To solve most problems in high school mathematics, knowledge of proportions is needed. This simple skill will help not only perform complex exercises from a textbook, but also delve into the very essence of mathematical science. How to make a proportion? Now we will analyze.
The simplest example is a problem where three parameters are known, and the fourth needs to be found. The proportions are, of course, different, but often you need to find a percentage by some number. For example, the boy had ten apples in total. He gave the fourth part to his mother. How many apples does a boy have? This is the simplest example that allows you to make a proportion. The main thing is to do it. Initially, there were ten apples. Let it be 100%. This we have marked all his apples. He gave one quarter. 1/4 = 25/100. So, he has left: 100% (it was originally) - 25% (he gave) = 75%. This figure shows the percentage of the remaining fruit to the number of available first. Now we have three numbers by which we can already solve the proportion. 10 apples - 100%, x apples - 75%, where x is the desired amount of fruit. How to make a proportion? You need to understand what it is. Mathematically, it looks like this. An equal sign is placed 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 is this number from the original. We solve this proportion and get that x = 7.5 apples. Why the boy decided to give an integer amount, we do not know. Now you know how to proportion. The main thing is to find two relations, in one of which there is the unknown unknown.
The solution of proportion often comes down to simple multiplication, and then to division. Schools do not explain to children why this is so. Although it is important to understand that proportional relations are mathematical classics, the very essence of science. To solve the proportions, you must be able to handle fractions. For example, it is often necessary to translate interest into ordinary fractions. That is, a record of 95% will not work. And if you immediately write 95/100, then you can carry out substantial reductions without starting the main calculation. It’s worth saying right away that if your proportion turned out to be with two unknowns, then it cannot be solved. No professor will help you here. And your task, most likely, has a more complex algorithm of the right actions.
Consider another example where there is no interest. A motorist bought 5 liters of gasoline for 150 rubles. He thought about how much he would pay for 30 liters of fuel. To solve this problem, denote by x the required amount of money. You can solve this problem yourself and then check the answer. If you still do not understand how to make a proportion, then look. 5 liters of gasoline is 150 rubles. As in the first example, we write 5l - 150r. Now find the third number. Of course, this is 30 liters. Agree that a pair of 30 l - x rubles is appropriate in this situation. We turn to the mathematical language.
5 liters - 150 rubles;
30 liters - x rubles;
5/30 = 150 / x.
We 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 with a wrong decision, cars reach unrealistic speeds of 5,000 kilometers per hour and so on. Now you know how to proportion. You can also solve it. As you can see, this is not a big deal.