Mathematical cross method How to use, the principle of cross method The mathematical principle of cr

Criss-cross method.

Open Categories: Chemistry, Chemical Calculations, Chemical Formulas.

Note: It is only applicable to mixtures composed of two substances m A: molar mass of substance A m B: molar mass of substance B m Mixture: molar mass of mixture composed of A and B n: amount of substance, m B: A: m A m mixed - m B.

m mixed. B: mB, mA-m mixed.

It is obtained: n A: n B = (m mixed - m B) :( m A - m mixed ).

1. Cross-cross multiplication.

This is a method of writing the chemical formula of a substance using valency, and it is suitable for compounds composed of two elements or two groups. It is based on the principle of valence: the algebraic sum of the total number of positive and negative prices is 0 or the absolute value of the total number of positive and negative prices is equal.

Let's take a look at the steps below.

Second, the criss-cross comparison method.

What we often call the cross method is actually the cross comparison method, which is a graphical method. The cross diagram method is actually a simple algorithm instead of the summation formula, which is particularly suitable for the calculation of mixtures of two total quantities and two relationships (i.e., the calculation of 2-2 type mixtures), which is used to calculate the ratio of the two components in the mixture.

3. Cross-cross elimination method.

The cross elimination method is referred to as the cross elimination method, which is a type of ion inference problem solution, using "cross elimination" to narrow the scope of unknown substances, so as to use the problem to determine the substance and find the correct answer.

In fact, the cross method is a simple form of solving a binary equation, if you are really not used to it, you can solve the equation for example, but I will tell you about it, like a density of 10 b is 8, their mixture density is 9, you can put 9 in the middle, write 10 and 8 on the left, mark ab, and then subtract 9 respectively, you can get 1 1 on the right, at this time, the ratio of this 1:1 is simpler, but the difficulty is the same, you can experience it yourself, this method is actually very good, saving time, especially when taking the comprehensive examination.

1. Principle: Before the mixed envy faction, the whole one, the quantity x, the index quantity A overall two, the quantity y, the index quantity b (a>b) after mixing, the quantity (x + y), and the index quantity c can obtain the following relation: x a + y b = (x + y) c launch:

x (a-c) = y (c-b) to get the formula: (a-c) :(c-b) = y:

x knows any four of x, y, a, b, and c, and can find the unknown. However, if you find C, it is easier to calculate directly. When x+y is known, any one of x or y can also be used;Know x:

Y is also available. 2. The essence of the cross method is to solve the simple form of binary equations, this kind of problem can also be solved by the equation, the specific method of using the law is as follows: like the density of a brother is 10, the density of b is 8, and the density of their mixed ridge complex is 9, you can put 9 in the middle, write 10 and 8 on the left, mark ab, and then subtract 9 respectively, you can get 1 and 1 on the right respectively. In this case, the ratio is 1:1.

The factorization cross method is simply as follows:

The multiplication of the left side of the cross equals the quadratic term, the right multiplication equals the constant term, and the cross multiplication and addition equals the primary term. In fact, it is to use multiplication formula operations to factorize. The cross decomposition method can be used to decompose the factor of a quadratic trinomial (unary quadratic) omission (not necessarily in the range of integers).

Decide. For a polynomial of the form ax +bx+c, δ=b -4ac can be used to determine whether it can be factored using the cross decomposition method. When the δ is a perfectly squared number, the polynomial can be cross-multiplied in an integer range.

Difficulty: Flexible use of the cross decomposition method to decompose factors. Because not all quadratic polynomials can be factored by cross multiplication. Back to boredom.

Focus: Correctly use the cross decomposition method to factor some quadratic trinomials whose coefficient is not 1.

Precautions. The first point is to solve the problem of proportionality between the two.

The second point: the proportional relationship obtained is the proportional relationship of the base.

The third point: the total mean is placed **, on the diagonal, the large number is reduced, and the result is placed on the diagonal.

Solve the factorization of quadratic trinomial ax + bx+c.

For example: 2x -5x-12=(2x+3)(x-4) Through observation, it is found that 2x x=2x is the first term, 3 (-4)=-12 is the last term, and 2x (-4)+3 x=-5x is the middle term.

That is, the 2 of the first term is decomposed into 2 and 1, and the last term -12 is decomposed into 3 (-4) and cross-multiplied and then added, which is the middle term.