Write $5 \frac{1}{4}$ as an improper fraction.
A mixed number, expressed as \(A \frac{b}{c}\), represents the sum of an integer part \(A\) and a proper fraction \(\frac{b}{c}\). In this problem, we are given the mixed number \(5 \frac{1}{4}\). Here, the integer part \(A = 5\), the numerator \(b = 1\), and the denominator \(c = 4\). The goal is to express this as an improper fraction \(\frac{N}{D}\), where \(N\) is the numerator and \(D\) is the denominator.
To convert a mixed number \(A \frac{b}{c}\) into an improper fraction, we use the formula:
\[ \frac{A \cdot c + b}{c} \]
This formula essentially combines the whole number with the fractional part by finding a common denominator, which is \(c\). By multiplying the whole number \(A\) by the denominator \(c\) and adding the numerator \(b\), we obtain the total number of fractional parts of size \(\frac{1}{c}\).
Substituting the values \(A = 5\), \(b = 1\), and \(c = 4\) into the conversion formula:
\[ \frac{5 \cdot 4 + 1}{4} \]
First, perform the multiplication in the numerator:
\[ 5 \cdot 4 = 20 \]
Then, add the numerator value:
\[ 20 + 1 = 21 \]
Placing this back into the fraction, we get:
\[ \frac{21}{4} \]
The conversion of the mixed number \(5 \frac{1}{4}\) results in the improper fraction \(\boxed{\frac{21}{4}}\).
Imagine you are baking cookies and a recipe calls for \(5 \frac{1}{4}\) cups of flour. If your measuring cup is marked only in units of \(\frac{1}{4}\) cup, converting the mixed number to an improper fraction helps you realize that you need to fill the \(\frac{1}{4}\) cup exactly \(21\) times to get the total amount required. Understanding this conversion is a fundamental skill in cooking, construction, and any task involving measurement.