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Proportionality: Two related quantities, one quantity changes, the other quantity also changes, if the ratio of the two numbers corresponding to these two quantities (that is, the quotient) is constant, their relationship is called proportional relationship
Inverse proportionality: A change in one quantity causes an opposite change in another quantity. These two quantities are inversely proportional quantities, and their relationship is inversely proportional.
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The notes on proportionality and inverse proportionality are as follows:
1. Proportionality: two related quantities, one quantity changes, the other quantity also changes, if the ratio of the two numbers corresponding to these two quantities is certain, these two quantities are called proportional quantities, their relationship is called proportional relationship, and the proportional image is a ray. Proportional relationship: The change law of the two related ruler guesses:
At the same time, it expands and shrinks at the same time, and the excitation ratio remains the same.
When judging whether two related quantities are proportional, it should be noted that these two related quantities are also one kind of quantity and change with the change of the other, but the ratio of the two numbers corresponding to them is not necessarily, and they cannot be proportional. For example, a person's age is not proportional to his weight, and the length of the sides of a square is not proportional to its area.
2. Inverse proportionality: two related quantities, one quantity changes, and the other quantity also changes with the opposite direction. If the product of the two numbers corresponding to these two quantities is fixed, these two quantities are called inversely proportional quantities, and their relationship is called inversely proportional relations. Mausoleum lead type.
Inversely proportional quantities include three quantities, one quantitative and two variable. Investigate the relationship between changes in expansion (or contraction) between two variables. A change in one quantity causes the opposite change in another quantity.
These two quantities are inversely proportional quantities, and their relationship is inversely proportional.
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Proportion is the relationship between the quantities that are associated.
If the ratio of the two quantities (i.e., quotient k) is constant, these two quantities are called proportional quantities, and their relationship is called proportional relations.
For example: y x=k (k certainly) or kx=y.
Two variables satisfying the relation y x = k (k is a constant) are said to be proportional to each other.
Obviously, if y is proportional to x, then y x = k (k is constant); Vice versa.
For example, in the travel problem, if the speed is constant, the distance is proportional to the time; In engineering problems, if the efficiency of the source of work is constant, the total amount of work is proportional to the working time.
When the value of x (the value of the independent variable) in the inverse proportion is also converted to its reciprocal, the inverse proportion is converted into the positive proportion; When the value of x in a positive proportion (the value of the independent variable) is converted to its reciprocal, the positive proportion is converted to an inverse proportion.
Two related quantities, one quantity knows the change, and the other quantity also changes, and the product of the two corresponding numbers in these two quantities is fixed. These two quantities are called inversely proportional quantities. Their relationship is called an inverse proportional system.
It is expressed by k=y*x (certainly) x is not equal to 0 and k is not equal to 0.
To put it simply, if one thing increases and another decreases, it decreases and another thing increases, and the relationship between the two things is called inverse proportion.
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Two associated quantities, one quantity.
change, the other quantity also changes with it, if the two quantities correspond.
The ratio of the two numbers (i.e., the quotient) is certain, and these two quantities are called proportional quantities, and their relationship is called proportional relations, and the proportional image is a straight line. Moreover, the change law of the two related quantities in the proportional relationship is to expand and shrink at the same time, and the ratio remains unchanged. There are two related quantities, one quantity changes, and the other quantity also changes in opposite directions as it changes.
If the product of the two numbers corresponding to these two quantities must be p>
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Proportionality: two related quantities, one quantity changes, the other quantity also changes, if the ratio of the two numbers corresponding to these two quantities (that is, the quotient) is constant, these two quantities are called proportional quantities, their relationship is called proportional relationship, and the proportional image is a ray. Indicated by letters:
If the letters x and y are used to represent the two related quantities, and k is used to represent their ratio (certainly), the proportional relationship can be expressed by the following relation: x y=k (certainly) can also be expressed as: x=ky, proportional relationship The change law of the two related quantities:
Expand at the same time, shrink at the same time, and the ratio remains the same
Inverse proportionality: two related quantities, one quantity changes, and the other quantity also changes, if the product of the two numbers corresponding to these two quantities is certain, these two quantities are called inversely proportional quantities, and their relationship is called inverse proportional relations If the letters x and y are used to represent two related quantities, and k is used to represent their products, (certainly) the inverse proportional relationship can be expressed by the following relation: x y=k (certainly) inversely proportional quantities Premise:
These two quantities are called inversely proportional quantities, and their relationship is called inverse proportional relations. .Letter notation:
Let x and y be two related quantities (with a multiplicative relationship), and k is the product of x and y (k certainly), that is: x*y=k (certainly) Then, the letters x and y are used to represent the two related quantities, and the proportional relationship is further abstracted and summarized as =k (certainly).
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One is bigger, the other is bigger, and it's very regular, and it's growing in a straight line, and it's the same as the bigger and the smaller it is, and it's going to be the opposite of it, and it's like a parabola.
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