Question

question 3 of 6 a pitcher contains $2\frac{1}{4}$ quarts of juice. after pouring some juice in a glass, the change in the pitcher is $-\frac{1}{3}$ quart. how many quarts of juice are in the pitcher now? $2\frac{2}{5}$ $1\frac{11}{12}$ $1\frac{1}{2}$ $2\frac{1}{3}$

Explanation:

Step1: Convert mixed number to improper fraction

The initial amount of juice is \( 2\frac{1}{4} \) quarts. Convert this to an improper fraction: \( 2\frac{1}{4}=\frac{2\times4 + 1}{4}=\frac{9}{4} \) quarts. The change is \( -\frac{1}{3} \) quarts (negative because juice is poured out).

Step2: Subtract the change from the initial amount

We need to calculate \( \frac{9}{4}-\frac{1}{3} \). First, find a common denominator, which is 12. Convert the fractions: \( \frac{9}{4}=\frac{9\times3}{4\times3}=\frac{27}{12} \) and \( \frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12} \). Then subtract: \( \frac{27}{12}-\frac{4}{12}=\frac{23}{12} \).

Step3: Convert back to mixed number

Convert \( \frac{23}{12} \) to a mixed number: \( 23\div12 = 1 \) with a remainder of 11, so \( \frac{23}{12}=1\frac{11}{12} \).

Answer:

\( 1\frac{11}{12} \) (the option with \( 1\frac{11}{12} \))