Algebraic Operations and Distributivity

This page focuses on calcul littéral (literal calculation) and the concept of distributivity in algebra. It covers simple and double distributivity, providing examples and exercises to reinforce understanding.

Definition: Distributivity is a property of operations that allows the multiplication of a number over a sum.

Key concepts covered:

1. Simple Distributivity: k$a + b$ = ka + kb

   Example: 5$x + 4$ = 5x + 20

2. Double Distributivity: a + b$$c + d = ac + ad + bc + bd

   Example: x + 3$$2 - x = 2x + 6 - x² - 3x = -x² + 2x + 6

The page also includes an area calculation problem that applies algebraic concepts:

Example: Calculate the shaded area of a square with side length 5, where a smaller square with side length $x + 3$ is removed from one corner.

Solution:

• Area of large square: 5 × 5 = 25
• Area of small square: $x + 3$²
• Shaded area: 25 - $x + 3$²

Highlight: This page provides excellent practice for distributivité simple exercices and introduces more complex algebraic manipulations, which are essential for students studying calcul littéral 3ème.

Volume Calculations and Formulas

This page introduces various volume formulas for 3D shapes and provides an exercise to apply these concepts. The shapes covered include cubes, parallelepipeds, pyramids, cones, cylinders, and prisms.

Definition: Volume is the amount of three-dimensional space occupied by an object.

Key formulas presented:

• Cube: V = C × C × C (where C is the length of a side)
• Parallelepiped: V = L × l × H (where L is length, l is width, and H is height)
• Pyramid and Cone: V = $1/3$ × Base Area × Height
• Cylinder and Prism: V = Base Area × Height

Example: An exercise is provided to calculate the volume of a triangular prism with the following dimensions:

• Base: 4 cm
• Height of triangular face: 3 cm
• Length: 3.5 cm

The solution demonstrates how to calculate the area of the triangular base $1/2 × 4 × 3 = 6 cm²$ and then multiply it by the length to get the volume $6 × 3.5 = 21 cm³$.

Highlight: This page provides a comprehensive overview of volume calculations, which is crucial for students studying calcul littéral 5ème and preparing for more advanced geometry topics.