Exploring Marble Combinations in a Box

In a creative and engaging scenario, we have a box that is filled with marbles of three different colors—red, yellow, and green. These marbles make up various proportions of the box. Let's explore the composition of the box and the different parts that these marbles occupy together.

Introduction to Marbles in the Box

In the given problem, a box is completely filled with marbles. The distribution of these marbles is as follows: 3/8 of the box is filled with red marbles. 4/8 of the box is filled with yellow marbles. The remaining part of the box is filled with green marbles. Let's start with understanding the total composition of the marbles in the box.

Total Marbles in the Box

We are given the specific number of marbles for red, yellow, and green individually, but let's calculate these fractions to better understand the box's contents.

Given:

Red marbles 3 / 8 of the box Yellow marbles 4 / 8 of the box Green marbles 1 / 8 of the box

Part A: Red and Green Marbles Together

First, we need to determine the portion of the box that is filled with red and green marbles together. This can be calculated by adding the fractions of red and green marbles.

Part A: Red and Green Marbles Together (Red Marbles) (Green Marbles)

Substituting the given values:

Red and Green Marbles Together 3/8 1/8 4/8 1/2

So, 1/2 of the box is filled with red and green marbles together.

Part B: Green and Yellow Marbles Together

Next, we need to determine the portion of the box that is filled with green and yellow marbles together. This can be calculated by adding the fractions of green and yellow marbles.

Part B: Green and Yellow Marbles Together (Green Marbles) (Yellow Marbles)

Substituting the given values:

Green and Yellow Marbles Together 1/8 4/8 5/8

So, 5/8 of the box is filled with green and yellow marbles together.

Calculating the Remaining Fraction

To better understand the distribution of marbles, we can also determine the remaining fraction of the box that is filled with green marbles.

Part of the box filled with green marbles is: 1 - (Red Marbles) - (Yellow Marbles)

Substituting the given values:

Part of the box filled with green marbles 1 - 3/8 - 4/8 1 - 7/8 1/8

Using this remaining fraction, we can verify our previous calculations.

Recalculating Part A and B Using the Remaining Fraction

To confirm our earlier results, let's use the remaining fraction of green marbles to find the combined portions with red and yellow again.

Part A: (Red Marbles) (Remaining Fraction of Green Marbles) 3/8 1/8 4/8 1/2

Part B: (Remaining Fraction of Green Marbles) (Yellow Marbles) 1/8 4/8 5/8

Both methods confirm our initial calculations. This detailed analysis not only verifies the correctness of our solution but also provides a deeper understanding of the problem.

Conclusion

In the given problem, the distribution of marbles in the box is as follows: 1/2 of the box is filled with red and green marbles together. 5/8 of the box is filled with green and yellow marbles together. Use this knowledge to solve similar problems and develop a better understanding of fractions and combinations in real-world scenarios.