Question

A class is presented with the following problem.

In a bag of marbles, the ratio of white marbles to red marbles is 2:3 and the ratio of red to black marbles is 6:11. What is the ratio of white to black marbles?
Connor, who likes using fractions, writes 2/3 *6/11 = 4/11 announces, without explanation, that the ratio of white to black marbles is 4:11. Explain why he is right. (Hint: taking the number of black marbles to be the whole unit, what fraction are red, and then what fraction are white?)

Answer 1

Therefore, Connor is correct in his explanation that the ratio of white to black marbles is 4:11.

Explanation:

Connor is correct in his reasoning. Let's break down the problem step by step to understand why.

Given:

Ratio of white marbles to red marbles = 2:3

Ratio of red marbles to black marbles = 6:11

To find the ratio of white to black marbles, we can follow these steps:

Step 1: Consider the black marbles as the whole unit.

Let's assume there are 11 black marbles (since the ratio of red to black marbles is 6:11).

Step 2: Determine the number of red marbles.

Since the ratio of red marbles to black marbles is 6:11, out of the assumed 11 black marbles, there are (6/11) * 11 = 6 red marbles.

Step 3: Determine the number of white marbles.

Using the ratio of white marbles to red marbles (2:3), we can find the number of white marbles. Since the ratio is 2:3, the number of white marbles would be (2/3) * 6 = 4.

Step 4: Find the ratio of white to black marbles.

Now that we have determined there are 4 white marbles and 11 black marbles, the ratio of white to black marbles is indeed 4:11.