Page 2: Direct and Inverse Proportionality

This page delves into the concepts of direct and inverse proportionality, explaining how quantities relate to each other in different scenarios.

Definition: Two quantities are directly proportional when their ratio remains constant as both quantities vary.

Example: If 3 people can paint 6 walls, then 6 people can paint 12 walls in the same time, showing direct proportionality.

Highlight: In inverse proportionality, when one quantity is multiplied by a number, the other is divided by the same number.

Vocabulary: The constant of proportionality is the fixed ratio between two directly proportional quantities.

Page 3: Percentages and Proportional Distributions

This section covers percentages and their applications in real-world scenarios, including discounts and proportional distributions.

Definition: A percentage is a ratio with denominator 100, written using the % symbol.

Example: To calculate 20% of 50 students: (20/100) × 50 = 10 students.

Highlight: Proportional distributions can be either direct or inverse, depending on how quantities are related.

Example: In a job payment scenario, money is distributed in direct proportion to hours worked.

Page 7: Proportional Distribution Problems

This page covers problems involving multiple participants and proportional distribution of prizes.

Example: Three people contributing different amounts to a lottery ticket and calculating their proportional shares.

Highlight: Both direct and inverse proportional distributions are demonstrated through practical examples.

Page 1: Introduction to Ratios and Proportions

This page introduces fundamental concepts of numerical proportionality, starting with fractions as ratios. The relationship between quantities is explained through practical examples using colored balls.

Definition: A ratio between two quantities a and b is the quotient between them, expressed as a/b or a:b.

Example: The relationship between blue and white balls can be expressed as 3/2 or 3:2.

Vocabulary: Magnitude refers to a measurable property, characteristic, or attribute of objects or situations.

Highlight: Two ratios a/b and c/d are in proportion when they are equivalent as fractions, expressed as a/b = c/d.