Question

1. multiply or divide the fractions. write answers in simplest form. $5\frac{1}{2} \times 1\frac{1}{4} = $

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(5\frac{1}{2}\) to an improper fraction, we multiply the whole number (5) by the denominator (2) and add the numerator (1). So, \(5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2}\).

To convert \(1\frac{1}{4}\) to an improper fraction, we multiply the whole number (1) by the denominator (4) and add the numerator (1). So, \(1\frac{1}{4}=\frac{1\times4+1}{4}=\frac{5}{4}\).

Step2: Multiply the improper fractions

Now we multiply \(\frac{11}{2}\) and \(\frac{5}{4}\). When multiplying fractions, we multiply the numerators together and the denominators together. So, \(\frac{11}{2}\times\frac{5}{4}=\frac{11\times5}{2\times4}=\frac{55}{8}\).

Step3: Convert the improper fraction to a mixed number (optional, but often preferred)

To convert \(\frac{55}{8}\) to a mixed number, we divide 55 by 8. 8 times 6 is 48, and 55 - 48 is 7. So, \(\frac{55}{8}=6\frac{7}{8}\).

Answer:

\(6\frac{7}{8}\) (or \(\frac{55}{8}\))