Question

question 21 of 45
what fraction of $4\frac{1}{4}$ is $2\frac{1}{8}$?
a $\frac{1}{4}$
b $\frac{1}{2}$
c $2\frac{1}{8}$
d $9\frac{1}{32}$

Explanation:

Step1: Convert mixed numbers to improper fractions

To find what fraction of \(4\frac{1}{4}\) is \(2\frac{1}{8}\), we first convert the mixed numbers to improper fractions.

For \(4\frac{1}{4}\):
\[
4\frac{1}{4}=\frac{4\times4 + 1}{4}=\frac{16+1}{4}=\frac{17}{4}
\]

For \(2\frac{1}{8}\):
\[
2\frac{1}{8}=\frac{2\times8+1}{8}=\frac{16 + 1}{8}=\frac{17}{8}
\]

Step2: Divide the two fractions

We need to find what fraction \(\frac{17}{8}\) is of \(\frac{17}{4}\), which means we divide \(\frac{17}{8}\) by \(\frac{17}{4}\).

Recall that dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{17}{8}\div\frac{17}{4}=\frac{17}{8}\times\frac{4}{17}
\]

Step3: Simplify the multiplication

We can cancel out the common factors. The 17 in the numerator and denominator cancels out, and we can simplify \(\frac{4}{8}\) to \(\frac{1}{2}\) (since \(4\div4 = 1\) and \(8\div4=2\)):
\[
\frac{17}{8}\times\frac{4}{17}=\frac{1\times4}{8\times1}=\frac{4}{8}=\frac{1}{2}
\]

Answer:

B. \(\frac{1}{2}\)