Calculating power of proportion
Publish: 2021-04-04 03:17:38
1. The proct of internal terms of ratio is equal to the proct of external terms
2. The solution of proportion is based on the basic properties of proportion: the proct of two external terms equals the proct of two internal terms.
If any three terms in the proportion are known, another unknown term in the proportion can be found. The unknown term in the proportion can be found.
the basic properties of proportion:
① the formula that two ratios are equal is called proportion, such as 3:4 = 9:12, 7:9 = 21:27
in 3:4 = 9:12, Among them, 3 and 12 are external terms of proportion, 4 and 9 are internal terms of proportion. The four numbers of proportion cannot be 0.
proportion has four terms, namely two internal terms and two external terms; In the case of 7:9 = 21:27, 7 and 27 are external terms of proportion, and 9 and 21 are internal terms of proportion.
there are four terms of proportion, namely two internal terms and two external terms.
② ratio, &; For example, the proportion of teachers and students has reached the requirements.
③ for example, the proportion of domestic goods is relatively large.
④ after the proportion is written in the form of score, the left denominator and the right numerator are internal items.
the left numerator and the right denominator are external items.
⑤ in a proportion, the proct of two external items equals the proct of two internal items, This is called the basic property of proportion.
6. The same point and different point of positive proportion and inverse proportion
the relationship between the same point and different point
there are two related quantities of positive proportion, one of which changes, and the other changes with it. If the ratio of the two corresponding quantities is constant, the two quantities are called the quantity of positive proportion, Their relationship is called positive proportional relationship. If the letters X and y are used to represent the two related quantities and K is used to represent their ratio, the positive proportional relationship can be expressed by the following formula: y ÷ X = K (definite)
inverse proportion two related quantities, one of which changes, and the other changes with it. If the proct of two corresponding numbers in two quantities is definite, these two quantities are called inverse proportion quantities, and their relationship is called inverse proportion relations. If the letters X and y are used to express two related quantities, and K is used to express their proct, the inverse proportion relations can be expressed by the following formula: X × Y = K (definite)
proportion is the proportion of the quantity of each part of a population to the total quantity, which is used to reflect the composition or structure of the population.
proportion is divided into scale and proportion. The formula that indicates that two ratios are equal is called proportion. To judge whether two ratios can form a proportion, it depends on whether their ratios are equal, In proportion, the proct of two external terms equals the proct of two internal terms. Finding the unknown term of proportion is called solution proportion. For example: X: 3 = 9:27
solution:
X: 3 = 9:27
27x = 3 × 9
27x = 27
x = 1
6 there are two math problems, try to do it< br />125% ：7=4 ：x
125%x=4 × 7
1.25x =28
x =28 ÷ 1.25
x =22.5
13.5 ：6=x ：4
6x=13.5 × 4
6x=54
x=54 ÷ 6
x = 9
7 the proportion has the following properties:
If a: B = C: D (B.D ≠ 0), then there are
1) ad = BC
2) B: a = D: C (a.c ≠ 0)
3) a: C = B: D; c: A = D: B
4) (a + b): B = (c + D): d
5) a: (a + b) = C: (c + D) (a + B ≠ 0, C + D ≠ 0)
6) (a-b): (a + b) = (C-D): (c + D) (a + B ≠ 0, C + D ≠ 0)
the proof process is as follows
let a: B = C: D = k,
∵ a: B = C: d < br /} > A = Bk; c=dk
1∴ad=bk*d=kbd BC = b * DK = KBD
2) obviously B: a = D: C = 1 / K
3) a: C = BK: DK = B: D; The binding property 2 is C: a = D: B
4) ∵ A: B = C: d
(A / b) + 1 = (C / D) + 1
(a + b) / b = (c + D) / D = 1 + K; In the case that (a + b) is (a + b) (b) (b) (c + D) (c + D) and in the case that (a + b) is (a + b) = D: (c + D)
and B / (a + b) = D / (c + D) (c + D) = 1 / (K + 1) / (c + D) (c + D) (c + D): d
A + B = 0, C + D = 0, C + D = 0, C + D = 0, C + D = 0, and in the case of properties 2, there are B: (a + b) = D: (a + b) (a + b) (a + B / (a + B + b) = D / (a + B + B + B) = D / (A-D / (c + C + D) (c + D) (c + D) = 1-1-1-1-1-1-1-1 / (C / (c + 1 / (c + 1 / (c + 1) (c + 1) (all) (all) (all) (all) (all) (all) (all) (all) (when + D ≠ 0, the binding property 2 is (a + b): a = (c + D): C
6) ② - ①, Subtract both sides of the equation at the same time to get (a-b) / (a + b) = (C-D) / (c + D) = (k-1) / (K + 1)
7) do this problem: a rectangle, the ratio is 2:3, the area of the rectangle is 36 square centimeters, find its length and width.
