Written Proportion Applications and Graphical Representations

This page focuses on practical applications of proportion through written problems and visual representations through graphs.

Example: A practical written proportion question involving man-hours demonstrates how 3 mechanics taking 40 minutes to service a car can be calculated for 5 mechanics using inverse proportion.

Highlight: When solving man-hours problems, it's crucial to assume all workers maintain the same work rate.

Definition: In man-hours calculations, more workers result in less time (inverse proportion), following the principle that time × number of workers = constant.

Example: The solution process involves:

1. Finding total man-minutes $3 × 40 = 120$
2. Dividing by new number of workers (120 ÷ 5 = 24 minutes)

Highlight: The page includes graphs showing various proportional relationships, including y = k/x² and y = k√x, helping visualize different types of proportional relationships.

Direct and Inverse Proportion Fundamentals

This page introduces fundamental concepts of direct and inverse proportion, with detailed explanations of more complex relationships involving squares and roots.

Definition: Direct proportion occurs when one quantity increases in the same proportion as another quantity.

Example: When A is directly proportional to B, and B = 4 results in A = 0.8, we can find A when B = 3 using the formula A = KB, where K is the constant of proportionality.

Highlight: For direct proportion with squares and roots, problems can involve relationships like w ∝ v³ or p ∝ √m.

Vocabulary: The symbol ∝ means "proportional to" and is used to express relationships between quantities.

Example: In a problem where p is directly proportional to the square root of m, with p = 18 when m = 36, we can find m when p = 100 using the formula p = K√m.