Number System Case Study for DAV Class 8 Students
The Number System Case Study for DAV Class 8 Students helps learners understand whole numbers, integers, and rational numbers. It builds conceptual clarity through practical examples and real-life applications. Moreover, it supports exam preparation by enhancing problem-solving and logical reasoning skills.
Benefits of Practicing Number System Case Studies
Regular practice of the Number System Case Study for DAV Class 8 Students improves speed and accuracy. Additionally, these case studies align with the DAV and CBSE curriculum, ensuring better exam results. Therefore, students can confidently solve both objective and descriptive questions.
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Students can watch video tutorials for the Number System Case Study for DAV Class 8 Students. These videos include solved examples, transitions between concepts, and visual explanations to make learning interactive and engaging.
Case Study 4: Math Case Study for class 8 on Number system
An architectural firm is designing a new museum building with multiple floors at different elevations. The ground floor is considered level 0. The floor levels (in meters) are: Basement 1: -4.5, Basement 2: -9.0, Mezzanine: +2.25, First Floor: +4.5, Second Floor: +9.0, Third Floor: +13.5. The architects need to represent these elevations as rational numbers to calculate stair heights, elevator movements, and structural loads. They are particularly interested in the mathematical relationships between these levels and how the rational number operations apply to real-world architectural calculations. The design team must ensure that all mathematical operations on these elevation values maintain the properties of rational numbers, especially when calculating total vertical distances between floors and verifying that all results remain within the closure property of rational number operations for accurate structural engineering.
Solution: Distance = 13.5 – (-9.0) = 13.5 + 9.0 = 22.5 meters. As rational numbers: 27/2 – (-18/2) = 27/2 + 18/2 = 45/2 = 22.5.
Solution: Second Floor: +9.0, Basement 1: -4.5. Relationship: -4.5 × (-2) = +9.0 or +9.0 × (-1/2) = -4.5.
Solution: Movement = Final position – Initial position = -9.0 – 13.5 = -22.5 = -45/2 meters.
Solution: The closure property of rational numbers under addition and division (by non-zero numbers) guarantees that the average of any two rational numbers will also be a rational number.
Solution: Ratio = 4.5/-4.5 = -1. In simplest form, the ratio is -1:1, indicating they are at equal magnitudes but opposite directions from ground level.