(interested, please do it later.)
suppose that the rectangle is 2 wide and 3 long, then:
width: 2x2 = 4, length: 3x3 = 9
A: the length of the rectangle is 9, The width is 4.
we decompose 36 into prime factors and find that there are multiples of 2 and 3
If any three terms in the proportion are known, another unknown term in the proportion can be found. The unknown term in the proportion can be found.
the basic properties of proportion:
① the formula that two ratios are equal is called proportion, such as 3:4 = 9:12, 7:9 = 21:27
in 3:4 = 9:12, Among them, 3 and 12 are external terms of proportion, 4 and 9 are internal terms of proportion. The four numbers of proportion cannot be 0.
proportion has four terms, namely two internal terms and two external terms; In the case of 7:9 = 21:27, 7 and 27 are external terms of proportion, and 9 and 21 are internal terms of proportion.
there are four terms of proportion, namely two internal terms and two external terms.
② ratio, &; For example, the proportion of teachers and students has reached the requirements.
③ for example, the proportion of domestic goods is relatively large.
④ after the proportion is written in the form of score, the left denominator and the right numerator are internal items.
the left numerator and the right denominator are external items.
⑤ in a proportion, the proct of two external items equals the proct of two internal items, This is called the basic property of proportion.
6. The same point and different point of positive proportion and inverse proportion
the relationship between the same point and different point
there are two related quantities of positive proportion, one of which changes, and the other changes with it. If the ratio of the two corresponding quantities is constant, the two quantities are called the quantity of positive proportion, Their relationship is called positive proportional relationship. If the letters X and y are used to represent the two related quantities and K is used to represent their ratio, the positive proportional relationship can be expressed by the following formula: y ÷ X = K (definite)
inverse proportion two related quantities, one of which changes, and the other changes with it. If the proct of two corresponding numbers in two quantities is definite, these two quantities are called inverse proportion quantities, and their relationship is called inverse proportion relations. If the letters X and y are used to express two related quantities, and K is used to express their proct, the inverse proportion relations can be expressed by the following formula: X × Y = K (definite)
proportion is the proportion of the quantity of each part of a population to the total quantity, which is used to reflect the composition or structure of the population.
proportion is divided into scale and proportion. The formula that indicates that two ratios are equal is called proportion. To judge whether two ratios can form a proportion, it depends on whether their ratios are equal, In proportion, the proct of two external terms equals the proct of two internal terms. Finding the unknown term of proportion is called solution proportion. For example: X: 3 = 9:27
solution:
X: 3 = 9:27
27x = 3 × 9
27x = 27
x = 1
6 there are two math problems, try to do it< br />125% ：7=4 ：x
125%x=4 × 7
1.25x =28
x =28 ÷ 1.25
x =22.5
13.5 ：6=x ：4
6x=13.5 × 4
6x=54
x=54 ÷ 6
x = 9
7 the proportion has the following properties:
If a: B = C: D (B.D ≠ 0), then there are
1) ad = BC
2) B: a = D: C (a.c ≠ 0)
3) a: C = B: D; c: A = D: B
4) (a + b): B = (c + D): d
5) a: (a + b) = C: (c + D) (a + B ≠ 0, C + D ≠ 0)
6) (a-b): (a + b) = (C-D): (c + D) (a + B ≠ 0, C + D ≠ 0)
the proof process is as follows
let a: B = C: D = k,
∵ a: B = C: d < br /} > A = Bk; c=dk
1∴ad=bk*d=kbd BC = b * DK = KBD
2) obviously B: a = D: C = 1 / K
3) a: C = BK: DK = B: D; The binding property 2 is C: a = D: B
4) ∵ A: B = C: d
(A / b) + 1 = (C / D) + 1
(a + b) / b = (c + D) / D = 1 + K; In the case that (a + b) is (a + b) (b) (b) (c + D) (c + D) and in the case that (a + b) is (a + b) = D: (c + D)
and B / (a + b) = D / (c + D) (c + D) = 1 / (K + 1) / (c + D) (c + D) (c + D): d
A + B = 0, C + D = 0, C + D = 0, C + D = 0, C + D = 0, and in the case of properties 2, there are B: (a + b) = D: (a + b) (a + b) (a + B / (a + B + b) = D / (a + B + B + B) = D / (A-D / (c + C + D) (c + D) (c + D) = 1-1-1-1-1-1-1-1 / (C / (c + 1 / (c + 1 / (c + 1) (c + 1) (all) (all) (all) (all) (all) (all) (all) (all) (when + D ≠ 0, the binding property 2 is (a + b): a = (c + D): C
6) ② - ①, Subtract both sides of the equation at the same time to get (a-b) / (a + b) = (C-D) / (c + D) = (k-1) / (K + 1)
7) do this problem: a rectangle, the ratio is 2:3, the area of the rectangle is 36 square centimeters, find its length and width.
