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Showing posts with label units of measurement. Show all posts
Showing posts with label units of measurement. Show all posts

## 8.08.2016

### Variable units of measure

Subject of occupations:
TRIGONOMETRIC FUNCTIONS IN A RECTANGLE
Subject of the previous lesson
Quantity

Lesson 7

Variable units of measure

Example of variable units of measure are exchange rates of the different countries. The main world currencies are in continuous fluctuation. They are connected by laws of the inverse symmetry – rise in price of one currency means reduction in cost of other currency.

One more example. Why people never celebrate such significant day how "The Middle of Life"? Because nobody knows the precise duration of characteristic life. After death such important parameter as "life expectancy", ceases to change. Similar indeterminacy is characteristic of all living beings.

If to take duration of existence of an alive organism for unit, then the description in variable units of measure will be the most precise mathematical description of any life. As the beginning of this unit of measure it is necessary to consider the conception moment (at sexual manifolding), the end is the death. It is necessary to notice that increase in life expectancy of concrete organisms is not a priority in natural selection.

Quantity, the back symmetric life expectancy, the age is. The age allows to express the variable characterizing life in constant units of measure of time.

From the point of view of mathematics, emergence of life can be considered as transition from constant units of measure (inanimate nature) to variables (wildlife).

At the following lesson we will consider
Multiplication

## 2.08.2011

### How many will be metres and decimeters?

"How many there will be 22 metres of 2 decimeters a minus of 1 metre of 8 decimeters?" Difficulty of this problem consists that for a designation of one number is used at once two units of measurement: metres and decimeters. If to translate told on normal language of blondes it almost the same that "I have bought yesterday a phrase two jackets and one has presented to the girl-friend" to replace with a phrase "I yesterday has bought two jackets and four sleeves, and then one jacket and two sleeves has presented to the girl-friend". It is natural that last phrase will confuse you at once: "And sleeves that, separately from jackets are on sale?". Certainly, no. Sleeves are sewn to jackets, here we only consider them separately. What for? What you to confuse. Problems in the mathematician always get confused, as a ball of threads. You should untangle and receive them the right answer. It develops ingenuity, here. And simple writing off from the answer book develops dullness. Now we will start the decision.

Means, a problem at us such: how many will be, if from 22 metres and 2 decimeters to take away 1 metre and 8 decimeters? The main thing what it is necessary to know at the decision of this problem - how many decimeters in one metre? Or how many metres in one decimeter.

1 metre = 10 decimeters

1 decimeter = 0.1 metres

One metre is equal to ten decimeters. One decimeter is equal the one tenth metre. Here now we have everything what to solve a problem. Is the whole three ways of the decision of this problem - in metres, in decimeters, in two units of measurement at once.

We solve a problem in metres. For this purpose decimeters reduced (this that number from which subtract) and subtracted (this that number which subtract) it is translated in metres.

2 decimeters = 0.2 metres

8 decimeters = 0.8 metres

We add these tails to our numbers in metres:

22 metres + 0.2 metres = 22.2 metres

1 metre + 0.8 metres = 1.8 metres

Now it is possible to execute subtraction and to receive a difference of these metres. It is possible to translate the answer at once in metres and decimeters:

22.2 metres - 1.8 metres = 20.4 metres = 20 metres of 4 decimeters

The second way is to solve the same problem in decimeters. For this purpose we will translate metres in decimeters:

22 metres = 220 decimeters

1 metre = 10 decimeters

To the received decimeters it is added those decimeters which at us are on a statement of the problem:

220 decimeters + 2 decimeters = 222 decimeters

10 decimeters + 8 decimeters = 18 decimeters

We carry out subtraction and we translate decimeters again in metres and decimeters:

222 decimeters - 18 decimeters = 204 decimeters = 20 metres of 4 decimeters

It was the mathematics. Now for blondes. What to understand that we did, let's replace metres with bows, and decimeters on ruches. Thus we will agree that it is possible to make ten ruches of one bow, and it is possible to make one bow of ten ruches – well to sew. We copy a statement of the problem: «you have 22 bows and 2 ruches. And 8 ruches you should give 1 bow to the girl-friend». With bows all is simple – we take one and we give. And how to be with ruches? They obviously do not suffice us. We will look, as we solved this problem math in two ways. From outside it looks so.

The first way. You take all bows and untie them, smooth all ruches. Take a needle with a thread and sew all it in one long tape. After you have stopped to sew, measure the necessary quantity from a tape and cut off scissors. Solemnly hand over to the gone nuts girlfriend a tape piece. Then you with the girlfriend cut the tapes, do of them bows and ruches. As a result you with the girlfriend, all in bows and ruches, stand, as two marriageable silly women.

The second way. You untie all bows and cut them on ruches. Do a heap of ruches and from this heap select 18 pieces for the girl-friend. After that solemnly hand over to the gone nuts girl-friend a small group of ruches. Then together begin to smooth ruches and to sew from them bows. Thus your girl-friend thinks: «In the silly woman! Because of this ugly creature I should sew now a bow». You think: «In the silly woman! Because of this ugly creature I at first cut, and now should sew already twenty bows». To tell the truth, I do not envy you.

As you can see, math correct ways from outside look is not absolutely practical. How any blonde will arrive in this situation? As the two-nuclear processor. Takes one bow from a small group of bows and will make of it ten ruches. Now you have one small group from twenty one bows and the second small group from twelve ruches. From the first small group you take one bow, eight ruches a beret from the second small group. Hand over to the happy girl-friend one bow and eight ruches. Then you admire the treasures and is simple blah-blah-blah instead of puffing with scissors or needles. It also is the third way of the decision of a problem. Coming back to our metres and decimeters, math it can be written down so:

22 metres and 2 decimeters = 21 metre and 12 decimeters

(21 metre and 12 decimeters) – (1 metre and 8 decimeters) = (21 metre – 1 metre) and (12 decimeters – 8 decimeters) = 20 metres and 4 decimeters

We with two different units of measure carry out two mathematical actions of subtraction simultaneously, in the same way, as two-nuclear processors Intel for computers work. I think, after such decision in your writing-book mathematicians will start to go nuts. Though so all calculations practically become. In the mathematician it is accepted to say that it is necessary to execute at first subtraction of decimeters, and already then subtraction of metres. Basically, mathematicians are right. So it is heavier to get confused. At subtraction of decimeters you can always steal one metre from metres if decimeters do not suffice you. Then from the remained metres subtract metres. Only do not forget about one metre if you have already dissipated it in decimeters.