To solve most problems in high school mathematics, knowledge of proportioning is required. 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 a proportion? Let's take a look now.
The simplest example is a problem where three parameters are known, and the fourth must be found. The proportions are, of course, different, but often you need to find some number by percentage. For example, the boy had ten apples in total. He gave the fourth part to his mother. How many apples does the boy have left? This is the simplest example that will allow you to make a proportion. The main thing is to do it. There were originally ten apples. Let it be 100%. This we marked all his apples. He gave one-fourth. 1/4=25/100. So, he has left: 100% (it was originally) - 25% (he gave)=75%. This figure shows the percentage of the amount of fruit left over the amount of fruit that was 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?It is necessary to understand what it is. Mathematically it looks like this. The equal sign is 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 x=7.5 apples. Why the boy decided to give a non-integer amount, we do not know. Now you know how to make a proportion. The main thing is to find two ratios, one of which contains the desired unknown.
Solving a proportion often comes down to simple multiplication and then division. Children are not taught in schools why this is so. While it is important to understand that proportional relationships are mathematical classics, the very essence of science. To solve proportions, you need to be able to handle fractions. For example, it is often necessary to convert percentages to ordinary fractions. That is, a record of 95% will not work. And if you immediately write 95/100, then you can make solid reductions without starting the main count. It’s worth saying right away that if your proportion turned out with two unknowns, then it cannot be solved. No professor can help you here. And your task, most likely, has a more complex algorithm for correct actions.
Let's consider another example where there are no percentages. The 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, we denote by x the required amount of money. Cansolve this problem yourself and then check the answer. If you have not yet figured out how to make a proportion, then look. 5 liters of gasoline is 150 rubles. As in the first example, let's write 5l - 150r. Now let's find the third number. Of course, it's 30 liters. Agree that a pair of 30 l - x rubles is appropriate in this situation. Let's switch to mathematical language.
5 liters - 150 rubles;
30 liters - x rubles;
5/30=150 / x.
Solve this proportion:
5x=30150;
x=900 rubles.
So we decided. In your task, do not forget to check the adequacy of the answer. It happens that with the wrong decision, cars reach unrealistic speeds of 5000 kilometers per hour and so on. Now you know how to make a proportion. Also you can solve it. As you can see, this is not difficult.
