Question

unit: fractions and mixed numbers
progress:
question id: 106079
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
alan mixes $1\frac{1}{3}$ cups of milk with a can of condensed soup. he makes a total of $2\frac{5}{8}$ cups of soup. how many cups of condensed soup were in the can?
\\(\circ\\) $1\frac{1}{6}$
\\(\circ\\) $1\frac{4}{5}$
\\(\circ\\) $3\frac{23}{24}$
\\(\circ\\) $1\frac{7}{24}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{1}{3}\) to an improper fraction. \(1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3}\).
Then, convert \(2\frac{5}{8}\) to an improper fraction. \(2\frac{5}{8}=\frac{2\times8+5}{8}=\frac{21}{8}\).

Step2: Subtract the amount of milk from the total soup

Let \(x\) be the amount of condensed soup. We know that total soup = milk + condensed soup, so \(x = 2\frac{5}{8}-1\frac{1}{3}\).
Substitute the improper fractions: \(x=\frac{21}{8}-\frac{4}{3}\).
Find a common denominator, which is \(24\). Convert the fractions: \(\frac{21}{8}=\frac{21\times3}{8\times3}=\frac{63}{24}\) and \(\frac{4}{3}=\frac{4\times8}{3\times8}=\frac{32}{24}\).
Now subtract: \(x=\frac{63}{24}-\frac{32}{24}=\frac{31}{24}\).

Step3: Convert the result back to a mixed number

Convert \(\frac{31}{24}\) to a mixed number. \(31\div24 = 1\) with a remainder of \(7\), so \(\frac{31}{24}=1\frac{7}{24}\).

Answer:

\(1\frac{7}{24}\) (corresponding to the option \(1\frac{7}{24}\))