Understanding Proporcje (Proportions)

This page introduces the concept of proporcje (proportions) and provides examples of how to solve them. Proporcje Matematyka is a fundamental topic in mathematics that deals with the equality of ratios.

A proportion is defined as an equation stating that two ratios are equal. The general form of a proportion is written as a:b = c:d, where a and d are called the extreme terms, while b and c are the middle terms.

Definition: A proportion is an equation showing that two ratios are equal, typically written in the form a:b = c:d.

The page presents several examples to illustrate how to work with proportions:

1. Simple numeric proportion: 2/3 = 12/18
2. Equation with one unknown: 6/x = 2/18
3. Word problem involving proportions

Example: In a word problem, the proportion is used to calculate the cost of 12 rolls when 5 rolls cost 6.50 zł.

The page also introduces the cross multiplication method for solving proportions, which is a key technique students should master.

Highlight: The cross multiplication method is an efficient way to solve proportions, especially when dealing with unknowns.

Vocabulary:

• Stosunek: ratio
• Iloraz: quotient
• Wyrazy środkowe: middle terms
• Wyrazy skrajne: extreme terms

The page concludes with a more complex proportion problem involving algebraic expressions, demonstrating the versatility of proportional reasoning in mathematics.

Example: A proportion involving algebraic expressions: x/12 = (x² + 10)/14

Understanding these concepts and techniques is crucial for students as they progress in their mathematical education, particularly for those studying Proporcje Klasa 8 zadania PDF or Proporcje zadania klasa 7.