Road grade. A local road has a grade of 6 %. The grade of a...

Road grade. A local road has a grade of $6 \%$. The grade of a road is its slope expressed as a percent. Find the slope of the road as a fraction and then simplify. What rise and run would reflect this slope or grade?

Key Concepts

Fraction Simplification

Fraction simplification involves reducing a fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). In the context of slope, this process helps present the incline in a reduced and clearer ratio format.

Slope

Slope represents the measure of the steepness or incline of a surface and is calculated as the ratio of the vertical change (rise) to the horizontal change (run). It is a fundamental concept in both geometry and real-world applications like road design, where controlled slopes are crucial for safety and functionality.

Percentage Grade

The percentage grade of a slope is a way to express the slope as a percentage, indicating how many units the elevation rises for every 100 units of horizontal distance. This is calculated by converting the slope’s fraction (rise/run) into a percent, making it easier to understand the steepness in real-world terms.

Rise and Run Representation

The rise and run are the two components that express the slope: the 'rise' is the vertical change, and the 'run' is the horizontal change. For a given percentage grade expressed as a simplified fraction, the numerator represents the rise and the denominator represents the run. This ratio directly translates the abstract concept of slope into measurable distances that can be applied in construction and engineering.

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