Let's solve the problem.

We have:

• 5 red marbles
• 6 blue marbles

The total number of marbles in the bag is: $5 + 6 = 11$

(a) Ratio of blue marbles to all marbles

The ratio of blue marbles to the total number of marbles is: $\frac{6}{11}$

(b) Ratio of red marbles to all marbles

The ratio of red marbles to the total number of marbles is: $\frac{5}{11}$

So, the answers are:

• (a) $\frac{6}{11}$
• (b) $\frac{5}{11}$

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. What would the ratio be if there were 7 red and 8 blue marbles?
2. How would the ratio change if 3 additional blue marbles were added to the bag?
3. What is the percentage of red marbles in the bag?
4. If 2 red marbles are removed, what is the new ratio of red to total marbles?
5. How does the ratio change if both red and blue marbles double?

Tip: Ratios provide a way to compare quantities relative to each other; they are often simplified to their smallest terms.