Question

multiply the fractions and reduce to lowest terms. use cancellation whenever possible.
$7\frac{1}{4} \times 3\frac{2}{3}$

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(7\frac{1}{4}\) to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So for \(7\frac{1}{4}\), we have \(a = 7\), \(b = 1\), \(c = 4\). Then \(\frac{7\times4+1}{4}=\frac{28 + 1}{4}=\frac{29}{4}\).

For \(3\frac{2}{3}\), using the same formula with \(a = 3\), \(b = 2\), \(c = 3\), we get \(\frac{3\times3+2}{3}=\frac{9+2}{3}=\frac{11}{3}\).

Step2: Multiply the improper fractions

Now we multiply \(\frac{29}{4}\times\frac{11}{3}\). When multiplying fractions, we multiply the numerators together and the denominators together. So \(\frac{29\times11}{4\times3}=\frac{319}{12}\).

Step3: Convert back to a mixed number (optional, but often preferred)

To convert \(\frac{319}{12}\) to a mixed number, we divide 319 by 12. \(12\times26 = 312\), and \(319-312 = 7\). So \(\frac{319}{12}=26\frac{7}{12}\).

Answer:

\(26\frac{7}{12}\) (or \(\frac{319}{12}\))