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 8: Percentage Reduction Problems

This section focuses on sequential percentage reductions and their cumulative effects.

Example: A shirt's price reduced by 25% in January and 20% in February from the previous month's price.

Highlight: The importance of understanding how successive percentage changes combine.

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.