Junior high school mathematics is the key stage of learning career. In order to make students make achievements in mathematics, the following mathematical network shares the positive and negative proportions of basic mathematics knowledge for everyone. I hope everyone will study hard!
What is direct ratio?
Two related quantities, one variable and the other variable. If the corresponding ratio (i.e. quotient k) of these two quantities is certain, these two quantities are called proportional quantities, and their relationship is called proportional relationship. For example: y/x=k(k must be) or kx = y.
The significance of positive proportion
Two variables that satisfy the relation y/x=k(k is a constant) are said to be proportional.
Obviously, if y is proportional to x, then y/x=k(k is a constant); or vice versa, Dallas to the auditorium
For example, if the speed is constant, the distance is proportional to the time; In engineering problems, if the work efficiency remains unchanged, the total amount of work is directly proportional to the working time.
Note: k cannot be equal to 0.
Examples of positive proportions:
The perimeter and side length of a square (ratio 4).
The circumference and diameter of a circle (ratio π).
Total purchase price and purchase quantity (ratio unit price).
Example of distance:
1. The speed is constant and the distance is proportional to the time.
2. Time is fixed, and distance is directly proportional to speed.
Rectangular area: the area is constant and the length and width are inversely proportional.
It's all about repairing one and changing another. For example, in aX=Y, if a is constant, then x and y are proportional.
Positive proportion and inverse proportion are the same and related.
similar
1. The relationship between things has two variables and a constant.
2. Among the two variables, when one variable changes, the other variable will also change.
3. The product or quotient of the corresponding two variables is certain.
reciprocal transformation
When the value of x in inverse proportion (the value of independent variable) is also transformed into its reciprocal, it is transformed from inverse proportion to positive proportion; When the value of x in a positive proportion (the value of independent variable) is transformed into its reciprocal, it is transformed from a positive proportion to an inverse proportion.
20 16 mathematical inverse proportion definition and test sites in Xiaoshengchu
What is inverse proportion?
Two related quantities, one of which changes and the other changes, and the product of the corresponding two numbers in these two quantities is certain. These two quantities are called inverse proportional quantities. Their relationship is called inverse relationship. Where k=y*x (sure) x is not equal to 0, and k is not equal to 0. Simply put, if one thing increases, another thing decreases, he decreases, and another thing increases, the relationship between these two things is called inverse ratio.
The meaning of inverse ratio
Two variables that satisfy the relationship xy=k(k is a constant), we say that the relationship between these two variables is inversely proportional;
Obviously, if y is inversely proportional to x, xy=k(k is a constant); or vice versa, Dallas to the auditorium
For example, if the distance is constant, the speed is inversely proportional to the time; In the work problem, if the total amount of work is fixed, the work efficiency is inversely proportional to the working time.
The essence of inverse proportion
Two related quantities, one of which varies with the other, but the product of these two quantities must be constant. At this time, these two quantities are inversely proportional. Quantity, their relationship is called inverse ratio. It is usually expressed by xy=k (constant).
Inverse proportional relation belongs to inductive problem in application. Reflected in division, when the divisor is fixed, the divisor and quotient are inversely proportional. In a fraction, when the numerator of the fraction is constant, the denominator is inversely proportional to the fractional value. In proportion, the former term of the proportion is fixed, and the latter term is inversely proportional to the proportion. If the relationship between the total number and the number of copies is embodied as: in the shopping problem, the total price is fixed, and the unit price is inversely proportional to the quantity. In the travel problem, the distance is fixed and the speed is inversely proportional to the time.
Positive proportion and inverse proportion are the same and related.
similar
1. The relationship between things has two variables and a constant.
2. Among these two variables, when one variable changes, the other variable will also change.
3. The product or quotient of the corresponding two variables is certain.
reciprocal transformation
When the value of x in the positive proportion (the value of independent variable) is transformed into its reciprocal, it is transformed from positive proportion to inverse proportion; When the value of inverse proportion x (the value of independent variable) is also converted into its reciprocal, it is converted from inverse proportion to positive proportion.
Inverse ratio in life
1 .100 meter race, distance 100 meter, speed and time are inversely proportional (that is, the distance is constant, speed and time are inversely proportional);
2. Queue for exercises, the total number of people is unchanged, and the number of people in line is inversely proportional to the number of people in each row;
3. The total number of cartons is fixed, and the number of cartons made by each person is inversely proportional to the number of people;
4. When buying something, the total price is fixed, and its unit price is inversely proportional to the quantity;
5. The area of a rectangle is certain, and its length and width are inversely proportional (hint: but the circumference of a rectangle is not directly proportional to its length and width, neither directly proportional nor inversely proportional);
6. A cuboid has a certain volume, and its bottom area is inversely proportional to its height.
7. Divide a piece of cake equally, and the cake each person gets is inversely proportional to the number of people.
8. The total amount of work is certain, and the work efficiency is inversely proportional to the working hours.
9. The numerator is fixed, and the denominator is inversely proportional to the fraction.
The above is the positive and negative ratio of the basic knowledge of mathematics shared by Mathematics Network. I hope it helps you!
;