Question

a chef ordered 3 3/6 pounds of red onions and 6 1/3 pounds of pounds of onions did the chef order in all? write your answer as a fraction or as a whole or mixed numbe pounds

Explanation:

Step1: Simplify the mixed numbers

First, simplify \(3\frac{3}{6}\). The fraction \(\frac{3}{6}\) simplifies to \(\frac{1}{2}\), so \(3\frac{3}{6}=3\frac{1}{2}\). Also, \(6\frac{1}{3}\) remains as is for now.

Step2: Convert mixed numbers to improper fractions

Convert \(3\frac{1}{2}\) to an improper fraction: \(3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}\). Convert \(6\frac{1}{3}\) to an improper fraction: \(6\frac{1}{3}=\frac{6\times3+1}{3}=\frac{19}{3}\).

Step3: Find a common denominator and add

The common denominator of 2 and 3 is 6. Convert \(\frac{7}{2}\) to \(\frac{21}{6}\) (by multiplying numerator and denominator by 3) and \(\frac{19}{3}\) to \(\frac{38}{6}\) (by multiplying numerator and denominator by 2). Now add the fractions: \(\frac{21}{6}+\frac{38}{6}=\frac{21 + 38}{6}=\frac{59}{6}\).

Step4: Convert back to a mixed number (optional, but to match the form)

\(\frac{59}{6}=9\frac{5}{6}\) (since \(59\div6 = 9\) with a remainder of 5). Alternatively, we can also add the mixed numbers directly: \(3\frac{1}{2}+6\frac{1}{3}\). Add the whole numbers: \(3 + 6=9\). Add the fractions: \(\frac{1}{2}+\frac{1}{3}=\frac{3 + 2}{6}=\frac{5}{6}\). Then combine: \(9+\frac{5}{6}=9\frac{5}{6}\).

Answer:

\(9\frac{5}{6}\)