(interested, please do it later.)
suppose that the rectangle is 2 wide and 3 long, then:
width: 2x2 = 4, length: 3x3 = 9
A: the length of the rectangle is 9, The width is 4.
we decompose 36 into prime factors and find that there are multiples of 2 and 3
3.
1. Write the word "Jie",
2, find out the internal and external terms, judge whether x is an internal or external term
3, if x is an internal term, put another internal term and X together
4, then the left and right sides are equal
To solve the equationgive an example
150:3 = x: 5
3x = 150 × 5
3x = 750
x = 250
firstly, the term containing unknown quantity is placed on one side of the equation, and the constant is placed on the other side of the equation, so that it is in the form of x = a (constant), The ratio of the sum of the preceding and following items of the first proportion to the following items of the first proportion is equal to the ratio of the sum of the preceding and following items of the second proportion to the following items of the second proportion
2, inverse ratio theorem
when the proct of two variables is a constant, the proportional relationship between two things or two aspects of a thing, if one side changes, the other side will have opposite changes. For example, with the growth of age, the physical strength of the elderly graally weakens, which is inverse ratio. If the preceding term of a ratio is regarded as the following term and the latter term as the preceding term, the ratio formed is inversely proportional to the original ratio. For example, 9:3 And 3:9 are inversely proportional to each other. Speed is inversely proportional to time, and time is directly proportional to distance
4. The expression that two ratios are equal is called proportion. To solve the proportion is the same as to solve the equation. To find the value of the unknown in the proportion is called to solve the proportion. So you can't add a unit at the end of the value of the solution proportion.
5. For example, 12:3 = 2 (x + 1): 5
12 × 5=3 × 2(x+1)
60=6x+6
6x=54
x=9
12 × 5=3 × 2(x+1)
60=6x+6
6x=54
x=9
6. Do
according to the fact that the proct of the inner two terms is equal to the proct of the outer two terms, or for the problem of solving proportion in fractional form, do it according to the multiplication of the diagonal two terms and the equality of the proct.
according to the fact that the proct of the inner two terms is equal to the proct of the outer two terms, or for the problem of solving proportion in fractional form, do it according to the multiplication of the diagonal two terms and the equality of the proct.
7. The solution proportion is a kind of solution equation. The solution proportion can be transformed into equation by multiplying the external term by the internal term, and then the solution of the equation can be obtained by solving the equation
the same thing is that they are all equations
the difference is that the solution proportion should be changed into the form of equation before solving the equation.
the same thing is that they are all equations
the difference is that the solution proportion should be changed into the form of equation before solving the equation.
8. 1. Write the word "Jie",
2. Find out the internal and external terms and judge whether x is an internal or external term
3. If x is an internal term, put another internal term and X together
4. Then the left and right sides are equal
5. Solve the equation
give an example
150:3 = x: 5
solution: 3x = 150 × 5
3x = 750
x = 250
first, put a term containing unknown quantity on one side of the equation and a constant on the other side of the equation, so that it is in the form of x = a (constant), The ratio of the sum of the preceding and following items of the first proportion to the following items of the first proportion is equal to the ratio of the sum of the preceding and following items of the second proportion to the following items of the second proportion
2. Inverse ratio theorem
when the proct of two variables is a constant, the proportional relationship between two things or two aspects of a thing, if one side changes, the other side will have opposite changes. For example, with the growth of age, the physical strength of the elderly graally weakens, which is inverse ratio. If the preceding term of a ratio is regarded as the following term and the latter term as the preceding term, the ratio formed is inversely proportional to the original ratio. For example, 9:3 And 3:9 are inversely proportional to each other. Speed is inversely proportional to time, and time is directly proportional to distance.
2. Find out the internal and external terms and judge whether x is an internal or external term
3. If x is an internal term, put another internal term and X together
4. Then the left and right sides are equal
5. Solve the equation
give an example
150:3 = x: 5
solution: 3x = 150 × 5
3x = 750
x = 250
first, put a term containing unknown quantity on one side of the equation and a constant on the other side of the equation, so that it is in the form of x = a (constant), The ratio of the sum of the preceding and following items of the first proportion to the following items of the first proportion is equal to the ratio of the sum of the preceding and following items of the second proportion to the following items of the second proportion
2. Inverse ratio theorem
when the proct of two variables is a constant, the proportional relationship between two things or two aspects of a thing, if one side changes, the other side will have opposite changes. For example, with the growth of age, the physical strength of the elderly graally weakens, which is inverse ratio. If the preceding term of a ratio is regarded as the following term and the latter term as the preceding term, the ratio formed is inversely proportional to the original ratio. For example, 9:3 And 3:9 are inversely proportional to each other. Speed is inversely proportional to time, and time is directly proportional to distance.
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