A science experiment calls for mixing 3 and two-thirds cups of distilled water with 1 and three-fourths cups of vinegar and Two-thirds cups of liquid detergent. How much liquid in all, in cups, is needed?
A. 2 and StartFraction 1 over 12 EndFraction
B. 4 and StartFraction 1 over 12 EndFraction
C. 5 and StartFraction 1 over 12 EndFraction
D. 6 and StartFraction 1 over 12 EndFraction
To find the total amount of liquid needed, we need to add the amounts of water, vinegar, and liquid detergent together.
First, let's convert the mixed numbers to improper fractions:
3 and two-thirds cups of distilled water = 3 + 2/3 = 9/3 + 2/3 = 11/3 cups of water
1 and three-fourths cups of vinegar = 1 + 3/4 = 4/4 + 3/4 = 7/4 cups of vinegar
Two-thirds cups of liquid detergent = 2/3 cups of detergent
Now, let's add the fractions together:
11/3 + 7/4 + 2/3
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12.
Converting the fractions to have a denominator of 12:
11/3 = (11/3) * (4/4) = 44/12
7/4 = (7/4) * (3/3) = 21/12
2/3 = (2/3) * (4/4) = 8/12
Adding the fractions:
44/12 + 21/12 + 8/12 = 73/12
Now, let's convert the improper fraction back to a mixed number:
73/12 = 6 and 1/12
Therefore, the total amount of liquid needed is 6 and 1/12 cups.
The answer is D. 6 and 1/12.