Inverse ratio, referred to as inverse ratio, refers to two relatedvariableOne kind of quantity changes, and the other kind of quantity also changes with itproductYes, then they are called inversely proportional quantities, and their relationship is calledInverse proportional relation。[1]
Where, x and y are called inverse proportional quantities, their relationship is called inverse proportional relationship, and k is constant.
Positive negative connection
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The similarities and connections between positive and negative proportion.
Positive proportion: two related variables, one variable changes, and the other changes with it. If the ratio of these two variables is certain, then these two numbers are in positive proportion. The relationship between these two variables is calledProportional。
Similarities
(1) There are two variables and one constant in the relationship between things.
(2) In the two variables, when one variable changes, the other variable also changes.
(3) The product or quotient of the corresponding two variables is certain.
Mutual transformation
WhenPositive proportionX value in（independent variableIs converted to its reciprocal byPositive proportionConversion into inverse proportion;When the value of x in the inverse scale (the value of the independent variable) is also converted to its reciprocal, the inverse scale is converted to the positive scale.
Positive proportion example:
1. The unit price is fixed, and the total price is proportional to the quantity.
2. The quantity is fixed, and the total price is in direct proportion to the unit price.
3. The length of a rectangle is certain, and its area is in direct proportion to its width.
4. The width of a rectangle is certain, and its area is in direct proportion to its length.
5. The speed is fixed, and the distance is proportional to the time.
6. Time is fixed, distance is proportional to speed.
7. The work efficiency is certain, and the total amount of work is proportional to the working time.
8. The working time is fixed, and the total amount of work is in direct proportion to the working efficiency.
9. The divisor is certain, and the dividend is in direct proportion to the quotient.
10. Quotient is certain. The dividend is in direct proportion to the divisor.
11. The number of bricks is fixed, and the area of the bottom is in direct proportion to the area of each brick.
12. The area of bricks is certain, and the area of the bottom is in direct proportion to the number of bricks.
Inverse scale example:
1. In the 100 meter race, the distance of 100 meters is unchanged, and the speed and time are inversely proportional;
2. The total number of people in line for exercises remains unchanged, and the number of lines in line is inversely proportional to the number of people in each line;
3. To make paper boxes, the total number is certain, and the number and number of people made by each person;
4. The total price is fixed, and its unit price and quantity are inversely proportional;
5. The area of a rectangle is certain, and the length and width are inversely proportional;
6. The cuboid has a certain volume, and the bottom area and height are inversely proportional;
7. Divide a piece of cake equally, and each person's share of cake is inversely proportional to the number of people;
8. The total price is fixed, and the unit price is inversely proportional to the quantity;
9. The total number of cartons is fixed, and the number of cartons made by each person is inversely proportional to the number of people.
application
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Inverse proportional relation is a generalization problem in word problems.Reflected indivisionMedium, when beingDivisorCertainly, divisor is inversely proportional to quotient.In fraction, when the numerator of fraction is certain,denominatorAndFractional valueIn inverse proportion.In proportion, the first term of the ratio is certain, and the second term of the ratio is inversely proportional to the ratio.If the relationship between the total number and the number of copies is further specified as: in the shopping problem,Total pricecertain,Unit PriceandnumberIn inverse proportion.stayTravel problemsMedium, the total distance is certain,speedandtimeIn inverse proportion.In engineering problems, the time spent digging a hole in the ground is also (roughly) inversely proportional to the number of people employed to dig the hole.
On the Cartesian coordinate plane, the figure of two variables with inverse scale relationship is a pair of hyperbolas.The product of the X and Y coordinate values of each point on the graph line is always equal to the scale constant (k).Since k is non-zero, the line does not intersect the coordinate axis.
Example
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Example: judge whether it is in inverse proportion.
(1) The total amount of coal is certain, the daily coal consumption and the number of days that can be burned.
(2) The total amount of seeds is certain, the sowing amount per hectare and the number of hectares sown.
(3) The speed and time required for Uncle Li to ride a bicycle from home to the factory.
(4) Hua Rong did 12 math problems, the finished problems and the unfinished problems.
