Question

eileen makes her own granola using $1\frac{3}{4}$ cups of oats and $\frac{2}{3}$ cups of puffed rice. how many cups of granola does she have?\
options: $1\frac{5}{12}$, $2\frac{5}{12}$, $2\frac{1}{3}$, $1\frac{5}{7}$

Explanation:

Step1: Convert mixed number to improper fraction

To add \(1\frac{3}{4}\) and \(\frac{2}{3}\), first convert \(1\frac{3}{4}\) to an improper fraction. \(1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}\).

Step2: Find a common denominator

The denominators are 4 and 3, so the least common denominator (LCD) is \(4\times3 = 12\).
Convert \(\frac{7}{4}\) and \(\frac{2}{3}\) to fractions with denominator 12:
\(\frac{7}{4}=\frac{7\times3}{4\times3}=\frac{21}{12}\)
\(\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}\)

Step3: Add the fractions

Now add the two fractions: \(\frac{21}{12}+\frac{8}{12}=\frac{21 + 8}{12}=\frac{29}{12}\)

Step4: Convert back to mixed number

Convert \(\frac{29}{12}\) to a mixed number: \(29\div12 = 2\) with a remainder of \(5\), so \(\frac{29}{12}=2\frac{5}{12}\).

Answer:

\(2\frac{5}{12}\) (corresponding to the option with \(2\frac{5}{12}\))