in a numerical expression.

## Quick interest calculation

Of course, calculating percentages using proportions is fundamental. However, with the use of fractional numbers, this procedure is simplified to impossibility. After all, what is 50% really? Half. That is 1/2 or 0.5 (based on the initial number 1).Now it is clear: to calculate the half, you need to multiply the desired number by 1/2, or by 0.5, or divide by 2. This method, however, is only suitable for numbers that are divided without remainder.

In the case of a residual or infinite characters in the period after the comma such as 0.33333333 ... it is better to use fractional expressions like 1/3. By the way, fractions (in some cases irrational) accurately reflect the number itself, because the periodic digits after the comma, no matter how much you ask, will not give an integer anyway. And so the same one third clearly and clearly expresses the essence.

In the same recipes, of course, one third can be determined, so to speak, by eye. But in chemical processes, especially those related to the fine dosage of components, for example, in the pharmaceutical industry, this method will not work. There is no need to rely on the eye. It is necessary to use exact ratios of ingredients, even if one of the indicators has the form of a number with a number in a period or is represented in the form of the same irrational fraction. But, as a rule, for example, when weighing, such numbers can be limited to a decimal point after the decimal point or a maximum of one thousandth.

## How to calculate the percentage of the amount

Very often one has to deal with several required numbers or their sum. The question of how to calculate percentages of the amount is solved as easily as in the case of using a single initial number. The only thing to consider in this case is the usual representation of the sum as a single value.

For example, we have two numbers, a and b, and the initial indicator is the number d. In this case, the proportion will be as follows:

*d = 100%;*

*(a + b) = x.*

Note that the sum (a + b) can still be represented as a single number. Let it be z. In the case when we set the formula a + b = z, the proportion takes on a completely standard form:

*d = 100%;*

*z = x.*

As you can see, nothing complicated about it.

There is another option when the sum (a + b) = 100%, and d = x.

Here the solution looks like this:

*(d x 100) / (a + b) or (d / (a + b)) + 100 / (a + b).*

As already understood, the principle of the common denominator for fractions is used here.

If we add a and b, the sum of which is equal to z, then the proportion again returns to the standard form:

*z = 100%;*

*d = x.*

The same applies in reverse order.

## Mathematical explanation

From the point of view of mathematics and its fundamentals, the solution of the problem of how to calculate the percentage of the sum,it comes down only to the application of the simplest rules for the disclosure of parentheses when multiplying the sum by a single number and searching for the common denominator, which, in general, is. In other words, it can be represented in formula terms as follows:

*a x (b + c) = ab + ac*,

where ab and ac are the products of the terms in brackets (b and c) by the number (coefficient) before the brackets a.

Actually, the same method works in proportion. Suppose we have a certain number z, representing 100%, and the sum of the numbers a and b. The percentage to be calculated is denoted by an unknown number y. In this embodiment, the proportion takes the form:

*z = 100%;*

*(a + b) = y.*

Hence the simple solution:

*((a + b) x 100%) / z = ((a x 100%) + (b x 100%)) / z*

The brackets of the action are taken in order to emphasize that the multiplication operation is performed in the first place, and the addition of works - in the second. The same action is performed if initially the sum of numbers is 100%.

## Reverse calculation

Very often in the question of how to calculate the percentage of the amount, there is an unambiguous reverse transfer. In practice, this is due, say, to the reverse calculation of the quarter. Everyone knows that this figure is 25% of the initial number. Let, for example, the price of goods increased by 25%, which amounted to 25 rubles. We need to find out how much this product has become.Now let's try to figure out how to calculate not the initial number, knowing the value of the percentage, but the entire amount, which should turn out in the end. It would seem that the solution is simple:

*25 = 25% (1/4 or 0.25);*

*x = 100%.*

No, absolutely wrong. So you can get only the original number, excluding 25%. To calculate the entire amount, taking into account 25%, you need to use the formula:

*25 = 25%;*

*x = 100% + 25%.*

Or 100 / 0.8, which will show the value 125 (100 + 25), since 100% plus 25% in the unit expression is the number 1.25 (one plus one-fourth), and in the opposite form (1 / x) it is exactly 0.8. Making calculations, we get that x = 125.

## Conclusion

As you can see, there is nothing particularly difficult in how to calculate the percentage of the amount. True, in the school program, the reverse translation is often omitted for some reason. Then many accountants who work on reports paying the same VAT often have problems.

So you just have to take into account the basic rules for calculating interest, and the problems will disappear by themselves.

On the other hand, for convenience, both proportions and the use of fractions can be applied equally. In the first case, we have, so to speak, the classic version, and in the second - a simple and universal solution.Again, it is better to use it in the case of division without remainder. But when calculating the most popular parts like half, quarter, third, etc., this method is very convenient.

Inverse calculations, as can be seen from the above examples, are also not complex. The main thing is to take into account the inverse coefficient when calculating the desired number. It seems that now everything fell into place. As they say, simple math.