How do you solve equations with proportions? How to solve the equation of proportions?

The controversy converts the ratio in the proportion into a fraction and then solves the equation.

x：y=3：2

x=3/2y

y：z=5：4

z=4/5y

x+y+z=66

3/2y+y+4/5y=66

33/10y=66

y=20x=3/2y=30

z=4/5y=16

x:y=5:6 （1）

x=y+5 （2）

Replace (2) with (1).

Available (y+5): y

Namely. y+5y 6 Multiplication of the cross by 6(y+5)=5y gives y y

Substituting x=y+5

x=-25

So x=-25 and y=-30 are the solutions of the original equations.

Replace x=y+5 with proportional formula, and you can solve (y+5) y=5 6

x/y=5/6

Cross multiply by 6x = 5y

And because. x=y+5

So bring in 6(y+5)=5y

Get. y=-30

Bring in x=-25

Because x:y=5:6

So 6x=5y

So x=5 6y

So 5 6y=y+5

y=-30, so x=-25

Formula 1 can be changed to x=5 6y generation 2 has 5 6y=y+5 solution, y=-30, x-25

Here's how to solve the equation for the proportionality of the old snuggler:

Scales are divided into scale bars and scales. The formula that indicates that two ratios are equal is called proportionality. To determine whether two ratios can form a ratio, it depends on whether their ratios are equal.

The four numbers that make up the proportions are called proportional terms. The two items at both ends are called the proportional Qinghan travel outer terms, and the middle two items are called the proportional inner terms. In the scale, the product of the two outer terms is equal to the product of the two inner terms.

Finding the unknown term of the proportion is called solving the proportion.

The solution of proportions is solved by using the basic properties of proportions, because the product of the two outer terms is equal to the product of the two internal terms, so we can multiply the two outer terms and the inner terms by each other to solve this equation. Introvert = Extrovert.

An equation is an equation containing unknowns, which is an equation that represents the equality relationship between two mathematical formulas (such as two numbers, functions, quantities, operations), and the value of the unknowns that make the equation true is called a "solution" or "root". The process of finding the solution of an equation is called "solving an equation".

By solving the equation, you can avoid the difficulty of reverse thinking, and directly list the equation containing the quantity you want to solve. Equations have a variety of forms, such as unary linear equations, binary linear equations, unary quadratic equations, etc., and can also form a system of equations to solve multiple unknowns.

The basis for solving the equation of proportions is the fundamental property of proportions, i.e., the product of the two inner terms of the ratio is equal to the product of the two outer terms.

For example: 2:7=4:x

2x=4×7

x=14

This is not proportional, it should be an equation. You can blindly and simply look at the comparison of the imitation edge of the equal sign left trouser as a division. Grinding pants.

Solution: x:10 9=

x÷10/9=

x×（9/10）=

x=12 x=20 and then look at another solution.

Ratio equivalent to the division chain potato rent shed trillion or fraction, quite hand Kai Yu:

x÷10/9=

x×9/10=

x=12÷x=20

x:10/9=

x×9/10=

x=20 knowledge points: the ratio is equivalent to dividing, divided by a fraction is equal to multiplying the inverse difference of the number of false answers. Branchy.

Solution: x=

x=

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Dear, the detailed solution process of this problem is given in the above **, you can take a look.

The difficulty in the problem is that the denominator is different from each other, so it is necessary to find the least common multiple of the two buckets of denominator 20 and 28 140, and the equation is multiplied by 140 left and right, and the denominator is removed, and then the calculation is much more convenient.

x 20 - x 28 = 2 solution (x 20 - x 28) * 140 = 2 * 140 x 20-140x 28 = 280 7x-5x = 280 2x = 280 x = 140

Dear, I'll re-enter the problem-solving process to make it easier for you to understand.

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Dear, the title in the picture above is the same as the one above, and the specific process has been written above.

x 20 - x 28 = 2 solution (x 20 - x 28) * 140 = 2 * 140 x 20-140x 28 = 280 7x-5x = 280 2x = 280 x = 140

The most radical approach:

The product of the inner term is equal to the product of the outer term.

For example: a b = c x

x=（b*c）/a.

The product of the inner terms of the equation of proportions is equal to the product of the outer terms.

For example: a:b=c:d, b and c are internal terms, a and d are external terms, b c = a d

The product of the inner term is equal to the product of the outer term.

12x+15y=10x+20y

2x=5y, i.e. x:y=5:2

There are many students who do not know how to solve the proportions. Why don't they solve the proportions? I can say that they have not yet absorbed The Basic Nature of Proportion. Why am I so sure? Listen to me one by one.

We know that the so-called solution ratio is to solve the equation, and its solution is no different from the equation, mainly in the first step. Let's start with an example: 1 4:

1 8 = x: 1 10, solution ratio. The first steps here are:

1 8x=1 4*1 10, if you make this step, students who can solve equations can continue to solve them. It can be seen that the students who can't solve the ratio are because they can't take the first step. And the first step is listed according to the "basic nature of proportion".

Therefore, students who do not know how to solve proportions do so because they have not absorbed the Basic Properties of Proportions. In this part of the application problems, there are problems such as finding the distance in the graph or the actual distance. When finding the distance in the graph or the actual distance, the solution in the book is the "proportional solution".

Actually, we can also use "arithmetic solutions".

First, let's recall what a scale is. Scale bar = distance in figure: actual distance. We can take a cue from this: think of the actual distance as a unit of 1. The distance in the graph is the "fraction of the corresponding quantity".

Therefore, there are two relations for the "arithmetic solution": "distance in the figure = actual distance * scale" and "actual distance = distance in the figure scale".