5. how many groups of $\frac{3}{4}$ are in $4\frac{1}{2}$?

Explanation:

Step1: Convert mixed - number to improper fraction

$4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2}$

Step2: Calculate the number of groups

We need to find $\frac{9}{2}\div\frac{3}{4}$. According to the division rule of fractions $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$, so $\frac{9}{2}\div\frac{3}{4}=\frac{9}{2}\times\frac{4}{3}$.

Step3: Simplify the product of fractions

$\frac{9}{2}\times\frac{4}{3}=\frac{9\times4}{2\times3}=\frac{36}{6} = 6$

Answer:

6