Question

multiply.
$5\frac{1}{4} \times 3\frac{1}{2}$
?\frac{}{}
answer as a mixed number in simplest form. enter the whole number first.

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(5\frac{1}{4}\) to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So for \(5\frac{1}{4}\), we have \(a = 5\), \(b = 1\), \(c = 4\). Then \(\frac{5\times4+1}{4}=\frac{20 + 1}{4}=\frac{21}{4}\).

For \(3\frac{1}{2}\), with \(a = 3\), \(b = 1\), \(c = 2\), we get \(\frac{3\times2+1}{2}=\frac{6 + 1}{2}=\frac{7}{2}\).

Step2: Multiply the improper fractions

Now we multiply \(\frac{21}{4}\times\frac{7}{2}\). When multiplying fractions, we multiply the numerators together and the denominators together. So \(21\times7 = 147\) and \(4\times2=8\), giving us \(\frac{147}{8}\).

Step3: Convert the improper fraction back to a mixed number

To convert \(\frac{147}{8}\) to a mixed number, we divide the numerator by the denominator. \(147\div8 = 18\) with a remainder of \(3\) (because \(8\times18=144\) and \(147 - 144 = 3\)). So the mixed number is \(18\frac{3}{8}\).

Answer:

\(18\frac{3}{8}\)