Question

How many groups of $\frac{3}{4}$ are in each of the following quantities? $\frac{11}{4},6\frac{1}{2}$

Answer 1

The number of groups of the given fraction:

To find the number of groups of $\frac{3}{4}$ in $\frac{11}{4}$, we have to divide $\frac{11}{4}$ by $\frac{3}{4}$.

$$\begin{gathered} \therefore \frac{11}{4}÷\frac{3}{4}=\frac{11}{4}\times \frac{4}{3} \\ \Rightarrow =\frac{44}{12}=3.67 \end{gathered}$$

Thus, there are complete $3$ groups of $\frac{3}{4}$ in $\frac{11}{4}$.

To find the number of groups of $\frac{3}{4}$ in $6\frac{1}{2}$, divide $6\frac{1}{2}$ by $\frac{3}{4}$:

$$\begin{gathered} \therefore 6\frac{1}{2}÷\frac{3}{4}=\frac{13}{2}\times \frac{4}{3} \\ \Rightarrow =\frac{52}{6}=8.67 \end{gathered}$$

Thus, there are complete $8$ groups of $\frac{3}{4}$ in $6\frac{1}{2}$.

Hence, there are complete $3$ groups of $\frac{3}{4}$ in $\frac{11}{4}$ and there are complete $8$ groups of $\frac{3}{4}$ in $6\frac{1}{2}$.