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Proportional assignments

bettermarks »Maths book» Algebra and functions »Assignments, percentages and interest» Proportional and anti-proportional assignments »Anti-proportional assignments

In these explanations you will learn what anti-proportional assignments are and how you can recognize, construct and represent them graphically.

Proportional assignments and their tables of values

Assignments are called anti-proportional if the product of values ​​assigned to one another is always the same. The product is then called the anti-proportionality factor. For an anti-proportional assignment, the statement “the more, the less” applies. If this is violated, the assignment is not anti-proportional. If it applies, it is possibly anti-proportional.
The anti-proportionality factor is always the product of two values ​​from one column.
You calculate the bottom line from the top line by dividing the anti-proportionality factor.
Assignments to value tables
A monetary prize should be shared fairly among all winners. The number of winners is assigned to the respective prize per person. Number of winners Profit per person Is this allocation disproportionate?

Proportional arithmetic

If there is a pair of values ​​in an inversely proportional assignment, you can calculate the assignment value of each additional number. The rule of three table will help you with the bills. The following examples show you how to use this table.
When doing the inverse calculation in the second column of the table, always do the opposite point calculation.
Proportional assignment with one as a transition value
Antiproportional assignment with greatest common divisor as transition value Sometimes the given numbers are such that it is awkward to calculate with the transition value 1. Then you can use the greatest common factor.
There is an anti-proportional allocation. Calculate the price you are looking for for 15 people by completely filling out the table for this allocation.
Proportional allocation
Proportional assignment in a word problem
The Meier family is planning a vacation in a holiday home; four of them would pay per person. But now they are planning to live there with six people and are considering how expensive it will be per person. Decide whether the assignment under consideration is inversely proportional and then calculate the result.
Recognize anti-proportional allocation
Proportional allocation
Complete the answer sentence
With six vacationers, the house costs € per person.