to solve most problems in mathematics secondary school requires knowledge on drawing proportions.This simple ability to help not only to carry out complex exercises in the textbook, but also delve into the essence of mathematics.How to make a proportion?Now we analyze.
The simplest example is the problem of where the three parameters are known, and the fourth to be found.The proportions are, of course, different, but often you want to find the interest some number.For example, only the boy was ten apples.The fourth part he gave to his mother.How many apples left the boy?This is a simple example that will create a ratio.The main thing to do.Initially, it was ten apples.Let it 100%.This we have designated all of its apples.He gave up one-fourth of.1/4 = 25/100.So he was left with 100% (originally) - 25% (he gave) = 75%.This figure shows the percentage of the number of remaining fruits to the number of available again.We now have three numbers, which is already possible to solve the proportion.10 Apples - 100%,
10 apples = 100%;
x = 75% of apples.
turns out that the 10 / x = 100% / 75.This is a basic property of proportions.The more x, the greater the percentage of the number of the original.We solve this proportion, and we find that x = 7,5 apples.Why did the boy decided to send a non-integer number, we do not know.Now you know how to make a proportion.The main thing is to find the two ratios, one of which is the desired unknown.
proportion decision often comes down to a simple multiplication, and then to divide.In schools, children do not explain why this is so.While it is important to understand that the proportional relationship is a mathematical classic, the very essence of science.To solve the proportions must be able to handle fractions.For example, often have to translate interest into ordinary fractions.That is a record of 95% will not do.And if you just write a 95/100, it is possible to carry out a solid reduction, not from the main counting.Immediately is to say that if your ratio has turned in two unknowns, it can not be solved.No professor will not help you.And your task is likely to have a more complex algorithm correct actions.
Consider another example, where there is no interest.Motorist bought five liters of petrol for 150 rubles.He thought about how much he would pay for 30 liters of fuel.To solve this problem for x denote the required amount of money.You can solve this problem yourself and then check your answer.If you have not figured out how to make a proportion, then look.5 liters of gasoline - is 150 rubles.As in the first example, we write 5l - 150r.Now we find the third number.Of course, this is 30 liters.Agree that the pair 30 L - X dollars is appropriate in a given situation.Go to the language of mathematics.
5 liters - 150 rubles;
30 liters - x rubles;
5/30 = 150 / x.
solve this proportion:
5x = 30 * 150;
x = 900 rubles.
So the decision.In its task be sure to check on the adequacy of the answer.It happens that the wrong decision automobiles achieve unreal speeds of 5,000 kilometers per hour, and so on.Now you know how to make a proportion.Also, you will be able to solve it.As you can see, this is no big deal.
