Question

find the value of the expression
$p \times 4 \frac{1}{4}$
for $p = \frac{1}{2}$.
write your answer as a fraction or as a whole or mixed number.

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(4\frac{1}{4}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(4\frac{1}{4}\), we have \(a = 4\), \(b = 1\), \(c = 4\). Then \(4\frac{1}{4}=\frac{4\times4 + 1}{4}=\frac{16+1}{4}=\frac{17}{4}\).

Step2: Substitute \(p\) and multiply

We know that \(p=\frac{1}{2}\), and the expression is \(p\times4\frac{1}{4}\). Substituting the values, we get \(\frac{1}{2}\times\frac{17}{4}\). When multiplying fractions, we multiply the numerators together and the denominators together, so \(\frac{1\times17}{2\times4}=\frac{17}{8}\).

Step3: Convert to mixed number (optional)

We can convert \(\frac{17}{8}\) to a mixed number. Dividing 17 by 8, we get 2 with a remainder of 1 (since \(8\times2 = 16\) and \(17-16 = 1\)). So \(\frac{17}{8}=2\frac{1}{8}\).

Answer:

\(2\frac{1}{8}\) (or \(\frac{17}{8}\))