Rosa poured 1 3/4 of orange juice into a container. She added 3 1/3 quarts of apple juice. She then poured 2 2/3 quarts of the mixed juice into a pitcher.

How many quarts of mixed juice were left in the container?

1 9/12 + 3 4/12 - 2 8/12 = ______ quarts left

To find the quarts of mixed juice left in the container, we first need to find the total amount of juice by adding the amounts of orange juice and apple juice.

Rosa poured 1 3/4 quarts of orange juice.
She added 3 1/3 quarts of apple juice.

To add these fractions:

1 3/4 + 3 1/3

Since the fractions have different denominators, we need to find a common denominator.

The common denominator of 4 and 3 is 12.

To convert the fractions to have a common denominator of 12:

1 3/4 = (1 * 4/4) + 3/4 = 4/4 + 3/4 = 7/4

3 1/3 = (3 * 3/3) + 1/3 = 9/3 + 1/3 = 10/3

Now, let's add the fractions:

7/4 + 10/3

To add these fractions, we need to have a common denominator.

The common denominator of 4 and 3 is 12.

Let's convert the fractions to have a common denominator of 12:

7/4 = (7 * 3/3) / (4 * 3/3) = 21/12

10/3 = (10 * 4/4) / (3 * 4/4) = 40/12

Now, we can add the fractions:

21/12 + 40/12 = (21 + 40) / 12 = 61/12

So, the total amount of juice in the container is 61/12 quarts.

Now, let's subtract the amount of mixed juice poured into the pitcher.

Rosa poured 2 2/3 quarts out of the container.

To subtract these fractions:

61/12 - 2 2/3

We need to convert the mixed number to an improper fraction:

2 2/3 = (2 * 3/3) + 2/3 = 6/3 + 2/3 = 8/3

Now, let's subtract the fractions:

61/12 - 8/3

To subtract these fractions, we need to have a common denominator.

The common denominator of 12 and 3 is 12.

Let's convert the fractions to have a common denominator of 12:

61/12 = (61 * 1/1) / (12 * 1/1) = 61/12

8/3 = (8 * 4/4) / (3 * 4/4) = 32/12

Now, we can subtract the fractions:

61/12 - 32/12 = (61 - 32) / 12 = 29/12

Therefore, there are 29/12 quarts of mixed juice left in the container.

To find out how many quarts of mixed juice were left in the container, we need to add up the amounts of orange juice and apple juice poured into the container, and then subtract the amount of mixed juice poured into the pitcher.

First, let's add the quantities of orange juice and apple juice:

Rosa poured 1 3/4 of orange juice, which is equal to (4/4 + 3/4) quarts.
1 3/4 quarts of orange juice = (4/4 + 3/4) quarts = 7/4 quarts.

Rosa added 3 1/3 quarts of apple juice.
3 1/3 quarts of apple juice = (3/1 + 1/3) quarts = 10/3 quarts.

Now let's add the quantities of orange juice and apple juice together:
7/4 quarts (orange juice) + 10/3 quarts (apple juice) = (7/4 x 3/3) + (10/3 x 4/4) = 21/12 + 40/12 = 61/12 quarts.

So, the total amount of mixed juice in the container is 61/12 quarts.

Now, let's subtract the amount of mixed juice poured into the pitcher:

Rosa poured 2 2/3 quarts of the mixed juice into the pitcher.
2 2/3 quarts of mixed juice = (2/1 + 2/3) quarts = 8/3 quarts.

To find out how much mixed juice is left in the container, we subtract:

61/12 quarts - 8/3 quarts = (61/12 x 1/1) - (8/3 x 4/4) = 61/12 - 32/12 = 29/12 quarts.

Therefore, there are 29/12 quarts (or 2 5/12 quarts) of mixed juice left in the container.