Elementary school positive proportional inverse proportional how to find who changes with whom

Proportionality is made up of two variables and a constant, and the two variables must be related quantities, one quantity expands or shrinks several times, and the other quantity expands or shrinks several times.

The inverse ratio is also made up of two variables and a constant, and the two variables must be related quantities, one quantity expands or shrinks several times, and the other quantity shrinks or expands several times. (Suppose one quantity is enlarged by several times, and the other quantity is reduced by the same multiple).

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Varies with the proportion of pigs.

Proportional: If the letters x and y are used to denote two related quantities, and k is used to denote their ratio (certainly), the proportional relationship can be expressed by the following relation: y: x=k (a certain amount).

The positive and inverse proportions of elementary mathematics are as follows:

What is proportionality?

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.

The meaning of proportionality

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 work efficiency is constant, the total amount of work is proportional to the working time. Note: k cannot be equal to 0.

Positive and inverse proportional are the same and linked

Similarities: There are two variables and a constant in the relationship between things. In two variables, when one variable changes, the other variable also changes. The product or quotient of the corresponding two variables is fixed.

Mutual transformation

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. 2016 Definition and Test Center of Mathematics Inverse Proportion for Elementary and Junior High School Mathematics.

What is inverse proportionality?

Two related quantities, one quantity changes, and the other quantity also changes, and the product of the two corresponding numbers in these two quantities is constant. These two quantities are called inversely proportional quantities. Their relationship is called an inverse proportional relationship.

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.

The meaning of inverse proportionality

The two variables that satisfy the relation xy=k (k is a constant) are inversely proportional to the relationship between these two variables; Obviously, if y is inversely proportional to x, then xy=k (k is constant); Vice versa. For example, in the travel problem, if the distance is fixed, the speed is inversely proportional to the time; In the workmanship problem, if the total amount of work damage is constant, the work efficiency is inversely proportional to the working time.

Key topics in the proportion of positive and negative in primary school.

Proportionality: two related quantities, one quantity changes, the other quantity also changes, if the ratio of the two corresponding numbers in these two quantities is constant, these two quantities are called proportional quantities, and their relationship is called proportional relationship.

Judge whether two quantities are proportional: some related quantities, although one quantity also changes with the change of another quantity, but the ratio of their corresponding numbers is not necessarily proportional, such as the subtracted number and the difference, the area and side length of the square, etc.

To determine whether two quantities are proportional, it depends on whether they meet two conditions, namely:

The ratio of the two corresponding numbers in the two quantities is constant.

In addition, if two variables are proportional to each other, the image is a straight line.

Inverse proportionality: two related quantities, one quantity changes, the other quantity also changes, if the product of the two corresponding numbers in these two quantities is constant, these two quantities are called the quantities in proportion to the anti-ripping brother, and their relationship is called the inverse proportional relationship.

To determine whether two quantities are inversely proportional, also to see whether they meet two conditions, namely:

The product of the two corresponding numbers in the two quantities is fixed.

An inversely proportional image is a smooth curve.

Difference Between Positive Proportional and Inverse Proportional.

Differences: The ratio of the two numbers corresponding to the positive proportion is fixed, and the spring raid of the two quantities changes in the same direction, that is, one quantity expands or shrinks, and the other quantity also expands or shrinks; The product of the two numbers corresponding to the inverse proportion is fixed, and the two quantities change in opposite directions, i.e.,

One quantity expands or shrinks, and the other shrinks or expands.

Proportional Two related quantities, one quantity changes with the change of the other quantity The ratio (quotient) of the corresponding two quantities must be (a certainty).

Inverse proportionality Two related quantities, one quantity changes with the other. The product of the corresponding two quantities must be xy=k (certain).

Determine whether two quantities are positive or inversely proportional 1 The difference between quantity and number is variable, while number is fixed; Quantities can be taken to different numbers. At the primary school level, a small number of students tend to confuse the two because they are exposed to fixed numbers.

The ratio is certain, the former term and the latter term. (proportional).

The fractional value is constant, the numerator and the denominator. (proportional).

The numerator is certain, the denominator and the fractional value. (inverse proportional).

The divisor is certain, the divisor and the quotient. (inverse proportional).

The quotient is certain, the dividend and the divisor. (proportional).

The product is certain, one factor and another. (inverse proportional).

and definitely, one plus and the other. (Disproportionately) a certain number of attendees, the number of attendees and the total number of people. (proportional).

The circumference and radius of the circle. (proportional).

The area and radius of the circle. (disproportionate).

The diameter and radius of the circle. (proportional).

The circumference and area of the circle. (disproportionate).

The circumference of the circle is fixed, the radius and the pi. (disproportionate).

The diameter of the wheel is certain, the distance traveled and the number of revolutions of the wheel. The area and side length of the (proportional) square. (disproportionate).

The side length and circumference of the square. (proportional).

The area of one face of the cube and the surface area of the square. (proportional) y = 6x, y and x. (proportional).

a = c: b, c definitely, a and b. (inverse proportional).

A pair of gears that bite each other, the number of gears and the number of revolutions. (inversely proportional) the number of copies of the newspaper ordered and the total amount of money. (proportional).

Take some money to buy exercise books, the price of each book and the number of books to buy. (inversely proportional) the number of pages in each exercise book is fixed, the number of books and the total number of pages. (proportional) Xiaohua does 12 questions, the number of questions completed and the number of questions not done.

Disproportionately) Xiao Ming walked from home to school, the speed of walking and the time it takes. Pave a section (inversely proportional) with the area of each square brick and the number of blocks required. Pave a section (inversely proportional) with the side length of each brick and the number of bricks required.

disproportionate) 12 certainly, 3 and 4(disproportionate).

The age of the person is certain, height and weight. (disproportionate).

At the same time and in the same place, the height and length of the person. (proportional).

The height of the parallelogram is certain, the area and the base. (proportional).

The area of the triangle is certain, the base and the height. (inverse proportional).

The volume of the cone is fixed, and the base area is the same as the height.

is the relation of the independent variable x to the dependent variable y positive: y=kx k is a real number inverse: y=k x

Image A proportional image is a straight line past the origin, and inverse proportionality is a symmetrical curve that is not the origin at one, three, or two, four.

The positive proportional relationship is that one quantity increases with the increase of another quantity, and the inverse proportionality is that one quantity decreases with the increase of another quantity.

It's simple, remember that for every day the date grows, the index drops a little. This is inversely proportional.

And the positive proportion is: for every day that the date increases, the grain **s***. Anything that conforms to 1 is inversely proportional, and anything that conforms to 2 is proportional.

Proportional changes at the same time.

Inverse proportionality changes backwards.