Compare and Order Fractions Whose Denominators Are All Multiples of the Same Number 3 - Reasoning

Leanna and Rosie faced a challenge to determine whose garden has a larger area covered with trees. Both having identical gardens, they approached the task by dividing their gardens into equal parts and planting trees in a portion of those parts. Leanna divided her garden into 6 equal parts and planted trees in 2 of those parts, resulting in the fraction 2/6 to represent the area covered with trees. Rosie, on the other hand, divided her garden into 8 equal parts and planted trees in 3, which is represented by the fraction 3/8.

To compare which garden has the larger area covered with trees, we must compare the two fractions. Since both denominators (6 and 8) are multiples of the same number, we can use this relationship to compare the fractions directly. Upon comparing 2/6 and 3/8, it's clear that 3/8 is greater than 2/6, meaning Rosie's garden has a larger area covered with trees. This is because when both fractions are converted to have a common denominator, the numerator of Rosie's fraction is larger, indicating a greater proportion of her garden is planted with trees.