How to make up the proportion? Any schoolboy and adult will understand

To solve most problems in high school math, knowledge on the composition of proportions is necessary. This simple skill will help not only perform complex exercises from the textbook, but also delve into the very essence of mathematical science. How to make up the proportion? Now we will disassemble.

The simplest example is the problem where three parameters are known, and the fourth one must be found. The proportions are, of course, different, but often it is required to find by interest a number. For example, the boy had ten apples. He gave the fourth part to his mother. How many apples did the boy have left? This is the simplest example, which will make up the proportion. The main thing is to do it. Initially there were ten apples. Let it be 100%. We labeled all his apples. He gave one quarter. 1/4 = 25/100. So, he had: 100% (was originally) - 25% (he gave) = 75%. This figure shows the percentage of the amount of remaining fruit to the number of available at first. Now we have three numbers on which it is already possible to solve the proportion. 10 apples - 100%, x apples - 75%, where x - the desired amount of fruit. How to make up the proportion? It is necessary to understand what it is. Mathematically, it looks like this. The sign is equally supplied for your understanding.

10 apples = 100%;

X apples = 75%.

It turns out that 10 / x = 100% / 75. This is the main property of proportions. After all, the more x, the more percent this number is from the original. Solve this proportion and get that x = 7.5 apples. Why the boy decided to give a non-integer amount, we do not know. Now you know how to make up the proportion. The main thing is to find two relations, in one of which there is the unknown unknown.

The solution of the proportion often comes down to simple multiplication, and then to division. In schools, children do not explain why this is so. Although it is important to understand that proportional relations are a mathematical classic, the very essence of science. To solve the proportions you need to be able to handle fractions. For example, you often have to transfer interest in ordinary fractions. That is, a 95% record will not work. And if you immediately write 95/100, then you can make solid cuts without starting the basic calculation. Immediately it is necessary to say that if your proportion turned out with two unknowns, then it can not be solved. No professor here will help you. And your task, most likely, has a more complicated algorithm of correct actions.

Consider another example where there is no interest. The motorist bought 5 liters of gasoline for 150 rubles. He thought about how much he would have paid for 30 liters of fuel. To solve this problem, we denote by x the required amount of money. You can solve this task yourself and then check the answer. If you have not yet figured out how to make up the proportion, then look. 5 liters of gasoline is 150 rubles. As in the first example, we write 5l - 150p. Now find the third number. Of course, this is 30 liters. Agree that the pair 30 l - x rubles is appropriate in this situation. Let's move on to the mathematical language.

5 liters - 150 rubles;

30 liters - x rubles;

5/30 = 150 / x.

Solve this proportion:

5x = 30 * 150;

X = 900 rubles.

So they decided. In your task, do not forget to check the adequacy of the answer. It happens that if the solution is wrong, cars reach unrealistic speeds of 5000 kilometers per hour and so on. Now you know how to make up the proportion. Also you can solve it. As you can see, there is nothing complicated in this.