Similarities and differences between positive and inverse proportions

Hope it helps you I wish you progress in your studies o(o

By the way, I'm in the sixth grade, and I find it hard to understand what the first floor says. ~~

The proportional function is y=kx (k is constant, k≠0) and the inverse proportional function is y=k x (k is constant, k≠0).

1.Similarities: both have a constant that is not equal to 0.

2.Differences: When k is a positive number, the proportional function is an increasing function, and the inversely proportional function is a decreasing function; When k is negative, the proportional function is a decreasing function, and the inversely proportional function is an increasing function.

Similarities: They all reflect the changing relationships between different variables.

Differences: First, the proportion relationship is different.

Second, the characteristics are different.

1. Proportionality: In the travel problem, if the speed is rolled and timed, the distance is proportional to the time; In engineering problems, if the work efficiency is constant, the total amount of work is proportional to the working time.

2. Inverse proportionality: reflected in division, when the dividend is fixed, the divisor and the quotient are inversely proportional. In fractions, when the numerator of the fraction is constant, the denominator is inversely proportional to the fractional value.

Third, the application is different.

1. Positive proportionality: when the x value (the value of the independent variable) in the inverse proportion is also converted into its reciprocal, the inverse proportion is transformed into positive proportionality; When the value of x in proportionality (the value of the independent variable) is converted to its reciprocal, it is quietly proportional to the inverse proportion.

2. Inverse proportionality: In the ratio, the previous term of the ratio is certain, and the latter term of the ratio is inversely proportional to the ratio. If the relationship between the total number and the number of copies is concretized, in the shopping problem, the total price is fixed, and the unit price and the quantity are inversely proportional.

Difference: Positive proportionality is the ratio of the two corresponding numbers in the two variables. The relation is y x k (certain) and the inverse ratio is that the product of the two corresponding numbers in the two variables is certain. The relation is x y k (certain meditation).

If the letters x and y are used to represent two related quantities, and k is used to denote their ratio (definitely), the y of x is equal to k (definitely).

Positive and inverse proportional similarities:

du1, the necessary zhi of the composition ratio must be two related dao quantities;

2. One quantity will change with the genus and another.

Difference between positive and inverse proportional:

1. Positive proportionality constitutes a division relationship, and inverse proportionality constitutes a multiplication relationship;

2. The positive proportion is the quotient and the reverse proportion is the product.

For example:1The speed is constant, and the distance is proportional to the time.

2.Time is constant, and distance and speed are directly proportional.

3.The distance is certain, and the speed is inversely proportional to the time.

Think your own things and do your own things.

Similarities: Both positive and inverse proportional contain three quantities, and in each of these three quantities, there is one quantitative and two variables.

In both positive and inverse proportional variables, one quantity changes, and the other quantity also changes. And the way of change is a change that expands (multiplied by a number) or shrinks (divided by a number) several times.

Difference: Proportional quantification is the ratio of two corresponding numbers in two variables. Inverse proportional quantification is the product of two numbers corresponding to each other in two variables.

Mutual conversion between positive and inverse proportions: when the value of x in positive proportions (the value of the independent variable) is converted into its reciprocal, it is transformed from positive proportional to inverse proportional; When the value of x in inverse proportionality (the value of the independent variable) is also converted to its reciprocal, the inverse proportion is converted into positive proportionality.

The similarities are: they both represent the relationship between the two quantities, and the points are proportional: y=kx(k≠0) and inversely proportional: y=kx(k≠0) Their expressions are different.

Positive and negative proportions are the same:

Both have one invariant quantity, two variables.

Positive and negative proportional differences:

The positive proportion is that the ratio is constant, the image is a straight line, and the law of change is the same increase and decrease.

The inverse proportion is a certain product, the image is a curve, and the law of change is one increase and one decrease.

Differences: 1) Positive proportion is a certain ratio; The inverse proportion is a definite product.

2) The expression relationship is different: the proportional is x y=k (certain); The inverse ratio is xy=k (definitely).

If the unit price is certain, what amount is certain, divide by the other two quantities, if the ratio is the same, it is proportional, such as: the unit price of watermelon is certain, the number and total amount of the number of buy trembling reputations, the diameter of the circle is certain, the perimeter and, and, you had better list a **, just like a line chart, draw a diagram, dots, if it is a straight line, it is proportional.

Inverse proportionality: the product of two quantities is multiplied, and the product obtained is certain, and these two quantities are inversely proportional, such as a certain distance, time and speed, and time and speed are multiplied, which is equal to the distance, which is inversely proportional.

Disproportionate: It is neither a business relationship nor a virtual product relationship, it is disproportionate.